How caffeine boosts your workout

Studies have shown that Caffeine benefit endurance performance, high-intensity exercise and power sports. There have been enumerable researches on the effectivness and safety of caffeine. It is the most studied supplement out there. Caffeine has health benefits, but the performance benefits are discussed in this article.

4 reasons why caffeine makes workouts better

1 – MORE ENERGY – the first reason why caffeine makes your workouts better is, it increases your energy levels. Here, energy means alertness. The way caffeine works in your brain is as a central nervous stimulator, it blocks certain receptors to increase the levels of adernaline, dopamine, epinephrine. The increased levels of epinephrine, dopamine and adernaline give you the drive and a little bit of euphoria. The “drive” that you get makes a large difference between a good workout and a bad workout.

2. MORE STRENGTH – the second reason why caffeine makes your workouts better is, it increases your muscle strength. The research on caffeine shows that “one dose” of caffeine before workout can have an effect on your strength and increase your strength immediately. One dose implies a high enough amount of caffeine, i.e 300mg or more. The main way it does this is by stimulating the nervous system. The nerves which activate muscle fibres, with the intake of caffeine now activate those muscle fibre’s with even more force . More force on muscle fibre’s equals more strength.

3. MORE ENDURANCE – the third reason why caffeine makes your workouts better is, it increases your endurance during workouts. There are several ways through which caffeine increases your endurance. The first way is, by increasing fat burning levels during workouts. This means that when you train with caffeine, you burn more fat.That spears muscle glycogen which means you have more energy later on in the workout, when you need it. Another way by which caffeine increases your endurance is by boosting nitric oxide levels. Research actually shows that caffeine can enhance vessel dilation. It makes your blood vessel’s wider, which ensures in greater blood flowing through muscles. More blood flowing through muscles delivers more oxygen and more nutrients, which indeed increase endurance during workouts

4. LESS MUSCLE PAIN – the fourth and final reason why caffeine makes your workouts better is, it decreases muscle pain during workout. Research actually shows that caffeine works better than ibuprofen for blunting your muscle pain during workouts. With less muscle pain, you can go off limits with your workout and hit those extra reps which wouldn’t be possible without caffeine. More reps equals better results.

Performance benefits research

In a research conducted by National Library of Medicine with the purpose of studying the duration of caffeine’s ergogenic effect and whether it differs between users and non users of the drug, where Twenty-one subjects (13 caffeine users and 8 nonusers) completed six randomized exercise rides to exhaustion at 80% of maximal oxygen consumption after ingesting either a placebo or 5 mg/kg of caffeine. Exercise to exhaustion was completed once per week at either 1, 3, or 6 hours after placebo or drug ingestion. 

 Exercise time to exhaustion differed between users and nonusers with the ergogenic effect being greater and lasting longer in nonusers.

In conclusion, both the duration and magnitude of the ergogenic effect that followed a 5 mg/kg dose of caffeine were greater in the nonusers compared with the users.

*ibuprofen – Ibuprofen is a medication in the nonsteroidal anti-inflammatory drug class that is used for treating pain, fever, and inflammation*

Star Clusters- The family of stars

Many Stars in the milky way spend at least part of their lives in clusters.  Clusters are scientifically interesting because all their stars formed around the same time and generally have similar characteristics. For example, if the cloud in which they formed was rich in certain kinds of elements, then the stars from that cloud will contain higher amounts of those materials. If the cloud was metal-poor (that is, it had a lot of hydrogen and helium but very little of other elements), then the stars that form will reflect that metallicity. Their similarity makes cluster stars good targets for the study of stellar evolution (how stars age and die). Very young clusters interact with the remains of the gas and dust cloud from which they formed. Understanding how all types of clusters form in our galaxy gives astronomers good insights into how the process happens in other galaxies as well.  There are two types—open and globular.  

Open Clusters

Open clusters usually have up to a thousand or so stars gathered into an irregularly shaped collection. They are often found in the plane of the galaxy, which is where they form. Most of the stars in these clusters are less than 10 billion years old, and some still lie embedded in what’s left of their birth clouds. Our Sun was created in an open cluster that formed about 4.5 billion years ago. It has since moved away from its stellar siblings and now travels the galaxy alone.  Open clusters are generally found in spiral galaxies such as the Milky Way and irregular-type galaxies such as the Large and Small Magellanic Clouds, which are two of our galaxy’s closest neighbors.  Example of Open Clusters:

Pleiades in Taurus constellation

Jewel Box in Crux constellation

Globular Clusters

Globular clusters are collections of hundreds of thousands of old stars. The gravitational influence of all those stars binds the cluster together into a spherical, globular shape. Globulars swarm around the central region of the galaxy, called the halo. The Milky Way Galaxy has about 160 of these tightly packed clusters, but other galaxies have many more. Globulars roam around the halo and probably formed about the same time as the galaxy did.  Example of Globular Cluster: Tucanae

Cluster Formation

A cluster begins to form when some event triggers motion and turbulence in the birth cloud. For an open cluster, it could be a supernova explosion or a fast-moving wind ejecting material from an aging star in the near neighborhood. For a globular cluster, a galaxy collision could be one kind of trigger event. Whatever happens, it sends fast-moving material and shock waves through the birth cloud and starts the process of star birth. Once formation is complete, the cluster stars continue to evolve. If they are not strongly bound together by gravity, after about 100 million years they start to go their separate ways. Even though members of the cluster may get separated by large distances, they all tend to move through space in the same direction and at about the same speed. Sometimes interactions in the cluster will “kick” some stars out into space, sending them on radically different trajectories into the galaxy. Eventually, these stellar associations dissipate into what’s called a moving group, before they finally scatter to become part of the larger stellar population in the galaxy.

http://en.wikipedia.org/wiki/Star_cluster
https://en.wikipedia.org/wiki/Open_cluster

Captain Cool turned 40 yesterday!

Captain Cool turns 40!

Can any Indian forget Ravi Shastri’s words from the commentry box?

“Dhoni finishes off in style. Magnificent strike into the crowd. India lifts the World Cup after 28 years.”

– Ravi Shastri, World Cup 2011

These are words that will remain engraved in our hearts and minds forever. MS Dhoni smashed the winning six to help India defeat Sri lanka and win World cup 2011 at Wankhade stadium. This World Cup winning moment is still cherished by every Indian cricket fan. Not only did Dhoni give millions of Indians a memory worth revisiting throughout their lives, but also transformed himself into a formidable “finisher”, one with ice in his veins.

The player with the most captaincy caps in international cricket, Dhoni is the only skipper in history with all 3 ICC titles (excluding WTC as it started after his retirement). He played 90 Tests, 350 ODIs and 98 T20Is before quitting international cricket in August 2020. He had quit the longest format in December 2014. India’s semi-final exit in the 2019 World Cup, a heartbreak against New Zealand, turned out to be Dhoni’s last appearance in the blue jersey. Dhoni, almost a year ago, drew curtains on an illustrious international career. He announced his retirement from all forms of international cricket on 15 August 2020. Dhoni, however, is yet to contemplate retirement from franchise cricket. He will be seen in action when CSK battles for yet another title in the remainder of IPL 2021 this year. Amid growing calls over not-so-young Dhoni’s ability to deliver with the bat, all we can say is — “Enjoy It While It Lasts”. 

The “Captain Cool”, India’s beloved skipper who has won all major cricketing accolades that one can achieve during his playing stint, and is still a fan favourite amongst all age group celebrated his 40th birthday yesterday with his family and friends.

Since the former India captain lives a private life and doesn’t make public appearances, the fans hadn’t been able to get a glimpse of their favourite player on his birthday. Dhoni lives a private life in Ranchi with his wife, daughter and parents. Dhoni also stays away from social media and the fans have to wait for Sakshi’s posts to get a glimpse of the icon. Dhoni has a staggering social media following but he hardly uses any of the platforms.

A fan managed to get his pic which has now gone viral on social media. The India legend can be seen holding a placard, which has a birthday wish for him. Dhoni is sporting his latest moustache look, a bold army one.

The former Indian Captain – who holds the honorary rank of Lieutenant Colonel in the Territorial Army — would like to spend more time with his unit in the Army now after his retirement, said the news agency PTI.

“One thing is for sure, he will be spending more time with the Army. He will also give time to his commercial ventures and other commitments. We will sit down soon and decide the way forward.”

Mahendra Singh Dhoni to the news agency

As our beloved Mahi turned 40, wishing him a great year ahead with lot more success in every step he takes. Hope his retirement life be brighter than the one before.

Wishing you a belated birthday Sir. Hope your smile never fades. It affects a million Indian hearts.

A smile which make millions smile. Stay cool, Captain Cool

Unpopular Opinion: Devdas was toxic, not a lover. (Book Review)

Book Cover of Novel, Devdas. (Photo Credits: Goodreads)

There’s a certain notion among Indians that every sad lover in the country is a real life Devdas. But deep down, let’s analyse, was Devdas really a lover or yet another male chauvinist?

Plot:

The story starts with two childhood family friends Devdas and Paro, both belonging to rich households and immediate neighbours. Both of their families are well connected to the each other as well. The story revolves around Indian state of Bengal.

Slowly, Devdas and Paro grow up and start developing love for each other. However, Devdas was a spoilt rich brat and this is the reason his father sends him to London for higher studies. Paro becomes sad on knowing this and waits for his return. Devdas returns home after 10 years of studies and is now a well grown up. Paro, on the other hand, exceptionally beautiful, fantasises about her childhood love Devdas.

On his return to Bengal, Devdas and Paro meet and resume their fairy tale love story. However, Dev’s family isn’t happy with their relationship as Paro was from a lower caste background. Things go worse when Devdas’s mother insults Paro’s mother for offering her daughter as a bride to Devdas’s family. This was followed my Paro getting insulted by Devdas’s father who calls her “characterless” as she went on to meet Dev at late night. Devdas seeing all this, refused to accept Paro as his family was against the relationship.

Paro’s mother, unable to bear the insult, vows to get Paro married in a family which would be lot more rich and influential than Devdas. And she does so! A week later Paro marries a rich old man from a nearby village. However, just before her marriage, Devdas suddenly arrives and offers his hand to Devdas to which Paro refuses. Devdas gets angry at the refusal and hurts Paro with a gold necklace and thus Paro suffers from an injury.

Months later Paro’s marriage to the old man, Paro pays a visit to Devdas where it’s revealed he’s completely alcoholic and lonely. Paro requests him to come with him but Devdas doesn’t agree but promises her that he would come to Paro once before his death. Devdas also meets a courtesan, Chandramukhi with whom he develops loves but leaves her yet again.

Finally, the story ends with Devdas fulfilling his promise of coming to Paro but Paro’s husband refuses to let her meet Devdas. At the end, an alcoholic Devdas passes away leaving Paro sobbing.

Character of Devdas.

1) Devdas was never a lover.

I wonder, how people have beautifully whitewashed the ignorant and abusive nature of Devdas. When Paro went to meet Devdas late at night putting her dignity at stake, Devdas refused to go with her fearing about his own family honour. If this is the case, how can he be called a lover? If family and society was more important to him, it shows he never actually loved Paro.

2) Devdas was a male chauvinist.

Devdas suddenly offered his hands to Paro when Paro was just about to marry. Paro taking into consideration her self respect questioned Devdas that why is he so late and why didn’t he come when Paro went out to meet him at his home the week before. She also asked Devdas about the reasons why her parents and she were insulted by Dev’s family. Devdas couldn’t tolerate a woman questioning him and instead of apologising to her, he shouted at her for being “too arrogant”. Devdas cared about his family honour but didn’t care about Paro’s family honour: This shows his ingrained patriarchy.

3) Devdas tries to justifies abuse!

Perhaps one of the most problematic chapters of the book was when Paro refuses Dev’s offer of running away with him on her wedding night with the old man. On getting a rejection from Paro, Dev goes intolerant and beats Paro with a gold necklace. Paro suffers from an injury and her head starts bleeding. Devdas asks Paro to keep this injury with her for life as it would always remind her of Devdas. Paro agrees to this and throughout the book she is shown to love that injury. This also shows how much the book has normalised and romanticised a brutal abuse and also definitely brutal abusers!

Minority Report : A Glimpse into the future

A world with a police force that could stop crimes even before they occur would be safe and devoid of major crimes. Minority Report by Steven Spielberg brings such a world to life, crime in Washington D.C in 2054 is at all time low due to an experimental PreCrime Police program going on from the past 6 years. The program makes use of 3 three clairvoyant humans known as Precogs who can visualize details of an impending homicide, the police force then analyses the data gathered to then apprehend the would be perpetuator. This method takes care of premeditated plans but fails to work on crimes of passion.

The Precogs are connected to a system to display and store their memories, wherein they lie floating in a pool with sleep inducing drugs to separate them from any and all stimulus of the real world. The criminals that are apprehended are sentenced to a virtual-reality as their penance. The system is not perfect and can generate errors, these imperfect predictions are analysed further and purged from the records if necessary. These imperfections occur if any one of the three precogs witnesses a different future, these are purged as group precognition agreement is the foundation of the precrime laws. The state wants to implement the PreCrime program on a national level despite of the issues.

The program is led by Chief John Anderton played by Tom Cruise. Danny Witwer an agent of the US Department of Justice played by Colin Farrell discovers a prediction made by the precogs while auditing the system for national implementation. He discovers a prediction made about Anderton hidden in the system, Anderton is going to kill Leo Crow a man with apparently no connection to Anderton. Anderton who learned about the future before Witwer decides to flee the office to save himself, which then causes Witwer to issue a manhunt.

Anderton tracks down Dr.Heinman the founder of the PreCrime program, he does so to learn about anything that he can use to save himself from being persecuted. He learns about the existence of the minority reports from Dr.Heinman and tries to use those to his advantage, the minority reports which are purged from the system are programmed to be saved to the lead Precogs mind. Anderton retuns to PreCrime to kidnap Agatha the lead Precog to try and prove his innocence, they decide to track Leo Crow down and find him in a hotel room with photos of children which includes a photo of Anderton’s own son believed to be dead. Anderton in a fit of rage attacks Crow but decides to spare his life after Crow claims that he was hired to plant the photos. Crow proceeds to kill himself to make sure his family is unharmed by whoever hired him.

Further research by Anderton points him to a murder that happened in the past, Agatha’s mother Anne was murdered even after the possible culprit was caught. Witwer deduces the murderer to be Director Lamar Burgess and is killed by him as the precog system is offline. Anderton is eventually apprehended but released when Burgess inadvertently reveals his hand in the murder of Anne Lively. Anderton displays the footage of lively death publicly and proves Burgess to be the man behind her murder, a new precrime report is generated which Predicts Burgess killing Anderton. Burgess commits suicide and precrime is abandoned, the 3 precogs are moved to an undisclosed location set to live normal lives.

In conclusion Minority Report manages to show both the benefits and the downsides to knowing ones future. An amazing movie worth watching not just for the plot but the subtle visual effects that looked like magic when it was first released.

Environmental pollution

“Humankind has not woven the web of life. We are but one thread within it. Whatever we do to the web, we do to ourselves. All things are bound together. All things connect.”

~ Chief Seattle

What is environmental pollution ?

Is it degrading our lifestyle ?

How can we improve our environment ?

Let’s get through the topic .

Introduction

One of the greatest problems that the world is facing today is that of environmental pollution, which is causing grave and irreparable damage to the natural world and human society with about 40% of deaths worldwide being caused by water, air and soil pollution and coupled with human overpopulation has contributed to the malnutrition of 3.7 billion people worldwide, making them more susceptible to disease.

Environmental pollution is defined as “the contamination of the physical and biological components of the earth/atmosphere system to such an extent that normal environmental processes are adversely affected.”

From: Environmental Management, 2017

We all are well known about the word Environmental pollution . It is not some kind of new phenomenon , yet it is a greatest problem facing by our society . Still , people are avoiding the topic to its utmost.

Environmental pollution is one of the most serious global challenges. Wild-type organisms have a slower degradation rate of hazardous materials.

Both developed and developing nations share this burden together, though awareness and stricter laws in developed countries have contributed to a larger extent in protecting their environment.

Reasons behind environmental pollution

  • The Burning of Fossil Fuels. Industrial Emission.
  • Indoor Air Pollution.
  • Wildfires.
  • Microbial Decaying Process.
  • Transportation.
  • Open Burning of Garbage Waste.
  • Construction and Demolition.
  • Urbanization and industrialization. Since the era of industrial revolution, man has continued to introduce hazardous materials into the environment at an alarming rate.Mining and exploration.
  • Agricultural activities.
  • Particulate matter.
  • Plastics.
  • Energy production.
  • Deforestation.
  • Mining.
  • Over population.
  • Increase in global average temperature.

Effects of environmental pollution

Environmental pollution is an incurable disease . It can only be prevented.

Barry commoner

1. Effects on Humans. The effects of environmental pollution on humans are mainly physical, but can also turn into neuro-affections in the long term. The best-known troubles to us are respiratory, in the form of allergies, asthma, irritation of the eyes and nasal passages, or other forms of respiratory infections. Other rarer diseases include hepatitis, typhoid affections, diarrhea, and hormonal disruptions.

2. Effects on Animals . Environmental pollution mainly affects animals by causing harm to their living environment, making it toxic for them to live in.

3. Effects on plants . As for animals, plants, and especially trees, can be destroyed by acid rains (and this will also have a negative impact on animals as well, as their natural environment will be modified), ozone in the lower atmosphere block the plant respiration, and harmful pollutants can be absorbed from the water or soil.

Solutions for environmental pollution.

  • Evironment planning.
  • Shifting to eco-friendly transportation.
  • Air pollution must involve moving away from fossil fuels, replace them with sustainable fuels .
  • Solar power .
  • Wind power.
  • Go green.
  • Storage facilities for solid waste.
  • Environmental friendly products.
  • Policies implimentation for environmental pollution.
  • We also need to work on electromagnetic radiation (ER) reduction.
  • Awareness through mass media.
  • More green parks and areas.
  • Environmental education, etc,.

“We say we love flowers, yet we pluck them. We say we love trees, yet we cut them down. And people still wonder why some are afraid when told they are loved.”

~ Paul Morley

Link

Are “They” Out There?

These days, the possibility of finding life “out there” is an integral part of astronomy. The exploration of mars has been spurred in large part by  the search for life or at least conditions that could support it. Extraterrestrial life is hypothetical life that may occur outside Earth and which did not originate on Earth. Such life might range from simple prokaryotes (or comparable life forms) to intelligent beings and even sapient beings, possibly bringing forth civilizations that might be far more advanced than humanity. Given the size of the universe – there are at least 100 billion stars in our home galaxy alone and perhaps 100 billion galaxies of much the same size scattered throughout deep space – few scientists believe that the Earth is the only home of life. But until quite recently, the field of exobiology – the study of extraterrestrial life also known as astrobiology – was almost moribund. It could come up with some interesting speculations but that was about all. The Drake equation speculates about the existence of sapient life elsewhere in the universe.

See the source image

The Drake Equation:

Astronomer Frank Drake (1930–), who was doing radio astronomy searches for signals from alien civilizations in the early 1960s, came up with an equation that can help estimate how many civilizations could be in the galaxy. His equation looks like this:

N = R* • fp • ne • fL • fi • fc • L

where N is the number of civilizations in our galaxy that have the ability to communicate with us. To get to N, you have to multiply the following factors: 

R*—the average star formation in our galaxy each year

fp —the number of those stars that have planets

ne —the number of planets that could potentially support life (for each star that has planets) 

fL —the number of those planets that actually go on to develop some kind of life

fi—the number of planets that actually do develop intelligent life 

fc—the number of civilizations that are technologically advanced enough to advertise their existence (through radio signals, etc.) 

L—the length of time it takes for those civilizations to start releasing their “I’m here” signals

Necessities for life

The most vital ‘exobiology’ discoveries, though, were made right here on Earth. Biologists have learned that life is much more robust than most scientists believed 30 years ago. Earth microorganisms have been found thriving in astonishingly hostile environments. Deep beneath the oceans, for example, near the volcanic vents known as black smokers, some microbes grow and multiply at temperatures above 110 degrees – according to some scientists, perhaps as high as 170 degrees. 

Others thrive in acid conditions that would strip the skin from a human, while others still make a comfortable living in hot rocks kilometres below the ground. Some even prefer cold to heat: Antarctic life-forms can manage very well in what amounts to a permanent deep-freeze.

The existence of these so-called extremophile organisms radically changed our view of what might be called “the necessities of life”. Extremophiles live happily without sunshine, without moderate warmth, without organic molecules to feed off and with no need for photosynthesis – many digest raw minerals and fuel themselves with basic chemical reactions.

The Kepler Mission

The Kepler mission is on the hunt for Earth-like planets around other stars, called exoplanets, and has found many planet candidates, not all of them suitable for life as we know it. Astronomers using the European Southern Observatory in Chile have even found an Earth-sized planet circling around Alpha Centauri B, which lies 4.37 light-years from Earth. While the newly discovered planet is too hot and close to its star to be hospitable to life, the discovery is another step towards finding life elsewhere.

I am sure that in the distant future we will find life elsewhere. The chances of ET being highly advanced or dangerous human eaters, is very very low. Most probably they will be some microscopic organisms(sorry to disappoint you). But, do not let this stop you from imagining.

https://en.wikipedia.org/wiki/Extraterrestrial_life https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/Exploration/Extraterrestrial_life

What are the Rules of Differentiation?

Differentiation is easy to deal with the following rules. It is considered to be easier than solving integrals. Most of the integrals can be evaluated using an antiderivative calculator while derivatives have some rules that students should grasp on priority.

These rules should be applied to according to the equation or underlying problem. We will explain the basic rules for students so that they can solve derivative problems like a pro.


1.  Power Rule

The power rule is applied to polynomial functions. The formula is:

   

The example of f(x2) we solved to learn derivatives is a perfect representation of the power rule. But for more understanding, see another example:

Example:

Derivative of x6. Solve this using limits as well as power rules.

Solution:

Solving using limits.

Step 1: Add delta x i.e and expand the equation.

= (x + )6

f(x + )6 = (x6 + 6x5 + … + 6)

Step 2: Apply the formula of the slope.

    

=    

=   

=                     … cancelling x6

=      

= 6x5 + 15x4 x + … +x5

Step 3: Apply limit.

f’(x6) =6x5 + 15x4 x + … +x5

= 6x5

Solving using power rule.

Step 1: Write the function.

f(x) = x6

Step 2: Identify the components and apply the power rule.

As yn = nyn-1,     (we formed the formula with y to remove any confusion.)

Here,     y = x 

n = 6

Applying the rule;

f’(x6) = (6)x6-1 = 6x5

The results of both methods are the same. This proves that the power rule is true for any n.

2.  Sum & Difference Rule

Two functions in addition or difference are also eligible for a differentiation rule. The rules applied in such situations are;

f + g =  f +g

f – g =  f –g

Find f’(x) for 2x + 3x2.

Solution:

Step 1: Apply derivative.

= ( 2x + 3x2) 

Step 2: Apply the rule.

=  2x +  3x2

=   2.1x1-1 + 3.2x2-1                      applying the power rule. 

=   2 + 6x    

3.  Product Rule

When the derivative of two functions in multiplications is computed, we then use the product rule. An example of such a function will be 4x4(3x + 9).

The formula of product rule is:

f(x)g(x) = fg + gf

What is the derivative of 4x4(3x + 9)?

Solution:

Step 1: Apply derivative.  

=4x4(3x + 9)

According to the product rule.

=4x4(3x + 9) + (3x + 9) 4x4

Step 2: Solve for (3x + 9).

=(3x + 9)

 Apply sum rule.

=3x + 9

= 3 + 0        … (power rule for 3x and constant rule for 9)

= 3

Step 3: Solve for 4x4.

Using power rule;

= 4.{(4)x4-1}

= 4.4x3

= 16x3

Step 4: Put the values and simplify.

= 4x4.3 + (3x +9)16x3

= 12x4 + 48x4 + 144x3

= 60x4 + 144x3

= x3(60x + 144)

4.  Constant Rule

It is probably the simplest derivative rule. When we don’t have a variable in a function e.g y=4, then the derivative is 0.

f’(c) = 0             

Where c is a constant number. This rule makes sense if you try to visualize it. 

Since x = 0, hence there is no slope. And the graph is a straight vertical line. But let’s see this with the help of differentiation.

Example:

What is the derivative of f(x) = 5.

Solution:

Step 1: Add delta x. 

    f(x + )  = 3 +  = 3                             

Step 2: Apply formula.

=    

=  

= 0/ = 0

5.  Quotient Rule

We have a formula for product but do we have a formula for division? Yes! And It is called the quotient rule. It is mainly derived from product rule for differentiation. 

 = 

A quotient equation looks something like this: . To find its derivative, it is divided into two parts; . You can see that actually, we have to perform the product rule.             

 = f(x) + f

All we need to do is to find the derivative of 1/g(x). Following all the familiar process of applying formula and limit, we will get:

 

  

 

 

Note that is the  with a negative sign.

  

Or it can be written as:

 

Now on putting this value in the product formula we discussed above:

  =  + 

Taking LCM.

  = 

  = 

This is the quotient rule.

Find the derivative of (x – 3)/(x3 + x).

Solution:

Directly apply the quotient rule. 

        

Step 1: Find the derivative of (x-3).  

=(x-3)

= 1

Step 2: Find derivative of (x3-x)

=(x3-x)

Using the rules discussed above;

= 3x2 – 1

Step 3: Use these in the main equation.

                 

After simplifying;

6.  Chain rule

Last but not the least, we have the chain rule. It states that:

                      

         or          f(g(x)) = f’{g(x)}g’(x)

This is for simplicity’s sake. When a function has many mathematical operations, it is better to convert it in terms of two functions e.g, we have a function:

f(x)= (X2 + 6)4

Let g =X2 + 6, then 

f(g) = (g)4  where g =X2 + 6   

f(g(x)) = (X2 + 6)4

To find its derivative, you first find the difference of f with respect to g and then g’(x). After that, multiply. 

Solve     (X2 + 6)4

Solution:

Let g(x) = x2 + 6

And f(g) = g4

So the derivative of f(g(x)) = f(g(x)) =f’(g(x)).g’(x).

Applying the chain rule.

Step 1: Find the derivative of g(x).

 = x2 + 6            … using power rule for x2 and constant rule for 6

 = 2x

Step 2: Find the derivative of f(g).

= g4

= 4g3

Step 3: Putting in the formula and multiplying.

= 4(x2+6)3. 2x

= 8x.(x2+6)3            

Wrapping up

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p class=”MsoNormal” style=”line-height: 22px”>All of the above listed rules of derivatives are most common rules that students have to deal with during their academic course. You should practice these rules to avoid any step backs during your exams. You should also try differentiation calculator after practicing these rules. This tool will help you out in solving derivatives while performing differentiation.

Whether people should solve their problems or accept them?

Many people think it is better to accept a situation the way it is even if it is not up to their expectation whereas, others are of the opinion that it is important to solve such problems. In my opinion the best case scenario is to make such situations better so that a person has no regrets.

To embark on, people accept a bad a situation because they fear that if they do not accept it they would not get another opportunity and will have what they have. Another reason why people do not improve their condition is because they do not have any other option and accepting it is the last resort. For an instance, an uneducated person working at a tea stall is not happy with his job and is not satisfied with the salary but he cannot do anything as he is uneducated and it the only source of income for him. Therefore it is impossible for him to improve his situation as he has no other option and even if he tries to do something else he might end up loosing everything. Hence the risk of loosing everything often makes a people stick to what they have even if they are not happy with it.

However many people believe that it is important to improve such situations because if a person does not try to make situations better they may end up regretting it in the later phase of their life. Furthermore if a person is not happy with what he is doing he may not do the same to his fullest potential and may end up loosing that opportunity. For example a person doing a job in which he is not happy and has no interest may end up loosing his job. Hence, not making a change will worsen the conditions.

According to me, it is very important to make things right so as to make full use of the opportunities . It is very important to at least try so that one does not have any regret.

To encapsulate, a person ought not accept a bad situation and must try to make it better to make the full use if the opportunities given. This will result in making life better and easier for some people.

Taking Care of your Mental Health during a Global Pandemic

“A soft reminder: not everything that weighs you down is yours to carry.”

The term “Mental Health” focus on our emotional, psychological and social wellbeing. It affects the way we perceive things, the way we feel and the way we react. It plays an important role in every stage of our lives from our childhood to our adulthood. Your health is more than what you are eating. It is also what you are thinking, saying and believing. We often tend to underestimate the importance of our mental health but, taking care of it is important, more than it is rewarding.

We began to hear about the virus outbreak in China during the last month of 2019, little did we all know that it would be identified as a global pandemic. On 25th of March,2020 the first lockdown was imposed in the country. The seriousness of the pandemic had intensified and the world was paused. During the lockdown everyone was paranoid and careful. A large number of people were stuck, they were away from their homes and families, there was a huge wave of unemployment and everything was falling apart. The only news that was telecasted was about how rapidly the virus is growing and it started to make people anxious. Every body was perplexed and overwhelmed.

 At the beginning of the outbreak, we were told to be isolated and strengthen our immunity, exercise at home and focus on our physical wellbeing, but what we kept neglecting was our emotional wellbeing. The most common feeling that millions of people are experiencing is loneliness. Being confined to a particular place and following the same monotony made a lot of people feel empty and lifeless. we weren’t focusing on how to take care of our emotions during the time and that has left us being on an emotional roller coaster with each day. All of us are in the midst of a global pandemic currently and it is undeniable that fear and anxiousness has spread rapidly among ourselves as well.

 This pandemic has given our lives a different meaning and has been recreational for a lot of people. We continue to build new normalcy during these times. Social media platforms have progressively churn out productivity contests every now and then, it is essential to remind ourselves that this is no competition that we are a part of, it is important to replace the feeling of guilt and let it go.

 Before corona virus had hit us, working from seemed like a cake walk but it has certainly caused a huge disbalance between work and personal space, one should allow themselves to give them breaks and assure that you are giving your mind and body some rest. Indulge in activities like cooking, reading, watching a movie, pursuing your hobbies or doing something that you’ve always wanted to do but never found the time to during these times. Start finding happiness in the small wins like being without your phone, cleaning the dishes, cooking something which you thought you never could and so on. If you feel that there is a lot going and it is constantly making you feel hopeless, take a step back and try to calm yourself if that doesn’t help talk to someone, express what you’re feeling. Resist yourself from checking the news and find a distraction. While video calling has helped creating a bridge between the people who are far from you, it is completely normal to crave for human touch.

During these hard times, an individual who is dealing through stress should make it a point to turn to the people who are optimistic and good listeners. Try to understand that your feeling is valid, in order to keep your mental health stable, it is important to acknowledge your feelings for that you can write it down, let it out or do something that relieves your stress. It is scientifically proven that exercising helps in reducing anxiety, negative emotions and boosts self-esteem. One of the main advantages of exercising regularly during a pandemic is having a proper sleep schedule.

An individual should practice mindfulness and gratitude during such challenging times. Its very important to count your blessings and make time for things that make you happy. Lastly, we should give ourselves credit for the days we made it when we thought we couldn’t have.

Anime movies to watch


Anime refers to the animation works produced in Japan. There are many famous anime series like death note, dragon ball z, Naruto, one piece etc. which have successfully captured the hearts of people all around the globe. Similarly, there are a many anime films which are very good to watch.
Here are some of the greatest anime films which are worth checking out:


• Your Name ( 2016):

The first thing that comes to mind about this film is it’s extraordinarily breath taking animation. It is directed by Makoto Shinkai and has a 98% Rotten tomatoes rating. It is a one of a kind romantic fantasy film. It is a timeless tale of love of two teenagers who share a magical connection of switching bodies but things get very complicated when they decide to meet in person. This film has a very different take on love. It also depicts the power time has on us and how it changes everything. The music in this film is very stunning and makes the experience even better.

• The Garden of Words (2013) :

This is another Makoto Shinkai’s film. It is rather a mini movie with a runtime of 45 minutes. The animation in this film is very realistic. This film is very soothing to watch. The music and the scenes of rain are very relaxing. T story revolves around a teenager who skips school and meets a mysterious older women who shares his feelings of alienation. This film depicts loneliness and the need of companionship very well. It shows how insecurities can be both cause and result of loneliness. It showcases very relatable thoughts and feelings. Not being able to let go of past, inability to move forward in life, fear of failure, fear of being judged etc. are very aptly portrayed.

• A Silent Voice (2016) :

This is a very emotional film. It is directed by Naoko Yamada. This film depicts the effects bullying has both on the victim and the bully. The story revolves around a boy who bullied a deaf girl to the point where she has to transfer to another school. Years later, he sets out to make amends. It is a very powerful story of redemption of a sinful past. It deals with issues like sucide, self loathe, guilt, bullying, disability etc. This film depicts how self acceptance leads towards healing and how strong karma is. Self love, self forgiveness etc. are portrayed very well. Over all , this film is a roller coaster of emotions.

• Spirited Away (2001) :

This is an all time classic. It has a 97% Rotten tomatoes rating and is the winner of 2003 Best Animated Feature in Academy Awards. It is a Studio Ghibli film and is directed by Hayao Miyazaki. It is one of the best film studio Ghibli has produced. The story revolves around a girl whose parents get cursed when they go to a strange amusement park. Then then meets a boy who tells her about that park and how he has to work there to free her self and her parents. Just like any other ghibli film, it is very detailed when it comes to animation, the pacing is not fast which makes it very relaxing to watch and world exploration is done neatly. There are a lot of mythological referencing in the film and is perfect for both children and adults.

Want to get Rich and Prosperous? Well, then I’ve got a book for you.

Robert Kiyosaki, in his book Rich Dad, Poor Dad, has significantly changed the way people think about money. This book teaches that you do not need to have a high income to become rich.
Ironic? So let’s dive into the ocean of thoughts the author shares through this book.

The author, initially, narrates a story of his childhood where he and his friend Mike aspire to earn money and end up meeting Mike’s dad who offers them a job as laborers. Apparently, they are too small to fit in the job, besides, the labor laws too did not permit minors to work as laborers. Despite, Mike’s dad makes them work very hard and pays relatively less remuneration. The world would’ve definitely called this as exploitation. But the boys kept working day after day, week after week. One day, the author’s father, who is a government official, comes to know about this. It was obvious that he would get furious. He suggested the author to quit ASAP and also went to the height of saying that the man should be criminally charged for child labor.

Later the author goes to his employer (Mike’s dad) and was about to file his informal, oral resignation. But Mike’s dad said something. Explained something. Taught something. That moment was trailblazing and revolutionary for him. Those words proved to be life-changing. Those preaching made the author as well as his friend Mike very rich. I would suggest you to read the book to end your curiosity of knowing as what was it that the man told these boys.

On becoming rich, the author shares, with us, the key aspects of making, sustaining, and making more money. The author has presented a rather unconventional idea that your house might not be an asset. On the contrary, for most people, their house is an asset. But the author says that anything that drains money out of your pocket is a liability. And anything that makes money to get into your pocket is an asset. Many people find loans as the best option for buying a house. Hence, every month a large part of your saving is paid out as EMI. Besides, the bank charges hefty interest as well. Then how is your house an asset?

The author materially emphasizes and criticizes the habit of spending your own money extravagantly on frivolous desires. The author doesn’t say that do not buy luxury. But he, instead, suggests that do not buy them on your salary. According to him, ‘you should not work hard for the money but money should work hard for you.’ Your salary and other incomes should be invested somewhere so that your investments make more for you. And only this extra money should be spent on buying whatever you wish.

Further, the author talks about the need of working for yourself. Many people hunt jobs, work there and think that they are working in order to make themselves rich. This is an illusion. When you work at a job, you work for the owner of the company. You work hard day and night to make him rich. Secondly, you work for the government. The rich also pay taxes, but they have numerous ways of escaping from taxes. But in the case of a job-going person, tax is already cut from the salary even before it reaches his hand. Thirdly, a person doing a job works to make the banks rich. Every luxury you buy, mostly can’t be afforded out of your savings. So you choose to take loans. A loan for a car, a loan for a house, etc. The banks enjoy sitting and watching you working hard and making them rich by paying heavy interest. A solution to this is mentioned in detail, in the book.
The author, further quotes the need to become a ‘jack of all trades’. Having said that, you need not be excellent at everything but you should definitely know a lot in many fields. This will make you self-reliant and capable of taking better decisions in your business or any other venture.

This is an amazing book and I would highly suggest you read his one to get insights into healthy money habits and start your journey to becoming a rich person.

England knocks out Denmark (EURO 2020 Semis)

England reach the final of a major tournament for the first time since 1966 after defeating Denmark after extra-time. Mikkel Damsgaard put the Danes ahead at Wembley with a stunning free-kick to breach the Three Lions’ defence for the first time of the tournament. An own goal from Simon Kjaer levelled the scores before half-time. Neither team could find a winner in 90 minutes, sending the contest to extra-time. Raheem Sterling drew a foul from Joakim Maehle, earning his team a penalty. Harry Kane missed the spot-kick as Kasper Schmeichel produced the save. However, luck was on the side of England as Kane converted the rebound. It was enough to send the Three Lions through to the final.

England will take on Italy in the European Championship final at Wembley on Sunday. Denmark deserve a huge amount of plaudits for their run in the competition in light of the circumstances following Christian Eriksen’s life-threatening collapse in their opener. They leave with their heads held high and return to action on September 1 against Scotland in their World Cup qualifying campaign.

Harry Kane celebrating the winning goal against Denmark.

Absurd Play

Absurd theatre came about as a reaction to world II. It took the basis of existential philosophy and combine it with dramatic element to create a style of theatre which presented a world which cannot be logically explained.

The absurdist play was initially created because critics and reviews were used to be more conventional: realism in practice. the absurd play departs from the realistic characteristic situation and all of the associated theatrical conventions. Time, place, and identity are ambiguous and fluid and even basic causality frequently breaks down. Meaningless plots repetitive or nonsensical dialogues and dramatic non-sequence are often used to create dreamlike or even nightmare life moods. There is a fine line, however between the careful and artful use of chaos and non-realistic elements and true, meaningless chaos. while many of the places described by this seem to be quite random and meaningless.

The character in the absurdist play is lost and floating in an incomprehensible universe and they abandon rational devices and discursive thought because these approaches are inadequate. Many characters appear as automatons stuck in runtime speaking only in cliche. Characters are frequently stereotypical, archetypal, or flat characters. In an absurd play, characters may also face the chaos of a world that science and logic have abandoned.

The plot of many plays features the character in interdependent pairs, commonly either two males or a male and a female. The two characters may be roughly equal or have a begrudging interdependence. One character may be dominant and may torture the passive character.

Language plays the most important role. Despite its reputation for nonsense language, much of the dialogue in the absurdist play is naturalistic. The movements when character restores their senses, when words appear to have lost their denotative function, thus creating misunderstanding among the characters. In other cases, the dialogue purposefully elliptical; The language of absurdist theatre becomes secondary to the poetry of the concrete and objectified image of the stage.

AWS technology

The AWS technology is enforced at server farms throughout the planet, and maintained by the Amazon subsidiary. Fees square measure supported a mix of usage (known as a “Pay-as-you-go” model), hardware, OS, software, or networking options chosen by the subscriber needed accessibility, redundancy, security, and repair choices. Subscribers will pay for one virtual AWS pc, an avid physical pc, or clusters of either. As a part of the subscription agreement,[9] Amazon provides security for subscribers’ systems. AWS operates from several world nations together with half-dozen in North America.[10]

Amazon markets AWS to subscribers as some way of getting giant scale computing capability a lot of quickly ANd cheaply than building an actual physical server farm.[11] All services square measure beaked supported usage, however every service measures usage in variable ways that. As of 2017, AWS owns thirty third of all cloud (IaaS, PaaS) vi whereas subsequent 2 competitors Microsoft Azure and Google Cloud have eighteen, and Sep 11 severally, in step with natural process cluster
AWS is close to launch fifteen a lot of of their accessibility zones and {again|once a lot of} individually 5 more zones in Australia, India, Indonesia, Spain, and Swiss Confederation.[10]

Each region is entirely contained among one country and every one of its information and services keep among the selected region.[9] every region has multiple “Availability Zones”,[101] that carries with it one or a lot of separate information centers, every with redundant power, networking and property, housed in separate facilities. accessibility Zones don’t mechanically offer further quantifiability or redundancy among a section, since they’re deliberately isolated from one another to stop outages from spreading between Zones. many services will operate across accessibility Zones (e.g., S3, DynamoDB) whereas others is organized to copy across Zones to unfold demand and avoid period of time from failures.
AWS launched AWS re/Start within the uk to assist young adults and military veterans retrain in technology-related skills. In partnership with the Prince’s Trust and therefore the Ministry of Defence (MoD), AWS can facilitate to supply re-training opportunities for youth from deprived backgrounds and former military personnel. AWS is functioning aboard variety of partner firms together with Cloudreach, Sage Group, EDF Energy