s l arora for physics r c mukharjee

Asked by Ravi Ranjan Singh 31/10/2014 Last Modified 07/10/2025

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Hi friends. I thought of sharing something wonderful i found on web so that it can help all of us & augment our understanding of the topic - 'Limit' . I have shared the complete pdf in my profile gallery or the original web link at the end of this post. An Intuitive Introduction To Limits Limits, the Foundations Of Calculus, seem so artificial and weasely: “Let x approach 0, but not get there, yet we’ll act like it’s there… ” Ugh. Here’s how I learned to enjoy them: What is a limit? Our best prediction of a point we didn’t observe. How do we make a prediction? Zoom into the neighboring points. If our prediction is always in between neighboring points, no matter how much we zoom, that’s our estimate. Why do we need limits? Math has “black hole” scenarios (dividing by zero, going to infinity), and limits give us a reasonable estimate. How do we know we’re right? We don’t. Our prediction, the limit, isn’t required to match reality. But for most natural phenomena, it sure seems to. Limits let us ask “What if?”. If we can directly observe a function at a value (like x=0, or x growing infinitely), we don’t need a prediction. The limit wonders, “If you can see everything except a single value, what do you think is there?”. When our prediction is consistent and improves the closer we look, we feel confident in it. And if the function behaves smoothly, like most real world functions do, the limit is where the missing point must be. Key Analogy: Predicting A Soccer Ball (associated pics in original post) Pretend you’re watching a soccer game. Unfortunately, the connection is choppy: So we missed what happened at 4:00. Even so, what’s your prediction for the ball’s position? Easy. Just grab the neighboring instants (3:59 and 4:01) and predict the ball to be somewhere in between. And… it works! Real world objects don’t teleport? they move through intermediate positions along their path from A to B. Our prediction is “At 4:00, the ball was between its position at 3:59 and 4:01?. Not bad. With a slow motion camera, we might even say “At 4:00, the ball was between its positions at 3:59.999 and 4:00.001?. Limits are a strategy for making confident predictions. Limits aren’t the only tool for checking the answers to impossible questions; infinitesimals work too. The key is understanding what we’re trying to predict, then learning the rules of making predictions. Happy math. (Original author - Mr. kalid ) Original post link: http://betterexplained.com/articles/an-intuitive-introduction-to-limits/ My profile link: https://www.urbanpro.com/delhi/pankaj-k/2531974 You may find more interesting stuff and information that can be of some help to you. I will be adding more pdfs in gallery soon . Sharing is caring.

If one wants the pdf in my galley on 'limits' can give a better understanding of the same material.

Pankaj

5 2

How to give perfect demo class? Which subject should teach for demo class? Ex. I went to give a demo class for x student

Hi Mr. Naveen. From my experience, I can tell that if you are giving demo class to your students, make it serious matter cause the class session itself will give the opportunity for future further...

Naveen Aerpula

0 0

What is the direction of friction on two wheels of a bicycle? Options: 1. Towards the front in the front wheel and towards the back in the rear wheel. 2. Towards the front in the rear wheel and towards the back in the front wheel. 3. Both rear. 4. Both front.

Both rear

Himanshu Yadav

0 0

A solid sphere of uniform density and radius 4 units is located with centre at origin.Two spheres of equal radii 1 unit, with centres at A(-2,0,0) and B (2,0,0) are taken out of the solidleaving behind spherical cavities.Then: 1. the gravitational force due to this at origin is zero. 2. the gravitational force at B is zero 3. the gravitational potential is same at all points of the circle y2+ z2= 36 4. the gravitational potential at all points on the circle y2 + z2= 4

The gravitational potential at all points on the circle y2 + z2= 4

Edify Coaching Classes

1 1

In library there are 2n+1 books if a student select at least n+1 books in 256 ways how many number of books in a library?

There are 9 books

Ravi

1 0

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Prove d/dx cos x = - sin x from first principles d/dx cos x = lim δx→0 = lim δx →0 . = - 2 = lim δx →0 (- 2 ) / δx = lim δx →0 (- 2 ) / δx =...

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Columns That Are Typically Used In The Purchase Journal.

A Purchase Journal is a record of all acquisitions made on credit during a period. In other words, this is the Journal that keeps track of the orders placed using vendor credit or accounts payable as well...

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Introduction To Accounting: Part 8: Accounting Concepts

In order to make the accounting language convey the same meaning to all people and to make it more meaningful, most of the accountants have agreed on a number of concepts which are usually followed for...

Nishant Kumar

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Essential Elements of a Valid Contract

Essential Elements of a Valid Contract: (i) Agreement: In order to constitute a contract, there must be an agreement in first place. An agreement in turn is composed of two elements-offer and acceptance....

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Consignment Meaning & Features

Meaning & Features Of Consignment Meaning: Consignment means the transaction of sending goods by one person (called CONSIGNOR) to another (called CONSIGNEE) who is to sell those goods on behalf of...

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