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## Calculus, all content (2017 edition)

### Course: Calculus, all content (2017 edition)>Unit 1

Lesson 1: Limits introduction

# Introduction to limits (old)

An older video of Sal introducing the notion of a limit. Created by Sal Khan.

## Want to join the conversation?

• Why do people say, "Find the LIMIT of a function as it approaches some number"? Why can't we just say, "Find the value of the function as it approaches this number"? What does it mean by taking the "limit" of a function? •  The limit may or may not be the same thing as the value of the function.
The limit is what it LOOKS LIKE the function ought to be at a particular point based on what the function is doing very close to that point. If the function makes some sudden change at that particular point or if the function is undefined at that point, then the limit will be different than the value of the function.
• I still don't understand after watching the video multiple times. Why is there a limit? What does it mean "as the limit of x approaches 0 or 2"? Why? Why? Why? I'm so confused. • The concept is important because it explains to us about the function's behavior on an x-y plane. The concept of limits may not seem important at this time, but in jobs, especially physics of motion, deals a lot with limits. If you were to take a rocket, for example, and want to know where it is at a certain time (x), you can use limits to identify where it is at. For example, as the limit of x approaches 3 seconds, the rocket is approaches 50 kilometers.

A strong background in Algebra II and PreCalculus will solidify your knowledge of limits. Those subjects explain the basics of limits, and Calculus will show you some application of those limits (in continuity, rate of change, velocity.....and so much more).
• does the hole represent discontinuity in the function? • Hello, can someone please give me some possible applications of limits in physics, engineering, etc. Just curious. • Some specifc examples might also be right here in mathematics. If you remember from conic sections we actually use limits to find the assympthotes of the hyperbola, also you can use limits to define other cool stuff. For example, imagine that suddenly the formula to get the area of a circle has been removed from all knowledge, texbooks, etc... and you want to calculate the area of a circle. You might say "G, it's imposible!" but actually limits can help with this problem. If you take a polygon, let's say a square, you can put it inside the circle and the area of the square is going to be somehow close to the area of the circle, but still very far off from the real value. However as you add more and more sides to the polygon (imagine an hexagon inside of the circle) then the area of the polygon APPROCHES the area of the circle more and more. Now let's say "S" denotes the number of sides of the polygon, then you can define a function in wich to determine quite precisely the area of the polygon in terms of "S". So you could state that as "S" (The number of sides of the polygon) approches infinity, then the area of the polygon approches or is basically the same as the area of the circle. Pretty cool Uhh?

Hope this gives you an insight to what you can do with limits and really encourage you to keep learning about this topic in particular.

P.S. If you'd like a more solid explanation about the math involved to the problem of the circle and the polygon feel free to tell me and i'll work out the math.
• What is the purpose of limits? What do they help you find out about a function? • hii..my question is that why the value of 0! and 1! is same.....till now i ask to many teacher but no one told me the reason....so please give me answer as soon as possible...because i very excite to know about it... • can a function have a circular graph? • Hi there.... if i multiply infinity with infinity, can i write it as infinity squared? And then can't we divide infinity by infinity?? Does both of them have any value?
(1 vote) • Infinity is not a proper number, so it has some special rules. Any positive number (except 0) multiplied by infinity is infinity, and that includes infinity, so `∞·∞ = ∞`.

Also, any number divided by infinite tends to 0, so `a/∞ = 0`

On the other hand, the division of infinity by infinity is undefined, as is the multiplication of infinity by 0: `∞/∞ = indeterminate`, `∞·0 = indeterminate`  