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Session 4: Limits and Continuity Course Use OCW to guide your own life-long learning, or to teach others. We don't offer credit or certification for using OCW. How to teach the concepts of limits, continuity, differentiation and integration in Introductory Calculus course, using real contextual activities where students

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What is Calculus? When Do You Use It In The Real World? limits, derivatives, and you can use calculus in a lot of ways and applications. We find many applications of limits and continuity in our daily life. If you drop an ice cube in a glass of warm water and measure the temperature with time, the temperature eventually approaches the room temperature where the glass is stored. Measuring the temperature is a limit again as time approaches infinity.

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In this page we try to intuitively understand the concepts of limits and continuity. This is read "the limit as x approaches 1 of x An Intuitive Introduction. Continuity вЂ“ In this section we will introduce the concept of continuity and how it relates to limits. section we will look at the lone application to

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Yes, Limits isn't particularly exciting. But it can, at least, be enjoyable. We dare you to prove us wrong. App Preview: Calculus I: Lesson 2: Continuity and Limits at Infinity I You can switch back to the summary page for this application by clicking here.

A limit symbol can be moved through a function symbol, if the function is continuous and the limit exists. Suppose that $\lim_{x\rightarrow a}g(x)=b$ and f is continuous at b, then $\lim_{x\rightarrow a}f(g(x))$ = $f(\lim_{x\rightarrow a}g(x))$ = f( b) = b This property allows the order to two symbols to be reversed. The limit of a function is the cornerstone of both differential and integral calculus. Derivatives depends on the notion of the limit of a function Limits are also used as real-life approximations to calculating derivatives. Real-life limits are used any time you have some type of real-world application approach a steady-state solution.

The concept of a limit is useful in applications Because is not approaching a unique real 754 Chapter 11 Limits and an Introduction to Calculus x 2 2 3 We need the concept of limits to explain how differentiation, 1. Limits and Differentiation . by M. Bourne. Continuity and Differentiation .

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