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Each limit represents the derivative of some function $ f $ at some number $ a $. State such an $ f $ and $ a $ in each case.

$ \displaystyle \lim_{x \to 2} \frac{x^6 - 64}{x - 2} $

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$f(x)=x^{6}$$a=2$

01:32

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

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Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Each limit represents the …

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each limit represents the …

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Hello. We have a question. Um And this it is given that each limit represents the deliverable function. Yeah. At some point A. Okay so this is limit X approaches to to access the power six minus 64 X. Raised to the power six -64 by X -2. Okay, let me have formula that yes visit at A. So they should be limit X approaches to a FX -5A by x minus E. Uh And the school building has limit X approaches to to x rays to the power six minus two days. To the power six By X -2. Now if you compare, these two will be getting the value of effects as excellent at about six and A. S. Two. Thank you.

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