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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 1/4} \frac{\frac{1}{x} - 4}{x - \frac{1}{4}} $

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$f(x)=\frac{1}{x}$$a=\frac{1}{4}$

01:23

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

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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 a de…

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each limit represents the …

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In Exercises $57-62,$ each…

We have a question And this we have been provided with a limit X approaches to one x 4. one by X -4 by X -1 x four. So we need to find the value of have A. We have F D. A. Cool too affects minus yeah F A. He went by x minus A. So This is one x 4. This could be 10 years. If you compare we can write F-1 by full, equal to FX. That is one by X one by one x 4, Divide by X -1 x four. So He is able to be equal to one x 4 and effects will be equal to one by X. So this should be the answer Thank you.

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