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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_{h \to 0} \frac{\cos (\pi + h) + 1}{h} $

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$f(x)=\cos (x) ; a=\pi$

01:58

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Oregon State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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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$31-36$ Each limit represe…

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Each limit represents a de…

we have a question and this uh we need to find the value of function efforts and ah quantity is there? It is. What we say it is derivative. Okay, so we have a formula for basic formula for derivative F dash a equal to Limit accidents to zero F April such limit That's tends to zero F A place at minus mm hmm. If they buy it F A by at and we have given quantity limit at not going to the expression course X. Let's get sorry caused by plus set bible assets minus F A. It is one here divide by at. So everything seems to be, everything seems to be normal at for it and as for it so they will be able to pie which means we can see that have facts equal to of course X. Okay. So uh if you write F A plus it it will be by plus set and equal to pi So that F of pie or I hope they will be caused by which is equal to Cameed by is equal to -1. of course by is -1. So Okay, okay, which is minus one. Sorry, it is plus one. Yes, of course it is great because this could be written as limit its approaches to zero of course five plus at minus minus one by at after comparing we can get affects equal to cossacks and equal to pi. Thank you so much

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