   Chapter 2.7, Problem 41E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Each limit represents the derivative of some function f at some number a. State such an f and a in each case. lim h → 0 cos ( π + h ) + 1 h

To determine

To state: The function f(x) and the number a.

Explanation

Given:

The derivative of a function f at a number a is f(a)=limh0cos(π+h)+1h.

Formula used:

The derivative of a function at a number a, denoted by f(a) is,

f(a)=limh0f(a+h)f(a)h (1)

Calculation:

Obtain the function f(x) and a.

Consider the given function f(a),

f(a)=limh0cos(π+h)+1h=limh0cos(π+h)cos(π)h(cos(π)=1)=limh0f(π+h)f(π)h=f(π)(By definition 1)

Note that, a=π since f(a)=f(π) and f(π+h)=cos(π+h) and f(π)=cos(π)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 