# To state: The limit and the derivative of the given function at some numbers a .

BuyFind

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.6, Problem 37E
To determine

Expert Solution

## Answer to Problem 37E

0 is limit and derivative of the function limh0cos(π+h)+1h .

### Explanation of Solution

Given: limh0cos(π+h)+1h

Concept used:

Definition of derivative: f'(a)=limh0f(a+h)f(a)h

limh0cos(π+h)+1h be a given function.

It has to find derivative of the function at some numbers a .

limh0cos(π+h)+1h

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

f'(a)=limh0cos(π+h)+1h[00]

Apply L.Hospital rule

f'(a)=limh0cos(π+h)+1h=limh0sin(π+h)=sinπ=0

Hence, 0 is limit and derivative of the function limh0cos(π+h)+1h .

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