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

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

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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