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

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2.6, Problem 36E
To determine

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

Expert Solution

12 is limit and derivative of the function limxπ/4tanx1xπ/4 .

### Explanation of Solution

Given: limxπ/4tanx1xπ/4

Concept used:

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

limxπ/4tanx1xπ/4 be a given function.

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

limxπ/4tanx1xπ/4

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

f'(a)=limxπ/4tanx1xπ/4[00]

Apply L.Hospital rule

f'(a)=limxπ/4tanx1xπ/4=limxπ/4sec2x=(secπ/4)2=12

Hence, 12 is limit and derivative of the function limxπ/4tanx1xπ/4 .

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