# the limit of the function.

### 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 4, Problem 30RE
To determine

## To find: the limit of the function.

Expert Solution

The limit of the function limx0e4x-1-4xx2 is 8 .

### Explanation of Solution

Given:

limx0e4x-1-4xx2 .

Concept used:

If the function will be in the form of indeterminate (00) which is not valid.

In this kind of situation L Hospital’s Rule.

Which state that the limit of a quotient of the functions is equal to the limit of quotient of the derivative.

This rule can be applied as much as necessary so to get not Indeterminate Forms.

Calculation:

limx0e4x-1-4xx2

By putting direct x=0 the function will be in the form of indeterminate (00) which is not valid.

In this kind of situation L Hospital’s Rule.

Which state that the limit of a quotient of the functions is equal to the limit of quotient of there derivative.

limx0e4x-1-4xx2

=limx0ddx(e4x-1-4x)ddx(x2) .

Finding derivative of numerator and denominator.

=limx04e4x-42x .

Taking limit of each term:

4e4(0)-42(0)=00

Which is in the form of indeterminate (00) which is not valid.

This rule can be applied as much as necessary so to get not Indeterminate Forms.

So, differentiating numerator and denominator.

ddx(limx04e4x-42x)=limx016e4x2=162=8 .

Hence the limit of the function limx0e4x-1-4xx2 is 8 .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!