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 4, Problem 30RE
To determine

To find: the limit of the function.

Expert Solution

Answer to Problem 30RE

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 .

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