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 4.5, Problem 2E

(a)

To determine

Whether limxa[f(x)p(x)] is of indeterminate form and if not then evaluate the limits.

Expert Solution

Answer to Problem 2E

The limit function limxa[f(x)p(x)] is of the indeterminate form.

Explanation of Solution

Given:

The limit functions are, limxaf(x)=0 and limxap(x)= .

Definition used:

If limit function is of the type limxaf(x)g(x) , where both f(x)0 and g(x)0 or both f(x) and g(x) , then the limit may or may not exist, which is called as indeterminate form of limit.

Quotient rule for limits: “Limit of the quotient is quotient of the limits”,

Calculation:

Rearrange the given function in quotient form and then use the Quotient rule.

limxa[f(x)p(x)]=limxaf(x)1p(x)=limxaf(x)limxa1p(x)=01=00

Therefore, limxa[f(x)p(x)] is of indeterminate form.

(b)

To determine

Whether limxa[h(x)p(x)] is of indeterminate form and if not then evaluate the limits.

Expert Solution

Answer to Problem 2E

The value of limxa[h(x)p(x)] is .

Explanation of Solution

Given:

The limit functions are, limxah(x)=1 and limxap(x)= .

Calculation:

Product rule for limits: “Limit of the product is product of the limits”.

Use product rule and find the limit as follows,

limxa[h(x)p(x)]=limxah(x)limxap(x)=1=

Therefore, limxa[h(x)p(x)] is not of indeterminate form and its limit is .

(c)

To determine

Whether limxa[p(x)q(x)] is of indeterminate form and if not then evaluate the limit.

Expert Solution

Answer to Problem 2E

The value of limxa[p(x)q(x)] is .

Explanation of Solution

Given:

The limit functions are, limxap(x)= and limxaq(x)= .

Calculation:

Product rule for limits: “Limit of the product is product of the limits”.

limxa[p(x)q(x)]=limxap(x)limxaq(x)==

Therefore, limxa[p(x)q(x)] is not of indeterminate form and its value is .

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!