Chapter 14: Q, 27 (page 883)

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} {(3 x - 2)}^{5 / 2}$ .

Short Answer

Expert verified

The answer is 32.

Step by step solution

Step. 1 Given Information

Given is the limit on which x tends to 2 and the function given is:

${(3 x - 2)}^{5 / 2}$

Step. 2 Solving the limit

Firstly, we check whether the given function is in indeterminant form or not.

Since if we put $x = 2$ then it doesn't create any indeterminant form. So, to solve the limit we can directly put the value of x in the function.

\lim_{x \to 2} {(3 x - 2)}^{5 / 2} = {(3 (2) - 2)}^{5 / 2} = {(6 - 2)}^{5 / 2} = 4^{5 / 2} = {(\sqrt{4})}^{5} = 2^{5} = 32 .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} {(3 x - 2)}^{5 / 2}$ .

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Solving the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraically.limx→23x-25/2.

Short Answer

Step by step solution

Step. 1 Given Information

Step. 2 Solving the limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 7– 42, find each limit algebraically.
$\lim_{x \to 2} {(3 x - 2)}^{5 / 2}$ .