Chapter 1: Q. 38 (page 120)

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x \to - 5} \sqrt{x} .$

Short Answer

Expert verified

Limit does not exist.

Step by step solution

Step 1. Given Information.

$G i v e n : \lim_{x \to - 5} \sqrt{x}$

Step 2. Theorem 1.16

$P o w e r f u n c t i o n s a r e c o n t i n u o u s o n t h e i r d o m a i n s . I n t e r m s o f l i m i t s, i f A i s r e a l a n d k i s r a t i o n a l, t h e n f o r a l l v a l u e s x = c a t w h i c h x^{k} i s d e f i n e d w e h a v e \lim_{x \to c} A x^{k} = A c^{k} .$

Step 3. Finding limit of given function.

According to the theorem power functions are continuous in their domains but $x = - 5$ is not in the domain of the function $\sqrt{x}$ . Therefore, theorem does not apply for this limit and also limit does not exist for this function as it is not even in the domain.

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.

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x \to - 5} \sqrt{x} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Theorem 1.16

Step 3. Finding limit of given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Statistics

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→-5x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Theorem 1.16

Step 3. Finding limit of given function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Statistics

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x \to - 5} \sqrt{x} .$