Chapter 1: Q. 37 (page 120)

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x 鈫� 0} x^{- 3} .$

Short Answer

Expert verified

Limit does not exist.

Step by step solution

Step 1. Given Information.

$G i v e n : \lim_{x 鈫� 0} x^{- 3} .$

Step 2. Theorem 1.16

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

Step 3. Finding limit of given function.

According to the theorem power functions are continuous in their domains but $x = 0$ is not in the domain of the function $x^{- 3}$ . 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.

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91影视

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x 鈫� 0} x^{- 3} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Theorem 1.16

Step 3. Finding limit of given function.

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91影视

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx鈫�0x-3.

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

Decision Maths

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

For each limit in Exercises 33鈥�38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x 鈫� 0} x^{- 3} .$