Chapter 1: Q. 36 (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.
$\lim_{x \to 3} x^{4} .$

Short Answer

Expert verified

The limit exists and it is equal to 81.

Step by step solution

Step 1. Given Information.

$G i v e n : \lim_{x \to 3} x^{4}$

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.

$U \sin g t h e a b o v e t h e o r e m, A = 1, c = 3 a n d k = 4 . S o, p u t t i n g t h e s e v a l u e s w e g e t o u r l i m i t a s : \lim_{x \to 3} x^{4} = 3^{4} = 81 .$

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For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
$\lim_{x \to 3} x^{4} .$

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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For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→3x4.

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

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Mechanics Maths

Probability and Statistics

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.
$\lim_{x \to 3} x^{4} .$