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Q. 36

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Calculus

Found in: Page 120

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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

The limit exists and it is equal to 81.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

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

Most popular questions for Math Textbooks

For each limit $\underset{x \to c}{l i m} f (x) = L$ in Exercises 43–54, use graphs and algebra to approximate the largest value of $δ$ such that if $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$ .

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