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Q. 33

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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.
$\lim_{x \to - 1} 6 .$

The limit exists and it is equal to 6.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

$G i v e n : \lim_{x \to - 1} 6 .$

Step 2. Theorem 1.16

$C o n s \tan t, i d e n t i t y, a n d l i n e a r f u n c t i o n s a r e c o n t i n u o u s e v e r y w h e r e . I n t e r m s o f l i m i t s, f o r e v e r y k, c, m, a n d b i n R w e h a v e \lim_{x \to c} k = k, \lim_{x \to c} x = c a n d \lim_{x \to c} (m x + b) = (m c + b) .$

Step 3. Finding limit of given function.

$U \sin g t h e a b o v e t h e o r e m' s 1 s t c a s e w e g e t, c = - 1 a n d k = 6 . P u t t i n g t h e s e v a l u e s w e g e t, \lim_{x \to - 1} 6 = 6 .$

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