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Q. 50

Expert-verified

Calculus

Found in: Page 108

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .
$\lim_{x \to - 3} (1 - x) = 4$ .

Delta-epsilon proofs for $\lim_{x \to - 3} (1 - x) = 4$ is, whenever $0 < |x + 3| < δ$ , we also have localid="1648022140552" $|(1 - x) - 4| < ε$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

$\lim_{x \to - 3} (1 - x) = 4$ .

Step 2. Consider 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localid="1648022159445" ε>0,choose 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localid="1648022174115" δ=ε.

For all $x$ with $0 < |x + 3| < δ$ , we also have localid="1648022193077" $|(1 - x) - 4| < ε$ .

localid="1648022202619" $|(1 - x) - 4| = |1 - x - 4| = |- x - 3| = |- (x + 3)| = |x + 3| < δ = ε$

Therefore, whenever $0 < |x + 3| < δ$ , we also have localid="1648022212066" $|(1 - x) - 4| < ε$ .

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