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Q. 44

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Calculus

Found in: Page 107

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

For each limit statement in Exercises $41 - 44$ , use algebra to find $δ$ or $N$ in terms of $ε$ or $M$ , according to the appropriate formal limit definition.
$\lim_{x \to \infty} (x^{2} + 2) = \infty$ ,find $N$ in terms of $M$ .

For $\lim_{x \to \infty} (x^{2} + 2) = \infty$ , $N = \sqrt{M - 2}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

$\lim_{x \to \infty} (x^{2} + 2) = \infty$ .

Step 2. From the limit expression,

$f (x) = x^{2} + 2 c = \infty L = \infty$

Now for $δ > 0$ .

$|x| < N {|x|}^{2} < N^{2} |x^{2} + 2| < N^{2} + 2 |x^{2} + 2| < M$

Therefore,

$N^{2} + 2 = M N^{2} = M - 2 N = \sqrt{M - 2}$

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