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Q. 64

Expert-verified

Found in: Page 136

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Calculate each of the limits:
$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

The solution of the limit $\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ is, $4$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The limit is,

$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

Step 2. Finding the solution.

$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$

Using ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ ,

$= \lim_{h \to 0} \frac{h^{2} + 4 h + 4 - 4}{h} = \lim_{h \to 0} \frac{h^{2} + 4 h}{h} = \lim_{h \to 0} h + 4$

Inputting $h = 0$

$= 0 + 4 = 4$

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Short Answer

Calculate each of the limits:
$\lim_{h \to 0} \frac{{(2 + h)}^{2} - 2^{2}}{h}$ .

Step by Step Solution

Step 1. Given Information.

Step 2. Finding the solution.

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