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Q. 13

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Precalculus Enhanced with Graphing Utilities

Found in: Page 876

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 7–16, use a table to find the indicated limit.
$13 . \lim_{x \to 0} (e^{x} + 1)$ .

$\lim_{x \to 0} (e^{x} + 1) = 2$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given.

Given function is $f (x) = e^{x} + 1$ whose limit tends to 0 is need to be found.

Step 2. The table is as follows.

Compare the given limit to .

Choose values of x close to 0 , arbitrarily starting with -0.01. Then we select additional numbers that get closer to 0 , but remain less than 0 .

Next choose values of x greater than 0 , staring with 0.01, which get closer to 0 .

Finally evaluate f(x) at each choice to obtain the required Table.

As x gets closer to 0 then f(x) gets closer to 2.

So, $\lim_{x \to 0} (e^{x} + 1) = 2$ .

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