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Q. 13

Expert-verified
Found in: Page 876

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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

$\underset{x\to 0}{\mathrm{lim}}\left({e}^{x}+1\right)=2$.

See the step by step solution

Step 1. Given.

Given function is $f\left(x\right)={e}^{x}+1$ 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, $\underset{x\to 0}{\mathrm{lim}}\left({e}^{x}+1\right)=2$.