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Q. 13

Expert-verifiedFound in: Page 876

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problems *7–16*, use a table to find the indicated limit.

$13.\underset{x\to 0}{\mathrm{lim}}({e}^{x}+1)$.

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

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

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

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