Question

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

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

Short answer

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

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.

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

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