Question

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

$14.\underset{x\to 0}{\lim }\frac{e^x-e^{-x}}{2}$.

Short answer

$\underset{x\to 0}{\lim }\frac{e^x-e^{-x}}{2}=0$.

Step-by-step solution

Step 1. Given.

Given a function $f\left(x\right)=\frac{e^x-e^{-x}}{2}$ whose limit needs to be found tending to 0.

Step 2. The table is as follows.

Compare the given function 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 close to 0 then f(x) gets close to 0.

So,$\underset{x\to 0}{\lim }\frac{e^x-e^{-x}}{2}=0$.