Question

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

$8.\underset{x\to 3}{\lim }(2x^2+1)$.

Short answer

$\underset{x\to 3}{\lim }(2x^2+1)=19$.

Step-by-step solution

Step 1. Given information.

A function is $f\left(x\right)=2x^2+1$ whose limit needs to be found tending to 3.

Step 2. Explanation and the table is as follows.

Compare the given function to .

Choose values of x close to 3, arbitrarily starting with 2.99. Then we select additional numbers that get closer to 3, but remain less than 3. Next choose values of x greater than 3, staring with 3.01, which get closer to 3.

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

As xgets closer to 3, f(x) gets closer to 19.

So,$\underset{x\to 3}{\lim }(2x^2+1)=19$.