Question

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

$7.\underset{x\to 2}{\lim }\left(4x^3\right)$

Short answer

$\underset{x\to 2}{\lim }\left(4x^3\right)=32$.

Step-by-step solution

Step 1. Given information.

A function is given as $f\left(x\right)=4x^3$ whose limit needs to be found tending to 2.

Step 2. Explanation.

Compare the given function to .

Choose values of x close to 2, arbitrarily starting with 1.99 then we select additional numbers that get closer to 2, but remain less than 2.

Next choose values of x greater than 2, staring with 2.01, which get closer to 2.

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

As x gets closer to 2thenf(x)gets closer to 32.

So, $\underset{x\to 2}{\lim }\left(4x^3\right)=32$