Question

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

$11.\underset{x\to 4}{\lim }\frac{x^2-4x}{x-4}$.

Short answer

$\underset{x\to 4}{\lim }\frac{x^2-4x}{x-4}=4$.

Step-by-step solution

Step 1. Given information.

A limit function is given as$\underset{x\to 4}{\lim }\frac{x^2-4x}{x-4}$.

Step 2. Form the table.

Choose values of x close to 4, arbitrarily starting with 3.99 then we select additional numbers that get closer to 4, but remain less than 4. Next choose values of x greater than 4, staring with 4.01, which get closer to 4.

Finally evaluate $f\left(x\right)=\frac{x^2-4x}{x-4}$at each choice to obtain the below Table:

Asx gets closer to 4 then f(x)gets closer to 4.

So,$\underset{x\to 4}{\lim }\frac{x^2-4x}{x-4}=4$.