Question

Math limit, time table problem.
Am I correct to think that the answer is Infinity?

Answer 1

No. For x=2 you have:

$f(2)=\dfrac{2^2-4}{2-2}=\dfrac{4-4}{2-2}=\dfrac{0}{0}$

This is the indeterminate form 0/0 and its value could be anything you want (0, any number or infinity).
But:

$\lim_{x\to2}\dfrac{x^2-4}{x-2}=\lim_{x\to2}\dfrac{(x+2)(x-2)}{x-2}=\lim_{x\to2}(x+2)=4$

So answer is B.

You could see that when you calculate

f(1.999) ≈ 3.999
and
f(2.001) ≈ 4.001