Question

The limit $\underset{x\to 2}{lim}\frac{x^2-4}{x-2}$ does not exist

• A. True
• B. False

Answer 1

The correct option is B

False

The limits we saw so far can be evaluated by direct substitution. If we substitute x=2 in the limit,

$\underset{x\to 2}{lim}\frac{x^2-4}{x-2}$ we will get $\frac{0}{0}$. This does not mean that the limit does not exist, it means the value of the

function is not defined at that point. The expression $\frac{x^2-4}{x-2}$ is equal to $x+2$ except at $x=2$. The graph of

$\frac{x^2-4}{x-2}$ will look like

We can see that the function is not defined at x=2. But the value of $\frac{x^2-4}{x-2}$ approaches 4 as x approaches

2.We can say that the limit is 4.