### Home > APCALC > Chapter 2 > Lesson 2.4.1 > Problem2-144

2-144.

Use the graph from problem 2-143 to complete the following table:

 $a$ $\lim\limits _ { x \rightarrow a } f ( x )$ $f (a)$ Continuous at $x = a$? $1$ $2$ $3$ $4$

At a vertical asymptote, $f(x)$ approaches $−\infty$ from the left and $+\infty$ from the right.

$\text{So there are two reasons why }\lim\limits _{x\rightarrow 3}f(x)= DNE.$

Reason 1: $\infty$ is not finite.
Reason 2: $+\infty$ does not agree with $−\infty$

Careful! Just because $f\left(4\right)$ exists, does not mean that the limit $x\rightarrow 4$ exists.