1. Limits and Continuity

Use the continuity of the absolute value function (Exercise 78) to determine the interval(s) on which the following functions are continuous.

$g\left(x\right)=\mid \frac{x+4}{x^2-4}\mid$

Limits of quotients

Find the limits in Exercises 23–42.

limu→1 (u⁴ − 1)/(u³ − 1)

Use graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$

$c=0$

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$.

$c=-2$

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$.

$c=3$

Use the graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$.

$c=4$

Determine the value(s) of $x$ (if any) for which the function is discontinuous.

$f\left(x\right)=\frac{x-4}{x^2-x-12}$

Determine the value(s) of $x$ (if any) for which the function is discontinuous.