Use graph of $f\left(x\right)$ to determine if the function is continuous or discontinuous at $x=c$
$c=0$

At what points are the functions in Exercises 13–30 continuous?

g(x) = { (x² − x – 6)/(x – 3), x ≠ 3

5, x = 3

Limits of quotients

Find the limits in Exercises 23–42.

limu→1 (u⁴ − 1)/(u³ − 1)

Is there a value of c that will make

f(x) = { (sin²(3x)) / x², x ≠ 0

c, x = 0

continuous at x = 0? Give reasons for your answer.

Limits and Continuity

Graph the function

1 , x ≤ ―1

―x , ―1 < x < 0

ƒ(x) = { 1 , x = 0 ,

―x , 0 < x < 1

1 , x ≥ 1

Then discuss, in detail, limits, one-sided limits, continuity, and one-sided continuity of ƒ at x = ―1 , 0 , and 1. Are any of the discontinuities removable? Explain.

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.

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