Continuity at a Point Quiz

Select the THREE conditions for Continuity at a Point  $x=c$ .

•  $\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$  

•  $f\left(c\right)$  must be positive

•  $f\left(c\right)$  is defined

•  $\lim_{x\rightarrow c}f\left(x\right)$  exists

•  $\lim_{x\rightarrow c}f\left(x\right)\ne f\left(c\right)$  

Use the graph shown to determine if the function is continuous at  $x=13$ . If the function is not continuous, select the condition for continuity at a point that the function fails.

• The function is continuous at  $x=13$ . 

• The function is not continuous at  $x=13$ because  $f\left(13\right)$ is undefined.

• The function is not continuous at  $x=13$ because  $\lim_{x\rightarrow13}f\left(x\right)$ does not exist.

• The function is not continuous at  $x=13$ because  $\lim_{x\rightarrow13}f\left(x\right)\ne f\left(13\right)$ .  

Use the graph shown to determine if the function is continuous at  $x=5$ . If the function is not continuous, select the condition(s) for continuity at a point that the function fails. 

SELECT ALL THAT APPLY, THERE ARE TWO ANSWERS.

• The function is continuous at  $x=5$ . 

• The function is not continuous at  $x=5$ because  $f\left(5\right)$ is undefined.

• The function is not continuous at  $x=5$ because  $\lim_{x\rightarrow5}f\left(x\right)$ does not exist.

• The function is not continuous at  $x=5$ because  $\lim_{x\rightarrow5}f\left(x\right)\ne f\left(5\right)$ .  

Use the graph shown to determine if the function is continuous at  $x=18$ . If the function is not continuous, state the type of discontinuity the function has at that point.

• The function is continuous at  $x=18$ .

• The function has a jump discontinuity at  $x=18$ .

• The function has a removable discontinuity (hole) at  $x=18$ .

• The function has a non-removable (infinite) discontinuity at  $x=18$ . 

Use the graph shown to determine if the function is continuous at  $x=1$ . If the function is not continuous, state the type of discontinuity the function has at that point.

• The function is continuous at  $x=1$ .

• The function has a jump discontinuity at  $x=1$ .

• The function has a removable discontinuity (hole) at  $x=1$ .

• The function has a non-removable (infinite) discontinuity at  $x=1$ . 

Use the graph shown to determine if the function is continuous at  $x=-7$ . If the function is not continuous, state the type of discontinuity the function has at that point.

• The function is continuous at  $x=-7$ .

• The function has a jump discontinuity at  $x=-7$ .

• The function has a removable discontinuity (hole) at  $x=-7$ .

• The function has a non-removable (infinite) discontinuity at  $x=-7$ . 

Use the graph shown to determine if the function is continuous at  $x=5$ . If the function is not continuous, state the type of discontinuity the function has at that point.

• The function is continuous at  $x=5$ .

• The function has a jump discontinuity at  $x=5$ .

• The function has a removable discontinuity (hole) at  $x=5$ .

• The function has a non-removable (infinite) discontinuity at  $x=5$ . 

Determine if the function shown is continuous at  $x=0$ .

Hint: You will have to use the Unit Circle to evaluate  $\cos\ x$ .

• The function is continuous at  $x=0$ 

• The function is not continuous at  $x=0$ 

Determine if the function shown is continuous at  $x=3$ .

• The function is continuous at  $x=3$ 

• The function is not continuous at  $x=3$ 

Evalaute $\lim_{x\rightarrow3}\ \left(\frac{x^2-9}{x^2+5x-24}\right)$  

•  $DNE$  

•  $\frac{6}{11}$  

•  $0$  

•  $\infty$