Limits and Jumps

Graph of $$y=\frac{\left|\ x-6\ \right|}{x-6}$$

​ (a)   ​ (b)   ​ (c)  

TERMINOLOGY

Jump​ (a)  

is the same as

​ (b)   Point of​ (c)   ​ (d)  

TERMINOLOGY

$$y=\frac{\left|\ x-6\ \right|}{x-6}$$

Graph​ (a)   at the jump

Determine the exact value for the following three limits

$$\lim_{x\ \rightarrow\ 6^-}\ \left(\ \frac{\left|\ x-6\ \right|}{x-6}\ \right)=$$ ​ (a)  

$$\lim_{x\ \rightarrow\ 6^{\ +}}\ \left(\ \frac{\left|\ x-6\ \right|}{x-6}\ \right)=$$ ​ (b)  

$$\lim_{x\ \rightarrow\ 6}\ \left(\ \frac{\left|\ x-6\ \right|}{x-6}\ \right)=$$ ​ (c)  

Right and Left Hand Limits

$$\lim_{x\ \rightarrow\ 6^{\ -}}\ \left(\ \frac{\left|\ x-6\ \right|}{x-6}\ \right)$$ ​ (a)   $$\lim_{x\ \rightarrow\ 6^{\ +}}\ \left(\ \frac{\left|\ x-6\ \right|}{x-6}\ \right)$$

Match each limit with its correct description.

Determine the exact value for the following three limits

$$\lim_{x\ \rightarrow\ 13^-}\ \left(\ \frac{\left|\ x-13\ \right|}{x-13}\ \right)=$$ ​ (a)  

$$\lim_{x\ \rightarrow\ 17^{\ +}}\ \left(\ \frac{\left|\ x-17\ \right|}{x-17}\ \right)=$$ ​ (b)  

$$\lim_{x\ \rightarrow\ 19}\ \left(\ \frac{\left|\ x-19\ \right|}{x-19}\ \right)=$$ ​ (c)  

Match each limit with its correct description.

Which function(s) has a Jump @ $$x=12$$ ?