## anonymous one year ago Find the indicated limit, if it exists. limit of f of x as x approaches negative 10 where f of x equals negative 4 minus x when x is less than negative 10, 6 when x equals negative 10, and x plus 16 when x is greater than negative 10

1. freckles

$\lim_{x \rightarrow -10} f(x) \\ f(x)=\left(\begin{matrix} x-4 , x<-10 \\ 6, x=-10 \\ x+16, x>-10 \end{matrix}\right)$ is this right? also pretend that isn't a matrix didn't know how to write a piecewise function in latex or i just keep forgetting how

2. freckles

You need to find both the left and right limit.

3. freckles

that is you need to evaluate both: $\lim_{x \rightarrow -10^-}f(x) =\lim_{x \rightarrow -10^-}(x-4) \\ \\ \text{ and } \\ \lim_{x \rightarrow -10^+} f(x)=\lim_{x \rightarrow -10^+}(x+16)$ if both of these are the same and they exist then your original limit you asked about exists and it it whatever the left and right limit equal if they are not equal then the original limit does not exist

4. anonymous

@freckles Would the answer be Does Not Exist?

5. anonymous

Sorry, was working through other problems.

6. freckles

well what did you get for the left and right limit? if they are not equal then you are right.

7. anonymous

4 and -16 @freckles

8. freckles

-10-4=-14 -10+16=6 left limit as x approaches -10=-14 right limit as x approaches -10=6 since -14 doesn't equal 6 then the limit does not exist

9. anonymous

Oh got it, thank you! Could you help me with a couple others? @freckles

10. freckles

post another question just in case but I think I can