Question

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

Answer 1

\[\lim_{x \rightarrow -10} f(x) \\ f(x)=\left(\begin{matrix} x-4 , x<-10 \\ 6, x=-10 \\ x+16, x>-10 \end{matrix}\right)\]
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

Answer 2

You need to find both the left and right limit.

Answer 3

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

Answer 4

@freckles Would the answer be Does Not Exist?

Answer 5

Sorry, was working through other problems.

Answer 6

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

Answer 7

4 and -16 @freckles

Answer 8

-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

Answer 9

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

Answer 10

post another question just in case
but I think I can