anonymous
  • anonymous
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
Mathematics
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SOLVED
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chestercat
  • chestercat
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freckles
  • 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
freckles
  • freckles
You need to find both the left and right limit.
freckles
  • 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

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anonymous
  • anonymous
@freckles Would the answer be Does Not Exist?
anonymous
  • anonymous
Sorry, was working through other problems.
freckles
  • freckles
well what did you get for the left and right limit? if they are not equal then you are right.
anonymous
  • anonymous
4 and -16 @freckles
freckles
  • 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
anonymous
  • anonymous
Oh got it, thank you! Could you help me with a couple others? @freckles
freckles
  • freckles
post another question just in case but I think I can

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