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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

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  1. freckles
    • one year ago
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    \[\lim_{x \rightarrow -10} f(x) \\ f(x)=\left(\begin{matrix} x-4 , x<-10 \\ 6, x=-10 \\ x+16, x>-10 \end{matrix}\right)\] 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
    • one year ago
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    You need to find both the left and right limit.

  3. freckles
    • one year ago
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    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
    • one year ago
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    @freckles Would the answer be Does Not Exist?

  5. anonymous
    • one year ago
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    Sorry, was working through other problems.

  6. freckles
    • one year ago
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    well what did you get for the left and right limit? if they are not equal then you are right.

  7. anonymous
    • one year ago
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    4 and -16 @freckles

  8. freckles
    • one year ago
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    -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
    • one year ago
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    Oh got it, thank you! Could you help me with a couple others? @freckles

  10. freckles
    • one year ago
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    post another question just in case but I think I can

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