In the piecewise function below, $k$ is a constant. $$f(x)=\begin{cases}\dfrac{x^2-k^2}{x-k},&x\neq k,\\ 4-k,&x=k.\end{cases}$$ What is the value of the limit $\lim_{x\to k^-}f(x)$?

  1. $-2k$.
  2. $2k$.
  3. $0$.
  4. Limit does not exist.

(The above text was originally posted as this image.).

I have a question from a released exam that I don't understand. I know the answer which is $2k$ but then I don't understand how to get the answer. It would be great if someone could explain it.

  • 2
    $\begingroup$ Please type up the question instead of asking people to click through. $\endgroup$ – Ross Millikan Jun 3 at 0:50
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  • $\begingroup$ Welcome to MSE. Please don't post images when you can easily type the material, as here. $\endgroup$ – saulspatz Jun 3 at 0:53
  • $\begingroup$ What is it that you don't understand about the question? $\endgroup$ – saulspatz Jun 3 at 0:54
  • $\begingroup$ I don't understand how the answer is 2k $\endgroup$ – Aryan Naik Jun 3 at 1:00

Hint: Cancelling out the numerator and denominator in the first equation, you get $x+k$ when x does not equal to k.

You are also approaching k from the left.

Hope that helps


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