# Determine the limit of a piecewise defined function

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.

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.

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• What is it that you don't understand about the question? – saulspatz Jun 3 at 0:54
• I don't understand how the answer is 2k – 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