When do i check the sides of a limit in order to find a limit?

Question

When do i need to check the sides to see if the limit exists? Do i do this only on multi type functions? Thanks!

Answer 1

One of the definitions of the limit is that if $$L=\lim\limits_{x\to a^-} f(x) = \lim\limits_{x\to a^+} f(x)$$ then $$L=\lim\limits_{x\to a} f(x)$$

That is, the limit only exists if the left and right sided limits are the same. If, for example, you have reason to believe that a function (in your case, a piecewise function) is discontinuous at $x=a$, then you can try to find the left and right sided limits to see if the limit exists.