how do I find the limit

Question

$\lim_{x\to1^+}f(x)$, $\lim_{x\to1^-} f(x)$, and $\lim_{x\to1} f(x)$, where

$f(x)= \begin{cases} 2x+1 & \mbox{if } x≤1 \\ 4-x^2 & \mbox{if } x>1 \end{cases}$

I do not understand how to solve this question, any help is appreciated!

Answer 1

So the question wants you to calculate the limit coming from the left and right, then limit overall. If the limit coming from the left is not the same as the limit coming from the right, then the overall limit does not exist. Does this help?

In this case,

$$\lim_{x \to 1^{-}} f(x) =\lim_{x \to 1^{-}} (2x+1).$$

$$\lim_{x \to 1^{+}} f(x) =\lim_{x \to 1^{+}} (4-x^2).$$