Question

Find the indicated limit, if it exists.

Answer 1

For the limit to exist, the limits from either side must also exist and be identical. We have

$\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}(x+3)=2+3=5$

$\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}(3-x)=3-2=1$

Since the limits do not match, the overall limit does not exist.