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.