Question

Find the indicated limit, if it exists.

Answer 1

Find ${\displaystyle\lim_{x \rightarrow ~-8}f(x)}$

where ${ f(x) = \begin{cases} & x+9,~~~~~~~~~~{\large x\ \textless \ -8} \\ & -7-x,~~~~~~{\large x\ge-8} \end{cases} }$

So to find the left sided limit, you need to plug in -8, into x+9 and to find the right sided limit, you need to plug in -8, into -7-x.

If the two sides of the limit are no equivalent, then ${\displaystyle\lim_{x \rightarrow ~-8}f(x)~~DNE}$

Since both sides are equal to 1, the limit is 1.