Question

Find the indicated limit, if it exists.

Answer 1

The limit is 1.

Explanation:

In this kind of problem, we can use the left and right-hand limit method.

Basically, we need to find the limit by the left side and then by the right side. If both of them are equal the limit does exist if not the limit does not exist.

Left hand

`lim_(-8^(-))(f(x))=lim_(-8^(-))(x+9)=-8+9=1`

Right hand

`lim_(-8^(+))(f(x))=lim_(-8^(+))(-7-x)=-7-(-8)=1`

As we see, both limits are the same, so the limit is equal to 1.

I hope it helps you!