Question

Find the indicated limit, if it exists.

limit of f of x as x approaches negative 8 where f of x equals x plus 9 when x is less than negative 8 and f of x equals negative seven minus x when x is greater than or equal to negative 8

-8
1
17
The limit does not exist.

Answer 1

1

Explanation:

just took the test

Answer 2

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.