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

i have no idea how to do this

Answer 2

let me interpret the question:

Find \(\large\color{black}{\displaystyle\lim_{x \rightarrow ~-8}f(x)}\) ?

where, \(\LARGE\color{black}{ f(x) = \begin{cases} & x+9,~~~~~~~~~~{\large x<-8} \\ & -7-x,~~~~~~{\large x\ge-8} \end{cases} }\)

Answer 3

is this interpretation correct?

Answer 4

correct

Answer 5

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.

Answer 6

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

Answer 7

it equal;s 1

Answer 8

yup!

Answer 9

oh. so to find the limit, just plug in the numbers that they give you

Answer 10

basically, but you need to verify that \(\Large\color{blue}{\displaystyle\lim_{x \rightarrow ~-8^{-}}f(x)=\displaystyle\lim_{x \rightarrow ~-8^{+}}f(x)}\)

Answer 11

oh. right.

Answer 12

if, \(\Large\color{blue}{\displaystyle\lim_{x \rightarrow ~-8^{-}}f(x) \ne\displaystyle\lim_{x \rightarrow ~-8^{+}}f(x)}\) then \(\Large\color{blue}{\displaystyle\lim_{x \rightarrow ~-8}f(x)~~\color{black}{\rm DNE}}\)

Answer 13

i have a couple of more. do you mind?

Answer 14

in your case, as you have already said both parts are equal to 1:)
so 1 is the answer you need

Answer 15

yes, sure.....

Answer 16

you can draw th piece wise functions and the limits, that would be faster for both of us:)