Question

Find the indicated limit, if it exists.

Answer 1

So this is what you basically got:
\[\LARGE \lim_{x \rightarrow 8}~(x+10)~=~\LARGE \lim_{x \rightarrow 8}~(10-x)~~~~~~~~(~??~)\]

Answer 2

ok

Answer 3

the left side of the equation is when 8 approaches from the left, and the right is when it approaches 8 from the right.
Are the sides equivalent?

Answer 4

yes

Answer 5

\[\LARGE \lim_{x \rightarrow 8}~(x+10)~=~\LARGE \lim_{x \rightarrow 8}~(10-x) \]
\[\LARGE ~~~~~~~~~(8+10)=(10-8)\]
SURE?

Answer 6

oh, alright .
No they are not equivalent

Answer 7

Yes, they are no equivalent.
So, we see that:
1) as \(\large\color{black}{ x \rightarrow 8^- }\), the \(\large\color{black}{ f(x)\rightarrow18 }\)
2) as \(\large\color{black}{ x \rightarrow 8^+ }\), the \(\large\color{black}{ f(x)\rightarrow 2 }\)

correct?

Answer 8

right

Answer 9

Can you answer your own question?

Answer 10

the limit is 2

Answer 11

Nope, that is only when it approaches 8 from the right side.

Answer 12

isn't that what the question is asking?

Answer 13

No, " what is \(\Large\color{black}{ \lim_{x \rightarrow 8}~f(x) }\) ", that is your question.

Answer 14

Can you tell me, (in this case) what is \(\Large\color{blue}{ \lim_{x \rightarrow 8}~f(x) }\) ?

Answer 15

does it not exist?

Answer 16

Yes, it doesn't exist.

Answer 17

oh alright, so if they are not equivalent. then it doesn't exist?

Answer 18

Thanks!

Answer 19

\[If,~~~~~\huge \lim_{x \rightarrow a^{\color{red}{-}}}f(x) \ne \lim_{x \rightarrow a^{\color{blue}{+}}}f(x)\]
\[then~~~~~~\huge~\lim_{x \rightarrow a}~f(x)~~DNE\]

Answer 20

yes, sides must be equivalent.

Answer 21

makes sense, right?

Answer 22

Yes, thanks for explaining it

Answer 23

Anytime!