Question

Find the indicated limit, if it exists.

http://prntscr.com/7ulwx5

Answer 1

for the part of the function that is GREATER than 9, that is:

\(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{+}}f(x)\)
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for the part of the function that is SMALLER than 9, that is:

\(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)\)

Answer 2

If these both limits are equal to each other, then whatever they are both equivalent to, is going to be your answer.

If the limit from the left side and the limit from the right side are not equivalent, then your limit DNE

Answer 3

If you don't understand what I am saying I can redo the explanation better.

Answer 4

ok

Answer 5

I understand what you are saying. I just need to know how to find the limit.

Answer 6

Just plug in 9 into each of the parts

Answer 7

ok so 18 and 18

Answer 8

yes, so your answer is 18

Answer 9

thanks

Answer 10

because the limit from both sides is equal to 18, that means that the two-sided limit is also 18.

Answer 11

yes

Answer 12

\(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{-}}f(x)=\lim_{x\rightarrow 9}(x+9)=9+9=18\)

\(\displaystyle \LARGE\lim_{x\rightarrow 9^\color{red}{+}}f(x)=\lim_{x\rightarrow 9}(27-x)=27-9=18\)

Therefore,

\(\displaystyle \LARGE\lim_{x\rightarrow 9}f(x)=18\)

Answer 13

the 27-x corresponds to the limit from the right side, because it is for greater-than-9 values of x,

and x+9 corresponds to the limit from the left side, because it is for smaller-than-9 values of x.

Answer 14

You are welcome...

Answer 15

That helps a lot. Thank you