## anonymous one year ago Find the indicated limit, if it exists. http://prntscr.com/7ulwx5

1. SolomonZelman

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

2. SolomonZelman

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

3. SolomonZelman

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

4. anonymous

ok

5. anonymous

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

6. SolomonZelman

Just plug in 9 into each of the parts

7. anonymous

ok so 18 and 18

8. SolomonZelman

9. anonymous

thanks

10. SolomonZelman

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

11. anonymous

yes

12. SolomonZelman

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

13. SolomonZelman

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.

14. SolomonZelman

You are welcome...

15. anonymous

That helps a lot. Thank you