## Babynini one year ago Limits of absolute values

1. Babynini

2. anonymous

@Astrophysics

3. Astrophysics

Ok lets first note, |dw:1443917561077:dw| if we plug the limit we will get 0/0 correct?

4. Babynini

Right

5. Astrophysics

All we really need to know is |dw:1443917619092:dw| so we have to break it up as such

6. Astrophysics

Now we have to take the limit as it approaches -5 from the left and right, so we have $\huge \lim_{x \rightarrow -5^{-}} \frac{ 5-(-x) }{ 5+x } = ...$ and $\huge \lim_{x \rightarrow -5^+} \frac{ 5-x }{ 5+x } = ...$does that make sense?

7. Babynini

Okay, but direct substitution still doesn't work there o.o

8. Babynini

They equal, 1 and - 1 respectively?

9. Zarkon

coming from either direction of -5 we have $\lim_{x \rightarrow -5} \frac{ 5-|x| }{ 5+x } =\lim_{x \rightarrow -5} \frac{ 5-(-x) }{ 5+x }$

10. Astrophysics

Yes, thanks @Zarkon

11. Babynini

So.. = 1

12. Astrophysics

Yes

13. Babynini

Yay!! ok, perfect. Thanks both of you :)

14. Astrophysics

Had to note x<0 for both :p

15. Astrophysics

Slight mistake

16. Babynini

Yeah, sorry o.0