cleverlikeme 2 years ago I need help with the steps involved to solve the following equation. lim x→−24 (square root(x^2 + 49) − 25)/x + 24 obviously when i plug it in its 0/0 but I'm unsure of the method to solve at this point. if there wasnt a square root i could try factoring and reducing, but with the root in there i don't know how to proceed. thanks!

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1. ParthKohli

Do you know l'hopital's rule?

2. ParthKohli

That should really be enough, in my opinion.

3. ParthKohli

Or the definition of derivative.

4. ParthKohli

Assume $$h =x + 24$$, then the limit is written as the following:$\lim_{h\to 0} \left(\sqrt{x^2 + 49} - 25 \over h\right)$

5. ParthKohli

Hmm, the definition of derivative doesn't apply here. NVM

6. cleverlikeme

surprisingly enough, we havent covered derivatives yet. or that rule

7. ParthKohli

Darn.

8. cleverlikeme

I haven't had math in years and I'm pretty lost in this class. what we have covered are the limit laws; sum, difference, constant multiple, product, quotient

9. shubhamsrg

You should rationalize the numerator. Must help.

10. ParthKohli

Yay, rationalizing helped me. Shubham, Y U NO REPLY TWO SECONDS LATER?

11. shubhamsrg

I may delete my comment if you ask for it! ;)

12. ParthKohli

13. ParthKohli

:-P

14. satellite73

try $\frac{\sqrt{x^2+49}-25}{x-24}\times \frac{\sqrt{x^2-49}+25}{\sqrt{x^2-49}+25}$

15. ParthKohli

Yes, that's what I did there. Conjugation for the win.

16. satellite73

ok that was wrong!!

17. ParthKohli

No it wasn't?

18. satellite73

$\frac{\sqrt{x^2+49}-25}{x+24}\times \frac{\sqrt{x^2+49}+25}{\sqrt{x^2+49}+25}$ is more like it

19. cleverlikeme

I tried that, which gets me $\frac{ (x^2+49)-625 }{ (x+24) * (\sqrt{x^2+49} +25) }$ Or I think it does. And I'm not sure where to go from there.

20. shubhamsrg

-49+625 = -576 = -(24^2) Does it help ?

21. cleverlikeme

yes! I'm so bad at factoring, I dont ever seem to see stuff like that

22. shubhamsrg