cleverlikeme Group Title 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! one year ago one year ago

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1. ParthKohli Group Title

Do you know l'hopital's rule?

2. ParthKohli Group Title

That should really be enough, in my opinion.

3. ParthKohli Group Title

Or the definition of derivative.

4. ParthKohli Group Title

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 Group Title

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

6. cleverlikeme Group Title

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

7. ParthKohli Group Title

Darn.

8. cleverlikeme Group Title

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 Group Title

You should rationalize the numerator. Must help.

10. ParthKohli Group Title

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

11. shubhamsrg Group Title

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

12. ParthKohli Group Title

13. ParthKohli Group Title

:-P

14. satellite73 Group Title

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

15. ParthKohli Group Title

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

16. satellite73 Group Title

ok that was wrong!!

17. ParthKohli Group Title

No it wasn't?

18. satellite73 Group Title

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

19. cleverlikeme Group Title

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 Group Title

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

21. cleverlikeme Group Title

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

22. shubhamsrg Group Title