Question

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!

Answer 1

Do you know l'hopital's rule?

Answer 2

That should really be enough, in my opinion.

Answer 3

Or the definition of derivative.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Darn.

Answer 8

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

Answer 9

You should rationalize the numerator. Must help.

Answer 10

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

Answer 11

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

Answer 12

No, you have your credit.

Answer 13

:-P

Answer 14

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

Answer 15

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

Answer 16

ok that was wrong!!

Answer 17

No it wasn't?

Answer 18

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

Answer 19

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.

Answer 20

-49+625 = -576 = -(24^2)

Does it help ?

Answer 21

yes!

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

Answer 22

Glad to have helped! ^_^