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cleverlikeme
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!
Do you know l'hopital's rule?
That should really be enough, in my opinion.
Or the definition of derivative.
Assume \(h =x + 24 \), then the limit is written as the following:\[\lim_{h\to 0} \left(\sqrt{x^2 + 49} - 25 \over h\right) \]
Hmm, the definition of derivative doesn't apply here. NVM
surprisingly enough, we havent covered derivatives yet. or that rule
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
You should rationalize the numerator. Must help.
Yay, rationalizing helped me. Shubham, Y U NO REPLY TWO SECONDS LATER?
I may delete my comment if you ask for it! ;)
No, you have your credit.
try \[\frac{\sqrt{x^2+49}-25}{x-24}\times \frac{\sqrt{x^2-49}+25}{\sqrt{x^2-49}+25}\]
Yes, that's what I did there. Conjugation for the win.
\[\frac{\sqrt{x^2+49}-25}{x+24}\times \frac{\sqrt{x^2+49}+25}{\sqrt{x^2+49}+25}\] is more like it
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.
-49+625 = -576 = -(24^2) Does it help ?
yes! I'm so bad at factoring, I dont ever seem to see stuff like that
Glad to have helped! ^_^