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 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!
 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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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know l'hopital's rule?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0That should really be enough, in my opinion.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Or the definition of derivative.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Assume \(h =x + 24 \), then the limit is written as the following:\[\lim_{h\to 0} \left(\sqrt{x^2 + 49}  25 \over h\right) \]

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm, the definition of derivative doesn't apply here. NVM

cleverlikeme
 2 years ago
Best ResponseYou've already chosen the best response.0surprisingly enough, we havent covered derivatives yet. or that rule

cleverlikeme
 2 years ago
Best ResponseYou've already chosen the best response.0I 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

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.4You should rationalize the numerator. Must help.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Yay, rationalizing helped me. Shubham, Y U NO REPLY TWO SECONDS LATER?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.4I may delete my comment if you ask for it! ;)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0No, you have your credit.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0try \[\frac{\sqrt{x^2+49}25}{x24}\times \frac{\sqrt{x^249}+25}{\sqrt{x^249}+25}\]

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, that's what I did there. Conjugation for the win.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0ok that was wrong!!

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\sqrt{x^2+49}25}{x+24}\times \frac{\sqrt{x^2+49}+25}{\sqrt{x^2+49}+25}\] is more like it

cleverlikeme
 2 years ago
Best ResponseYou've already chosen the best response.0I 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.

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.449+625 = 576 = (24^2) Does it help ?

cleverlikeme
 2 years ago
Best ResponseYou've already chosen the best response.0yes! I'm so bad at factoring, I dont ever seem to see stuff like that

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.4Glad to have helped! ^_^
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