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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!

  • one year ago
  • one year ago

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  1. ParthKohli
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    Do you know l'hopital's rule?

    • one year ago
  2. ParthKohli
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    That should really be enough, in my opinion.

    • one year ago
  3. ParthKohli
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    Or the definition of derivative.

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

    • one year ago
  5. ParthKohli
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    Hmm, the definition of derivative doesn't apply here. NVM

    • one year ago
  6. cleverlikeme
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    surprisingly enough, we havent covered derivatives yet. or that rule

    • one year ago
  7. ParthKohli
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    Darn.

    • one year ago
  8. cleverlikeme
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    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

    • one year ago
  9. shubhamsrg
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    You should rationalize the numerator. Must help.

    • one year ago
  10. ParthKohli
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    Yay, rationalizing helped me. Shubham, Y U NO REPLY TWO SECONDS LATER?

    • one year ago
  11. shubhamsrg
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    I may delete my comment if you ask for it! ;)

    • one year ago
  12. ParthKohli
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    No, you have your credit.

    • one year ago
  13. ParthKohli
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    :-P

    • one year ago
  14. satellite73
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    try \[\frac{\sqrt{x^2+49}-25}{x-24}\times \frac{\sqrt{x^2-49}+25}{\sqrt{x^2-49}+25}\]

    • one year ago
  15. ParthKohli
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    Yes, that's what I did there. Conjugation for the win.

    • one year ago
  16. satellite73
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    ok that was wrong!!

    • one year ago
  17. ParthKohli
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    No it wasn't?

    • one year ago
  18. satellite73
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    \[\frac{\sqrt{x^2+49}-25}{x+24}\times \frac{\sqrt{x^2+49}+25}{\sqrt{x^2+49}+25}\] is more like it

    • one year ago
  19. cleverlikeme
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    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.

    • one year ago
  20. shubhamsrg
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    -49+625 = -576 = -(24^2) Does it help ?

    • one year ago
  21. cleverlikeme
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    yes! I'm so bad at factoring, I dont ever seem to see stuff like that

    • one year ago
  22. shubhamsrg
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    Glad to have helped! ^_^

    • one year ago
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