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So I'm having trouble with the following limit:

$$\lim_{x\to2}{\frac{x^2-x-2}{\sqrt{x^2+5}-3}}$$

Common factor doesn't work. Any hints on how to tackle it?

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L'Hôpital's rule –  user22805 Sep 20 '12 at 4:47
    
Do you know how to differentiate the denominator? If so, you can apply L'hopital's Rule. –  Owen Biesel Sep 20 '12 at 4:48

2 Answers 2

up vote 8 down vote accepted

Hint:

  1. How about multiplying numerator and denominator by $\sqrt{x^2+5} +3$
  2. Can you then factor numerator and denominator and see any factors that cancel?
  3. You should be able to take it from there.

Make sense?

~A

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Thanks! I did an identical exercise this morning, I can't believe how I missed the conjugate!. –  Julián Sep 20 '12 at 4:54
    
Excellent! I would also suggest trying it using the definition of limits and see if you can work through it. –  Amzoti Sep 20 '12 at 4:55

Hint: Try using L'Hopital's rule

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I don't know it yet –  Julián Sep 20 '12 at 4:50
    
Ahh then Amzoti's answer is the way to go :) –  Noah Klein Sep 20 '12 at 4:56

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