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Homework Help: Find the limit of (sqrt(1+2x) - sqrt(1+3x))/(x + 2x^2) as x->0

  1. Nov 13, 2006 #1

    kreil

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    I'm having a lot of trouble making any progress on this limit. If someone could give me a direction to get started I would appreciate it.

    [tex]\lim_{x{\rightarrow}0}\frac{\sqrt{1+2x}-\sqrt{1+3x}}{x+2x^2}[/tex]
     
  2. jcsd
  3. Nov 13, 2006 #2
    Use L'Hopitals Rule.
     
  4. Nov 13, 2006 #3

    StatusX

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    Or you could multiply by the conjugate of the numerator. (ie, sqrt(1+2x)+sqrt(1+3x)).
     
  5. Nov 13, 2006 #4

    JasonRox

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    Go with StatusX's advice if L'Hopitals Rule wasn't taught yet because then it wouldn't be appropriate.

    If you haven't learned L'Hopitals Rule, I recommend to learn it and use it to check your answer

    Also, you can always test it numerically. I do that sometimes just to be 100% certain. I would try something like x=0.01, 0.001 and 0.0001.
     
  6. Nov 13, 2006 #5
    As stated above, L'Hopital's rule, or, if that's not allowed, rationalize the numerator.
     
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