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

  • Thread starter kreil
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  • #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]
 

Answers and Replies

  • #2
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Use L'Hopitals Rule.
 
  • #3
StatusX
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Or you could multiply by the conjugate of the numerator. (ie, sqrt(1+2x)+sqrt(1+3x)).
 
  • #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.
 
  • #5
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As stated above, L'Hopital's rule, or, if that's not allowed, rationalize the numerator.
 

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