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Finding limits

  1. Nov 3, 2013 #1
    1. lim θ→0 [itex]\frac{sinθ}{θ+tanθ}[/itex]

    2. Relevant equations

    lim x→0 [itex]\frac{sinx}{x}[/itex]=1

    lim x→0 [itex]\frac{cosx-1}{x}[/itex]=0

    3. The attempt at a solution

    lim θ→0 [itex]\frac{sinθ}{θ+sinθ/cosθ}[/itex]

    lim θ→0 [itex]\frac{sinθ}{(θcosθ+sinθ)/cosθ}[/itex]

    lim θ→0 sinθ × [itex]\frac{cosθ}{θcosθ+sinθ}[/itex]

    lim θ→0 [itex]\frac{θcosθ}{θcosθ+sinθ}[/itex]

    The answer is supposed to be [itex]\frac{1}{2}[/itex]. What did I do wrong?
     
  2. jcsd
  3. Nov 3, 2013 #2

    Dick

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    You haven't done anything wrong yet. You just aren't finished. Now divide numerator and denominator by θ and let θ go to zero.
     
  4. Nov 3, 2013 #3

    Student100

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    Have you covered L'Hospital's rule?
     
  5. Nov 3, 2013 #4

    Dick

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    Likely not, since the ingredients are the elementary trig limits.
     
  6. Nov 3, 2013 #5
    Not in class, but I know that it's a quick way to solve limits. Meaning the derivative of the top divided by the derivative of the bottom.
     
  7. Nov 3, 2013 #6
    I can't divide divide numerator and denominator by θ... If θ went to zero then that would make my denominator zero, which would be undefined.
     
  8. Nov 3, 2013 #7
    Nevermind, I got it! Thanks!
     
  9. Nov 3, 2013 #8

    Student100

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    Yeah, I shoulda picked up on that!

    Anyways, looks like you solved their problem Dick!
     
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