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Math Help - I'Hopital's rule

  1. #1
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    I'Hopital's rule

    Use I'Hopital's rule to find the limit of the sequence
    Attached Thumbnails Attached Thumbnails I'Hopital's rule-208a3q9.jpg  
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  2. #2
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    That is overkilling it.

    n\sin \frac{1}{n} = \frac{\sin \frac{1}{n}}{\frac{1}{n}}.
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  3. #3
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    thanks for your prompt answer, but how did pie get in?
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  4. #4
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    Hello,

    Quote Originally Posted by al1850 View Post
    thanks for your prompt answer, but how did pie get in?
    Where do you see any pie ?
    Or any \pi ?
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  5. #5
    Super Member flyingsquirrel's Avatar
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    Hi

    Maybe in the ThePerfectHacker's signature ?
    \boxed{ -\sin \frac{\pi}{7} + \sin \frac{2\pi}{7} + \sin \frac{3\pi}{7} + \sin \frac{4\pi}{7}+\sin \frac{5\pi}{7} - \sin \frac{6\pi}{7} = \sqrt{7} }<br />
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  6. #6
    Moo
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    Haha ! That's funny
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  7. #7
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    oh man, that's your signature? I thought that was the answer to the I'Hopital's rule question. lol
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  8. #8
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    So is (sin 1/n)/(1/n) the answer?
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  9. #9
    Super Member wingless's Avatar
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    \lim_{n\to\infty}\frac{\sin\frac{1}{n}}{\frac{1}{n  }}

    Substitute a=\frac{1}{n}.
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  10. #10
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    And remember the definition of the derivative :

    \lim_{x \to x_0} \frac{f(x)-f(x_0)}{x-x_0}=f'(x_0)

    Here, f(x)=\sin(x)

    Take x_0=0

    Or else, apply l'HŰpital's rule
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