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Math Help - Need Calculus I Help!!!!

  1. #1
    shopgirl
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    Need Calculus I Help!!!!

    I need help asap with a cal I question dealing with limits.
    The question:

    lim (1-cos sqrt(x)) / x
    x->0

    Please explain how its worked out....thanks in advance...
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shopgirl View Post
    I need help asap with a cal I question dealing with limits.
    The question:

    lim (1-cos sqrt(x)) / x
    x->0

    Please explain how its worked out....thanks in advance...
    this limit goes to 0/0, you can apply L'Hopital's rule, which basically says: \lim \frac {f(x)}{g(x)} = \lim \frac {f'(x)}{g'(x)}
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    I hate L'H˘pital (unless the limit be very messy)

    Rewrite the limit as follows

    \lim_{x\to0}\frac{1-\cos\sqrt x}x=\lim_{x\to0}\frac{\sin^2\sqrt x}{x(1+\cos\sqrt x)}=\lim_{x\to0}\left[\left(\frac{\sin\sqrt x}{\sqrt x}\right)^2\cdot\frac1{1+\cos\sqrt x}\right]

    Does that make sense?
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