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Math Help - Limit as x approaches 0

  1. #1
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    Limit as x approaches 0

    possibly L'Hopital & FTC
    Attached Thumbnails Attached Thumbnails Limit as x approaches 0-intggg.jpg  
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  2. #2
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    Exactly.

    If you apply L'Hospital's Rule and FTC, you will get:

    \frac{1}{3} \, \lim_{x\to 0} \dfrac{ \dfrac{sin(x)}{x} - 1 }{x^2}

    so ?
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  3. #3
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    Quote Originally Posted by General View Post
    Exactly.

    If you apply L'Hospital's Rule and FTC, you will get:

    \frac{1}{3} \, \lim_{x\to 0} \dfrac{ \dfrac{sin(x)}{x} - 1 }{x^2}

    so ?
    Does Si = Sin?
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  4. #4
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    No.
    Why did you ask that ?
    By the FTC:

    \frac{d}{dx} \left( \int_0^x f(t) \, dt \right) = f(x) ..
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  5. #5
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    Quote Originally Posted by General View Post
    Exactly.

    If you apply L'Hospital's Rule and FTC, you will get:

    \frac{1}{3} \, \lim_{x\to 0} \dfrac{ \dfrac{sin(x)}{x} - 1 }{x^2}

    so ?

    Do we have to do L'Hopital again? Since sinx/x =1
    and then subtracting 1 gets you 0. so 0/0 ?

    or is the limit just 0?
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  6. #6
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    Quote Originally Posted by UC151CPR View Post
    Do we have to do L'Hopital again? Since sinx/x =1
    and then subtracting 1 gets you 0. so 0/0 ?

    or is the limit just 0?

    Its still 0/0 not 0 ..

    We need to use L'Hospital's Rule two times again to evaluate the limit ..
    Or we can use the infinite series to evaluate it ..
    Your final answer should be \frac{-1}{18} ..
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