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Math Help - LiMiTs

  1. #1
    Member srirahulan's Avatar
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    Lightbulb LiMiTs

    \lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}{

    \lim_{x\rightarrow0}{\frac {sin^{-1}(x)}{x}}


    How Can I solve this?I Tried a lot,and i can't get the answer.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: LiMiTs

    I should split the first limit into three limits. Then use l'Hopital's rule where necessary and for the others try to use some goniometric idenitities to simplify.
    For the second one, use l'Hopital's rule.
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  3. #3
    Member srirahulan's Avatar
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    Re: LiMiTs

    What is l'Hopital's rule ?

    Happy New Year..
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  4. #4
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    Re: LiMiTs

    Quote Originally Posted by srirahulan View Post
    \lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}

    \lim_{x\rightarrow0}{\frac {sin^{-1}(x)}{x}}

    Here is the first:
    \lim_{x\rightarrow1}{\frac{sin3x+sinx-2sin2x}{xsin^2x}}=\frac{sin(3)+sin(1)-2sin(2)}{sin^2(1)}}
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  5. #5
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    Re: LiMiTs

    For the second limit just try substitution x = sin θ Observe that as x approaches 0, θ also approaches 0
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