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Math Help - Evaluating limits

  1. #1
    Junior Member Cyberman86's Avatar
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    Evaluating limits

    I got stuck on this two, they don't look that bad but they are using Sin and i don't know exactly what to do.

    lim (sin (3x) ) / over X
    x->0

    -------------------------------------------------------------

    lim -2 / over sin (x)
    x->0

    as x approaches zero from the right
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  2. #2
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    Quote Originally Posted by Cyberman86 View Post
    I got stuck on this two, they don't look that bad but they are using Sin and i don't know exactly what to do.

    lim (sin (3x) ) / over X
    x->0

    [snip]
     = 3 \lim_{x \rightarrow 0}\frac{\sin (3x)}{3x}.

    You know \lim_{t \rightarrow 0} \frac{\sin (t)}{t} = 1, right?
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  3. #3
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    Quote Originally Posted by Cyberman86 View Post
    [snip]
    lim -2 / over sin (x)
    x->0

    as x approaches zero from the right
    This is very sloppy but makes the point: \frac{-2}{0^+} = - \infty
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