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Math Help - Trig limits

  1. #1
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    Trig limits

    I know that csc is 1/sin.

    Would i do 3/6(1/sin)(3x)?

    Please show me the correct steps if i'm wrong. Wouldn't it just be 0/0 and become DNE?
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  2. #2
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    Re: Trig limits

    Quote Originally Posted by ritacame View Post


    I know that csc is 1/sin.

    Would i do 3/6(1/sin)(3x)?

    Please show me the correct steps if i'm wrong.
    note ...

    \frac{3}{6x \csc(3x)} = \frac{3 \sin(3x)}{6x} = \frac{3}{2} \cdot \frac{\sin(3x)}{3x}
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  3. #3
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    Re: Trig limits

    That means the answer would be 3/2 if one followed those steps. Thank You!
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  4. #4
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    Re: Trig limits

    Rewrite:
    \lim_{x\to 0} \frac{3}{6x\csc(3x)}=\lim_{x\to 0} \frac{3}{\frac{6x}{\sin(3x)}}=\lim_{x\to 0}\frac{3\sin(3x)}{6x}

    Use the fact:
    \lim_{x\to 0} \frac{\sin(x)}{x}=1

    And yes \frac{3}{2} is correct.
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