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Math Help - Trigonometric Limit problem

  1. #1
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    Trigonometric Limit problem

    I am taking a college level Calculus class that involves trignometry, but I haven't taken trig for over 10 years. Please help if you can.

    I need to find the limit of the following equation (or a helpful explanation of how I can find it).

    (x - tan 2x)/(sin 2x) as x approaches 0

    Thank you for your help!
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  2. #2
    Super Member wingless's Avatar
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    \lim_{x \to 0}\frac{x-\tan 2x}{\sin 2x}

    Taking x=0 gives \frac{0}{0}

    So we have to simplify it.

    \lim_{x \to 0}\frac{x}{\sin 2x}-\frac{\tan 2x}{\sin 2x}

    \lim_{x \to 0}\frac{1}{2}\cdot\frac{1}{\frac{\sin 2x}{2x}}-\frac{\frac{\sin 2x}{\cos 2x}}{\sin 2x}

    You should know that \lim_{x\to 0} \frac{\sin x}{x} = 1. Same goes for 2x, \lim_{x\to 0} \frac{\sin 2x}{2x} = 1.

    \lim_{x \to 0} \frac{1}{2}\cdot\frac{1}{1}-\frac{1}{\cos 2x}

    \frac{1}{2} - 1 = -\frac{1}{2}
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