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Math Help - Limit question, Please help

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    Limit question, Please help

    limit(x->infinity) (sin(2 x))/(x+sin(x))Please show workThanks in advance
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    Re: Limit question, Please help

    Quote Originally Posted by nubshat View Post
    limit(x->infinity) (sin(2 x))/(x+sin(x))Please show workThanks in advance
    Note that for all x greater then 1

    x-1 \le x+\sin(x) \le x+1 \iff \frac{1}{x+1} \le \frac{1}{x+\sin(x)} \le \frac{1}{x-1}

    and note that -1 \le \sin(2x) \le 1

    Putting these two facts together gives

     \frac{-1}{x+1} \le \frac{\sin(2x)}{x+\sin(x)} \le \frac{1}{x-1}

    Now what happens as you take the limit?
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