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Thread: Help with trig limit

  1. #1
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    Help with trig limit

    Can anyone show me how the limit of \frac{sin 5x}{x} as x goes to 0 equals 5?

    I'm only supposed to use the fact that \frac{sin x}{x} goes to 1 as x goes to 0.

    Any tips?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by paupsers View Post
    Can anyone show me how the limit of \frac{sin 5x}{x} as x goes to 0 equals 5?

    I'm only supposed to use the fact that \frac{sin x}{x} goes to 1 as x goes to 0.

    Any tips?
    If we let z=5x then our limit becomes \lim_{z\to0}\frac{\sin(z)}{\tfrac{z}{5}}........so
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