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Math Help - Limit Problem

  1. #1
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    Limit Problem

    We are working on indeterminates. The problem is finding the limit (x-tanx)/x^3 as x approaches 0. We have been using L'Hopital's so I'd assume that's the key. The calculator indicates a limit of infinity but I can't show it. Can anybody help me figure out how to do it?
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  2. #2
    Super Member Random Variable's Avatar
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    The limit is  - \frac{1}{3}

     \lim_{x \to 0} \frac{ x - \tan x}{x^3} = \lim_{x \to 0} \frac{ 1 - \sec^{2} x}{3x^{2}} = \lim_{x \to 0} \frac{ -2 \tan x \sec^{2} x}{6x}=  \lim_{x \to 0} \frac{-2 \sec^{4} x - 4 \tan^{2} x \sec^{2} x}{6} = -\frac{2}{6} = -\frac {1}{3}
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  3. #3
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    Ah I see! Thank you!
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