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Math Help - Finding this limit

  1. #1
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    Finding this limit

    Im just not able to wrap my head around how to find this limit:

    lim [arctan(x)] -x
    x-> 0 --------------
    x^3
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by trigoon View Post
    Im just not able to wrap my head around how to find this limit:

    lim [arctan(x)] -x
    x-> 0 --------------
    x^3
    What level of math are you at? Do you know L'hopital's?

    You could also use maclaurin series

    \begin{aligned}\lim_{x\to{0}}\frac{\arctan(x)-x}{x^3}&=\lim_{x\to{0}}\frac{x-\frac{x^3}{3}+\cdots-x}{x^3}\\<br />
&=\lim_{x\to{0}}\frac{\frac{-x^3}{3}+\cdots}{x^3}\\<br />
&=\frac{-1}{3}\end{aligned}
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