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Math Help - Limit of arctan and e

  1. #1
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    Limit of arctan and e

    Hello,

    This is my first post on this forum . I can't seem to decide what the limit of this relatively simple equation is:

    lim x approaches minus infinity of [arctan(e^-x)]

    Any help is greatly appreciated!

    Darren
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  2. #2
    Member Abu-Khalil's Avatar
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    Let t=-x so when x\to-\infty,t\to\infty and then \lim_{x\to -\infty}\arctan\left(e^{-x}\right)=\lim_{t\to\infty}\arctan\left(e^t\right), but \arctan(x) and e^x are continuos functions in \mathbb{R} so we can rewrite the limit as \arctan\left\{\exp\left(\lim_{t\to\infty}t\right)\  right\}=\arctan \left(\infty\right)=\frac{\pi}{2}.
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  3. #3
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    Thanks for the excellent response. It was a bit more involved than I thought. It makes perfect sense now.

    Darren
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