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Math Help - limits

  1. #1
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    Exclamation limits

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    Last edited by hinchcm; October 27th 2008 at 08:24 PM.
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  2. #2
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    Quote Originally Posted by hinchcm View Post
    If there is ANYONE out there who is a kind enough person to help me with this (and knows how to do it!) I would be VERY grateful!! I only have one more day to work on these problems!! Thank you so much!

    For the following functions:
    a) y = xe^(1/x)
    b) y = xe^(-x)

    I need to find:
    1) vertical and horizontal asymptotes.

    Mr F says: See main reply.

    2) relative extrema
    3) inflection points
    4) intervals where the function is increasing/decreasing
    5) where the function is concave up/down

    Mr F says: Do you know how to find dy/dx? Do you know how dy/dx relates to the above?

    Be sure to evaluate limits at the borders of the domain of the function (e.g. infinity, negative infinity, one sided limits around vertical asymptotes...)
    For y = x e^{1/x} note that:

    \lim_{x \rightarrow 0^+} x e^{1/x} = + \infty.

    \lim_{x \rightarrow 0^-} x e^{1/x} = 0.

    \lim_{x \rightarrow +\infty} x e^{1/x} = + \infty.

    \lim_{x \rightarrow -\infty} x e^{1/x} = -\infty.

    Note: x e^{1/x} = x \left( 1 + \frac{1}{x} + \frac{1}{2} \frac{1}{x^2} + \, .....\right)
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