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Math Help - Convergent sequence question

  1. #1
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    Convergent sequence question

    If y_n(x)=nxe^{-nx^2} show that for every x \in [0,1], y_n\rightarrow 0. I can show this for x=0 and x=1 but not sure for x \in (0,1). Help much appreciated.
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  2. #2
    Super Member girdav's Avatar
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    Re: Convergent sequence question

    The idea for x=1 is the same as the idea which solves the case x\in (0,1).
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    Re: Convergent sequence question

    Quote Originally Posted by worc3247 View Post
    If y_n(x)=nxe^{-nx^2} show that for every x \in [0,1], y_n\rightarrow 0. I can show this for x=0 and x=1 but not sure for x \in (0,1). Help much appreciated.
    You know that for all x we have e^{-nx}>0~\&~n>0.

    If 0<x<1 then 0<nxe^{-nx}<ne^{-nx}.
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