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Thread: Convergent sequence question

  1. #1
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    Convergent sequence question

    If $\displaystyle y_n(x)=nxe^{-nx^2}$ show that for every $\displaystyle x \in [0,1]$, $\displaystyle y_n\rightarrow 0$. I can show this for x=0 and x=1 but not sure for $\displaystyle x \in (0,1)$. 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 $\displaystyle x=1$ is the same as the idea which solves the case $\displaystyle x\in (0,1)$.
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    Re: Convergent sequence question

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

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