1. ## 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.

2. ## Re: Convergent sequence question

The idea for $x=1$ is the same as the idea which solves the case $x\in (0,1)$.

3. ## Re: Convergent sequence question

Originally Posted by worc3247
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 $e^{-nx}>0~\&~n>0$.

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