Convergent sequence question

**worc3247** · October 10th 2011, 01:44 PM

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.

**girdav** · October 10th 2011, 02:02 PM

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

**Plato** · October 10th 2011, 02:02 PM

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.