1. ## Prove (Limit)

Can someone help me prove this?

sqrt(x)e^sin(pi/x) = 0 , x--> 0+ (from the right)

2. Originally Posted by l flipboi l
Can someone help me prove this?

sqrt(x)e^sin(pi/x) = 0 , x--> 0+ (from the right)
$\left|\sqrt{x}e^{\sin\left(\frac{\pi}{x}\right)}\r ight|\leqslant e\sqrt{x}$

3. $sin(\pi/x)$ lies between -1 and 1 for all x so $e^{sin(\pi/x)}$ lies between $e^{-1}$ and $e^1$ for all x. The important point is that it is bounded. Since $\sqrt{x}$ goes to 0, the limit of this function is 0.