Evaluating the limit: $\lim _{x\to \infty }\left(2^x\sin\left(\frac{b}{2^x}\right)\right)$ I need to find the following limit :
$$\lim_{x\to \infty}\left(2^x\cdot \sin\left(\frac{b}{2^x}\right)\right)$$
I have tried it but I keep getting stuck, so any help would be helpful!
Thank you!

HINT:
$$\lim_{x\to\infty}2^x\sin\left(\frac{b}{2^x}\right)=\lim_{x\to\infty}b\frac{\sin(\frac{b}{2^x})}{\frac{b}{2^x}}$$
