Question

Evaluate
$\underset{x\to \infty }{lim}{2}^{-x}\sin \left(2^x\right)$.

Answer 1

$\underset{x\to \infty }{lim}{2}^{-x}\sin \left(2^x\right)$
$=\underset{x\to \infty }{lim}\frac{\sin \left(2^x\right)}{2^x}$
[Let, $z=2^{-x}$ and as $x\to \infty \Rightarrow z\to 0$.]
$=\underset{z\to 0}{lim}z\sin \left(\frac{1}{z}\right)$
$=0$.