Question

lim x-->infinity (xsin(1/x))

Answer 1

\[\lim_{x \rightarrow \infty} xsin(1/x)\]

Answer 2

\[\lim_{x \rightarrow \infty} (xsin(1/x))\]
\[=\lim_{x \rightarrow \infty} sin(1/x)/(1/x)\]
x goes to infinity = 1/x goes to 0

We know \[\lim_{x \rightarrow 0} sin (x)/x=1\]
Therfore, the answer is 1.

Answer 3

thx