Question 775765
{{{-1<=sin(1/x)<=1}}} for all {{{x<>0}}}
or
{{{abs(sin(1/x))<=1}}} for all {{{x<>0}}}
multiplying both sides times {{{abs(x)}}} we get
{{{abs(x*sin(1/x))=abs(x)*abs(sin(1/x))<=abs(x)}}}
Since
{{{system(lim( x->0, (x) )=0,abs(x*sin(1/x))<=abs(x))}}}
then
{{{lim( x->0, (x*sin(1/x)) )=0}}}