limit of x sin( 1/x ) as x approaches infinity
Replace with u = 1/x, x = 1/u
As x approaches infinity, u approaches zero
limit of x sin( 1/x ) as x approaches infinity =
limit of ( 1/u )( sin( u ) ) as u approaches zero
By definition,
http://en.wikipedia.org/wiki/Sine#Sine
sin( u ) = u -...