Limit as x approaches infinity of xsin(1/x)?

[nouras]

i know it is 1 but, i dont know how to get there..

 

[Depressed]

lim x --> inf (xsin(1/x))
lim x --> inf (sin(1/x)/ 1/x)
lim x --> inf ((-1/x^2)cos(1/x)/ -1/x^2)
lim x ---> inf (cos(1/x))

cos(1/infinity) ~ cos(0) = 1

 

[supastremph]

xsin(1/x) = sin(1/x)/(1/x)

by l'hopital's rule: lim = lim cos(1/x)ln(x)/lnx = lim cos(1/x) = 1, since cos(0) =1.