Feb 19, 2009 #1 N nouras New member Feb 18, 2009 4 0 1 i know it is 1 but, i dont know how to get there..
Feb 19, 2009 #2 D Depressed New member Nov 23, 2008 12 0 1 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
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
Feb 19, 2009 #3 S supastremph New member Feb 19, 2009 3 0 1 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.
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.