ISI PROBLEM

[tania]

Q- Let f(x)=xsin(1/x) for x>0. Then,

1- f is unbounded
2- f is bounded but lim x->0 f(x) dent exist
3- lim x->infinity f(x)=1
4 - lim x->infinity f(x)=o

PLEASE explain the answer.

Thanks.

[Vidit Chaudhary]

f(x)= sin(1/x)/(1/x)
for x--> infinity, f(x)= 1

Also f(x) is bounded between y=x & y=(-x)
 -1<sin(1/x)<1
 -x<xsin(1/x)<x

option 3 should be the right choice.

[onionknight]

C and the explanation by vidit looks perfect. Alternatively, you can use L'Hôpital's rule to determine the limit.