Question

Find the positive integers k for which
lim ->0 sin(sin(x))/x^k

exists, and then find the value the limit.
(hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find the limit in these cases as well)

I did this for the first one
lim x->0 sin(sinx))/x^0=0

then idk how to do the other ones

Answer 1

k=1 limit sinx/x=1
k=2 limit sinx/x *1/x= undefined
and so on.

Answer 2

for k=2 lim x->0 sin(sin(x))/x^2= error
so undefined So do I have to do sided limits? how?