If

r>0

is a rational number, let

f:R->R

be defined by

f(x):=x^(r)sin((1)/(x))

for

x!=0

, and\

f(0):=0

. Determine those values of

r

for which

f^(')(0)

exists.

2. If r>0 is a rational number, let f:RR be defined by f(x):=xrsin(1/x) for x=0, and f(0):=0. Determine those values of r for which f(0) exists