b.

- x < xsin(1/x) < x

as x->0

lim-x = limx = 0

therefore lim xsin(1/x) = 0

limx->0 (sin(1/x) = lim x->inf sin(x) DNE

c. g(x)

d. lim [g(x)-g(0)]/[x-0] = lim xsin(1/x)/x = lim sin(1/x) DNE from b)

e. lim [h(x)-h(0)]/ [x-0] = lim x^2sin(1/x) /x = lim xsin(1/x) = 0 from b)

f.limx->inf [g(x)] = lim x->0 [sin(x)/x] = 1