1) Let f(x)=x^2 sin(1/x^2) for x not equal to 0 and f(0)=0.

a)Show a is differentiable on R2) Let f(x)=x^2 if x is rational and f(x)=0 if x is irrational.

b)Show that f ' is not bounded on the interval [-1,1].

a)Prove that f is continuous at exactly one point, namely at x=0

b)Prove that f is differentiable at exactly one point, namely at x=0.