Suppose f is defined on R and lim y->1 f(y) = 2. Prove lim x->0 f(1 + 2 sin(x^3)) = 2 by using the formal epsilon-delta definition of the limit and continuity. Don't use any of the limit laws or other theorems. Hint: note that 1 + 2 sin(x^3) is continuous at 0.

Suppose f is defined on R and lim f(y) = 2. Prove lim f(1 + 2 sin(x3)) = 2 by using the formal y -+ 1 epsilon-delta definition of the limit and continuity. Don't use any of the limit laws or other theorems. Hint: note that 1 + 2 sin(23) is continuous at 0