1. (30pts) Let us consider a function f (t, y). (a) Find the (1D) Taylor series of f (t, y) near t = to up to order 3. (b) Find the (1D) Taylor series of f (t, y) near y = yo up to order 3. (c) Find the (2D) Taylor series of f (t, y) near t = to and y = yo up to order 3. (d) Find the (2D) Taylor series near { = 0 and y = 0 up to order 2 of f (t, y) = sin(t) (y> + 2y + 3) -4