4 (a) Consider the function f(x, y) = (y + 1) (x + cos x). i. Find the partial derivatives af af a²fa²f a² f and дх’ ду’ дх2' дхду dy²

ii. Find the Taylor Series for f(x, y) about the point x = 0, y = 0. iii. Find the Taylor Series for f(x, y) about the point x = π 2 (b) The function g(x, y) = 4 X has a first-order Taylor Series of g(x, y)≈1-(x − 1) + (y − 1) + ... which can also be written as y = 1. [3,2,3 marks] g(x, y) 1+ y - x With justification, explain which form is more useful for approximating g(x, y) in the vicinity of x = 1, y = 1. [2 marks]