Question

(a) Let f: R → R be a function given by f(x₁,x2,...,xn) = x².x² ... x2, where n Σx² = 1. Show that the maximum of f(x₁, x2,...,xn) is n¹/n. k=1
(b) Prove that the improper integral dx dy ÏÏ (1 + x² + y²)³/2 -[infinity]-[infinity] converges.