Problem. Let if x + 0 f (x) 2²+y? if x = 0 (1) Show that f, Dif, and D2f are continuous on R?. WHAT THIS MEANS YOU MUST D0 (a) Show lim f (x) = f (0) (b) Compute (Dif) (x) and (D2f) (x) for x + 0...

Solve Problem 4.6.1

Extracted text: Problem. Let if x + 0 f (x) 2²+y? if x = 0 (1) Show that f, Dif, and D2f are continuous on R?. WHAT THIS MEANS YOU MUST D0 (a) Show lim f (x) = f (0) (b) Compute (Dif) (x) and (D2f) (x) for x + 0 using Calc3 methods. Briefly argue that these are continuous for x + 0. (c) Compute (Dif) (0) and (D2f)(0) using limits. (d) Complete the following chart [? if x +0 (Dif) (x) if x = 0 (Da £) (x) = ? if x + 0