Graph and discuss the continuity of the function

(a) Show that f (x, y) → 0 as (x, y) → (0, 0) along any path through (0, 0) of the form y = mx^a with 0 < a < 4.
(b) Despite part (a), show that f is discontinuous at (0, 0).
(c) Show that f is discontinuous on two entire curves.

Transcribed Image Text:

sin xy f(х, у) — if ху %# 0 if ху — 0 ху