1. (a) Define f: R² → R by sin(r-y) f(x, y):= if y #x, f(t, t) = 1 Vt ER. Prove that f is continuous at all points of R?. (b) Define g: R2 → R by sin(ry) r² + y2" (x, y) E R? \ {(0,0)}, g(x, y) g(0,0) = 0. %3D Prove that g is separately continuous, but not continuous, at (0,0).
1. (a) Define f: R² → R by sin(r-y) f(x, y):= if y #x, f(t, t) = 1 Vt ER. Prove that f is continuous at all points of R?. (b) Define g: R2 → R by sin(ry) r² + y2" (x, y) E R? \ {(0,0)}, g(x, y) g(0,0) = 0. %3D Prove that g is separately continuous, but not continuous, at (0,0).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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