Exercise 4. Prove the following claims. (i) Let f: R² →→ R be defined as f(x, y) := { 3 xy x² + y² Show that f is continuous at (0,0). HINT: Recall that x² + y² ≥ 2x||y|. (ii) Let g : R² → R be defined as xy³ (x² + y²)² 0 if xy # 0 if xy = 0. g(x, y) := Show that g is not continuous at (0,0). if xy # 0 if xy = 0.

Exercise 4. Prove the following claims. (i) Let f: R² →→ R be defined as f(x, y) := { 3 xy x² + y² Show that f is continuous at (0,0). HINT: Recall that x² + y² ≥ 2x||y|. (ii) Let g : R² → R be defined as xy³ (x² + y²)² 0 if xy # 0 if xy = 0. g(x, y) := Show that g is not continuous at (0,0). if xy # 0 if xy = 0.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 48E

See similar textbooks