6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7. Let the function f : R² →→ R defined as follows xy² + 2x²y x² + 4y² 0 f(x, y) = (a) Calculate the partial derivatives (b) Show that: af dx si (x, y) = (0,0) si (x, y) = (0,0). af Əx (0,0) = 0 et 8 Let the function f R² (c) Show with the definition & - ō that: (x, y) ду and R be defined by af ду -(x, y) ,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 0.
6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7. Let the function f : R² →→ R defined as follows xy² + 2x²y x² + 4y² 0 f(x, y) = (a) Calculate the partial derivatives (b) Show that: af dx si (x, y) = (0,0) si (x, y) = (0,0). af Əx (0,0) = 0 et 8 Let the function f R² (c) Show with the definition & - ō that: (x, y) ду and R be defined by af ду -(x, y) ,0) = 0. lim (x,y) →(0,0) has a point (x, y) not= (0, 0). f(x, y) = 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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 15E
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