xy + Let f: R2 → R where f(x, y) = 0 if (x, y) = (0,0) and f(x, y) = 72²² if (x, y) = (0,0). (a) Prove that Duf (0,0) = 0 if u = (1,0). (b) Prove that Duf(0, 0) = 0 if u = (0, 1). (c) Prove that Duf(0, 0) does not exist if u = (a, b) where ab 0. (d) Prove that Df(0, 0) does not exist (this can be done by proving that f is not continuous at (0, 0)).
xy + Let f: R2 → R where f(x, y) = 0 if (x, y) = (0,0) and f(x, y) = 72²² if (x, y) = (0,0). (a) Prove that Duf (0,0) = 0 if u = (1,0). (b) Prove that Duf(0, 0) = 0 if u = (0, 1). (c) Prove that Duf(0, 0) does not exist if u = (a, b) where ab 0. (d) Prove that Df(0, 0) does not exist (this can be done by proving that f is not continuous at (0, 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 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
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