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Let f: R2R where f(x, y) = x² + y² if both x and y are rational and f(x, y) = 0 otherwise. Prove that Df(0, 0) exists. Note: Df(c) only exists at c = (0,0) and f is continuous only at (0,0).

Let f: R2R where f(x, y) = x² + y² if both x and y are rational and f(x, y) = 0 otherwise. Prove that Df(0, 0) exists. Note: Df(c) only exists at c = (0,0) and f is continuous only at (0,0).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Real Analysis II
3. Let f: R²R where f(x, y) = x² + y² if both x and y are rational and f(x,y) = 0 otherwise. Prove that Df(0, 0) exists. Note: Df(c) only exists at c = (0,0) and f is continuous only at (0,0).
Transcribed Image Text:3. Let f: R²R where f(x, y) = x² + y² if both x and y are rational and f(x,y) = 0 otherwise. Prove that Df(0, 0) exists. Note: Df(c) only exists at c = (0,0) and f is continuous only at (0,0).
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