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(c) Let z(x, y) = xr be a function defined on a disk D in the positive quadrant containing the point (1,2). Prove whether z(x, y) satisfies the Clairaut Theorem at (1,2).

(c) Let z(x, y) = xr be a function defined on a disk D in the positive quadrant containing the point (1,2). Prove whether z(x, y) satisfies the Clairaut Theorem at (1,2).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
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please help with (c)
(b) Show that the function defined by ay if (x, y) = (0,0), √x²+y² f(x, y) = { 0 if (x, y) = (0,0) is not differentiable at point (0, 0). (c) Let z(x, y) = x be a function defined on a disk D in the positive quadrant containing the point (1,2). Prove whether z(x, y) satisfies the Clairaut Theorem at (1,2).
Transcribed Image Text:(b) Show that the function defined by ay if (x, y) = (0,0), √x²+y² f(x, y) = { 0 if (x, y) = (0,0) is not differentiable at point (0, 0). (c) Let z(x, y) = x be a function defined on a disk D in the positive quadrant containing the point (1,2). Prove whether z(x, y) satisfies the Clairaut Theorem at (1,2).
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