Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (z*+6y") a) Show that (0, 0) and (0,0) exist. dy b) Show that f is not differentiable at (0,0) by showing that f is not continuous at (0,0).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 2.3., #22)
Let f (x, y) =
G if (x, y) + (0,0) and f (0,0) = 0.
(r*+6y*)
a) Show that
(0,0) and (0,0) exist.
b) Show that f is not differentiable at (0,0) by showing that f is not continuous at (0, 0).
Transcribed Image Text:5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 2.3., #22) Let f (x, y) = G if (x, y) + (0,0) and f (0,0) = 0. (r*+6y*) a) Show that (0,0) and (0,0) exist. b) Show that f is not differentiable at (0,0) by showing that f is not continuous at (0, 0).
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