1. True or False. Determine whether the following statements are true or false. If it is true, provide a brief explanation or proof. If it is false explain why or give a counterexample. a. If f(x, y) =√1-x2 y2, then Duf (0,0) = 0 for any unit vector u. b. If f(x, y)=x+y, then-1 ≤ Duf(x, y) ≤ 1 for any unit vector u. c. If Duf (x, y) exists, then Duf(x, y) = -Duf (x, y) for any unit vector u.

1. True or False. Determine whether the following statements are true or false. If it is true, provide a brief explanation or proof. If it is false explain why or give a counterexample. a. If f(x, y) =√1-x2 y2, then Duf (0,0) = 0 for any unit vector u. b. If f(x, y)=x+y, then-1 ≤ Duf(x, y) ≤ 1 for any unit vector u. c. If Duf (x, y) exists, then Duf(x, y) = -Duf (x, y) for any unit vector u.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 31E

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