Help me please Q4. Letif (x, y) # (0,0),f(x, y) =x² + y²if (x, y) = (0,0).(a) Using the definition of the directional derivative, find Daf(0, 0) where ū = (u1, u2) is anarbitrary unit vector.(b) Using your result from (a), find Vf(0,0).(c) By finding an appropriate unit vector ū, show that the equationDāf(0, 0) = Vf(0, 0) · ūfails for this f.

Given function is fx,y=x2yx2+y2 if x,y≠0,00 if x,y=0,0 Let u=u1,u2 is an…

Q4. Let x²y f(x, y) = x² + y² 0 if (x, y) ‡ (0, 0), if (x, y) = (0,0). (a) Using the definition of the directional derivative, find Düƒ(0, 0) where ū = (u₁, u2) is an arbitrary unit vector. (b) Using your result from (a), find Vƒ(0,0). (c) By finding an appropriate unit vector ū, show that the equation Daf(0,0) = ▼f(0,0).

Q4. Let x²y f(x, y) = x² + y² 0 if (x, y) ‡ (0, 0), if (x, y) = (0,0). (a) Using the definition of the directional derivative, find Düƒ(0, 0) where ū = (u₁, u2) is an arbitrary unit vector. (b) Using your result from (a), find Vƒ(0,0). (c) By finding an appropriate unit vector ū, show that the equation Daf(0,0) = ▼f(0,0).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Help me please

Q4. Let
if (x, y) # (0,0),
f(x, y) =
x² + y²
if (x, y) = (0,0).
(a) Using the definition of the directional derivative, find Daf(0, 0) where ū = (u1, u2) is an
arbitrary unit vector.
(b) Using your result from (a), find Vf(0,0).
(c) By finding an appropriate unit vector ū, show that the equation
Dāf(0, 0) = Vf(0, 0) · ū
fails for this f.

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