be de by 8
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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Question
Please solve all part's correctly
![Q1. Let f: R² !R be defined by
8
x³ + y3
x2 + y2
if (x, y) = (0, 0)
f(x, y) =
if (x, y) = (0, 0).
(a) Is f continuous at (0, 0)? Explain.
(b) Find fx(x, y) and fy(x, y) for all (x, y) 2 R2 (including (0, 0)). [Hint: Youmay use
symmetry to determine fy after calculating f.]
(c) Find the gradient vector rf (0, 0).
(d) Find the directional derivative Duf(0, 0) where = (u1, u2) is an arbitrary
unit vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fc645d9-fbc6-4432-a57e-08858a956f29%2Fb265aa95-afdd-4bd7-be24-e5c178e448ff%2F54oqmu6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. Let f: R² !R be defined by
8
x³ + y3
x2 + y2
if (x, y) = (0, 0)
f(x, y) =
if (x, y) = (0, 0).
(a) Is f continuous at (0, 0)? Explain.
(b) Find fx(x, y) and fy(x, y) for all (x, y) 2 R2 (including (0, 0)). [Hint: Youmay use
symmetry to determine fy after calculating f.]
(c) Find the gradient vector rf (0, 0).
(d) Find the directional derivative Duf(0, 0) where = (u1, u2) is an arbitrary
unit vector.
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