5. Let f: R² → R, f(x, y) = x²y, c = (1, 1), and u = (1,1). Find Duf(c) and prove your answer with the e-d definition of Duf(c). Hint (optional): Fix € > 0 and choose d = min{1, €/4}. Duf (c) if Review of Definition: Lu Ve > 0,380 such that {t € R and 0 < |t| < 8} ⇒ || } [ƒ(c + tu) − ƒ(c)] − Lu|| < €. - -
5. Let f: R² → R, f(x, y) = x²y, c = (1, 1), and u = (1,1). Find Duf(c) and prove your answer with the e-d definition of Duf(c). Hint (optional): Fix € > 0 and choose d = min{1, €/4}. Duf (c) if Review of Definition: Lu Ve > 0,380 such that {t € R and 0 < |t| < 8} ⇒ || } [ƒ(c + tu) − ƒ(c)] − Lu|| < €. - -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![5.
Let ƒ : R² → R, f(x, y) = x²y, c = (1, 1), and u = (1,1).
Find Duf(c) and prove your answer with the e-d definition of Duf(c).
Hint (optional): Fix > 0 and choose d = min{1, €/4}.
Review of Definition: Lu Duf(c) if
Ve > 0, 360 such that
{t € R and 0 < t < 8} ⇒ || } [ƒ(c+ tu) − f(c)] − Lu|| < €.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F8d694089-f362-456a-a87a-edec28432d23%2Fmr2j702_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.
Let ƒ : R² → R, f(x, y) = x²y, c = (1, 1), and u = (1,1).
Find Duf(c) and prove your answer with the e-d definition of Duf(c).
Hint (optional): Fix > 0 and choose d = min{1, €/4}.
Review of Definition: Lu Duf(c) if
Ve > 0, 360 such that
{t € R and 0 < t < 8} ⇒ || } [ƒ(c+ tu) − f(c)] − Lu|| < €.
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