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(1) Let F(t) = t²i+sin(t), f(x, y) = xy² - 2y, and F(x, y, z) = xyzi + (z² + y²)j. Calculate each of the following: (a) DF(x, y) = (b) Vf(x, y) = X₁ (c) Find the directional derivative of f(x, y) at (2,1) in the direction of u = 47+3j

(1) Let F(t) = t²i+sin(t), f(x, y) = xy² - 2y, and F(x, y, z) = xyzi + (z² + y²)j. Calculate each of the following: (a) DF(x, y) = (b) Vf(x, y) = X₁ (c) Find the directional derivative of f(x, y) at (2,1) in the direction of u = 47+3j

Advanced Engineering Mathematics
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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Answer all parts of this vector calc problem

(1) Let F(t) = t²i+sin(t), f(x, y) = xy² – 2y, and F(x, y, z) = xyzi + (z² + y²)j. Calculate each of the following: (a) DF(x, y) = (b) Vf(x, y) = X (c) Find the directional derivative of f(x, y) at (2,1) in the direction of u = 4i +3j
Transcribed Image Text:(1) Let F(t) = t²i+sin(t), f(x, y) = xy² – 2y, and F(x, y, z) = xyzi + (z² + y²)j. Calculate each of the following: (a) DF(x, y) = (b) Vf(x, y) = X (c) Find the directional derivative of f(x, y) at (2,1) in the direction of u = 4i +3j
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