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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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1. (a) Find the area of one petal of the rose r = |cos(20) 3. (b) Find a vector orthogonal to the direction of most rapid increase of f(x,y) = e" sin z at the point (, 0), and give the rate of change of f(r, y) at that point in that direction. (c) Let D C R? be a closed and bounded set, and let f(x, y) be a bounded function whose domain contains D. Must f achieve a maximum on D? Justify your answer. (d) Let P = r? – y², Q = -2ry and C denote the ellipse centered at (0,0) and passing through the points (0, 1) and (2,0). Compute the line integral fe P dx + Q dy. (e) If E C R³ is the ellipsoid (z/2)² + (y/3)² + (z/4)² = 1 and F evaluate the integral ffE curl F - n dS. (3²e=v=, z?e=y², z²e=y=),
Transcribed Image Text:1. (a) Find the area of one petal of the rose r = |cos(20) 3. (b) Find a vector orthogonal to the direction of most rapid increase of f(x,y) = e" sin z at the point (, 0), and give the rate of change of f(r, y) at that point in that direction. (c) Let D C R? be a closed and bounded set, and let f(x, y) be a bounded function whose domain contains D. Must f achieve a maximum on D? Justify your answer. (d) Let P = r? – y², Q = -2ry and C denote the ellipse centered at (0,0) and passing through the points (0, 1) and (2,0). Compute the line integral fe P dx + Q dy. (e) If E C R³ is the ellipsoid (z/2)² + (y/3)² + (z/4)² = 1 and F evaluate the integral ffE curl F - n dS. (3²e=v=, z?e=y², z²e=y=),
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 (a) Given,

             r=|cos(2θ)|12

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