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(d) Let P = xy², Q = x²y and C denote one petal of the four leaved rose defined by r = -450<. Compute the line integral fe P da +Q dy. cos(24),

(d) Let P = xy², Q = x²y and C denote one petal of the four leaved rose defined by r = -450<. Compute the line integral fe P da +Q dy. cos(24),

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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Need help with part (d). Thank you :)

 

1. (a) Does the limit lim(,y)→(1,1) yx² -y exist? x-1 (b) If the gradient of a function f(x, y) at the point (-1, –1) is given by Vf(-1, –1) = (2,3), then in what direction away from the point (-1, –1) does the function start to decrease fastest and what is the magnitude of the rate of change? %3D (c) If the set Dc R² is bounded and f(x, y) is continous on D, does f(x, y) have to acheive a maximum on D? (d) Let P = xy2, Q = x2y and C denote one petal of the four leaved rose defined byr= -1<0<. Compute the line integral fe P dx +Q dy. cos(20), (e) If S c R³ is the unit sphere and F = Sls curl F ndS. (e"y, sin(z2 + y), xyz), then evaluate the integral
Transcribed Image Text:1. (a) Does the limit lim(,y)→(1,1) yx² -y exist? x-1 (b) If the gradient of a function f(x, y) at the point (-1, –1) is given by Vf(-1, –1) = (2,3), then in what direction away from the point (-1, –1) does the function start to decrease fastest and what is the magnitude of the rate of change? %3D (c) If the set Dc R² is bounded and f(x, y) is continous on D, does f(x, y) have to acheive a maximum on D? (d) Let P = xy2, Q = x2y and C denote one petal of the four leaved rose defined byr= -1<0<. Compute the line integral fe P dx +Q dy. cos(20), (e) If S c R³ is the unit sphere and F = Sls curl F ndS. (e"y, sin(z2 + y), xyz), then evaluate the integral
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