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(a) Does the limit lim(æ,y)→(1,1) ya² -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? (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 by r = -1<0<. Compute the line integral fe P dx +Q dy. = cos(26), (e) If S c R³ is the unit sphere and F = Sls curl F n dS. (eªy, sin(z² + y), xyz), then evaluate the integral

(a) Does the limit lim(æ,y)→(1,1) ya² -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? (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 by r = -1<0<. Compute the line integral fe P dx +Q dy. = cos(26), (e) If S c R³ is the unit sphere and F = Sls curl F n dS. (eªy, sin(z² + y), xyz), then evaluate the integral

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) Does the limit lim(r,y)→(1,1) ya² -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? (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 = xy?, Q = x²y and C denote one petal of the four leaved rose defined by r = cost -<o<. Compute the line integral f. P dx + Q dy. (20), (e) If S c R³ is the unit sphere and F = STs curl F n dS. (e"y, sin(22 + y), xyz), then evaluate the integral
Transcribed Image Text:1. (a) Does the limit lim(r,y)→(1,1) ya² -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? (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 = xy?, Q = x²y and C denote one petal of the four leaved rose defined by r = cost -<o<. Compute the line integral f. P dx + Q dy. (20), (e) If S c R³ is the unit sphere and F = STs curl F n dS. (e"y, sin(22 + y), xyz), then evaluate the integral
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