Need help with part (e). 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 decreasefastest 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 amaximum 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

We will find out the required value.

Answered: If S c R³ is the unit sphere and F Sls…

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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If S c R³ is the unit sphere and F Sls curl F n dS. (e*y, sin(22 + y), xyz), then evaluate the integral