Question

(d) The line integral [(x+y?)dx + (x2 + 2xy)dy, where the positively oriented curve C is the boundary of the region in the first quadrant determined by the graphs of x=0, y=x2 and y=1, can be converted to A 2xdydx 0 0 BJ 2 xdxdy 0 0 С -2x)dyda 00 D none of the above (e) Consider finding the maximum and minimum values of the function f(x, y) = x + y2 - 4x + 4y subject to the constraint x + y = 9. The necessary condition for the extreme values are А (2x-4-0 2y+4= 0 [x² + y² =9 (2x - 4 + 2x²=0 (2y + 4 + 2y²=0 B С 2x - 4+21x=0 2y +4 +22 y = 0 (x² + y² =9 D none of the above

Answer 1

Que line Integral [(x2+x2)dx+(22+229) dy c is bounded by X=0, Y=72, Y=1 By Green's theorem & Modxt Ndy SS (ON-OM) DA θα Oy Here M= xty² => 2M =24 x²+2xy N = 21FY А. ру Na aa :: 562+v) dx + (x2+2xy) dy = 55((2x+2y) – 2Y)dA А. Ss 2x dady ny. psy=x2 Y=1 02 y OLY > 0 1 X=0 s gut 2x dx dy. AnsWER, Y=0 x=0

Que f(x,y) a = x²+x² - 4x + 4y Subject to constraint is . x² + y² = g. let g(x, y, d) f(x, y) + (27?+y2-9) Necessary condition is s dx (x,y,d)=o PY, Id (X, Y, d)=0 22-4 +2d2=0 2y +4 + 2 y = 0 x² + y2_g=0 Answer