y . x Let F(X, y) = I j. X2 + Y2 X2 + Y2 (a) Show that 6_N = 6H- 6X 63/ V 6" : 3.= (b) Let r(t) = cos(t)i + sin(t)j For 0 s t 5 TE. Find / F - dr. C H (c) Let r(t) = cos(t]i sin(t}j for 0 g ts TI. Find/ F - dr. C H (d) Let r(t) = cos(t)i + sin(t)j for D s t S 27:. Find/ F - dr. C H (e) Do the realm of parts [b}(d] contradict Theorem 15}? 0 Yes @ No V Why:r or whyr not? 0 "his does contradict Theorem 15.? because F is continuous at (O, D) in R enclosed by curve C. @ "his does not contradict Theorem 15.? because F is not continuous at (0, O) in R enclosed by curve C. V (1') Show that V(arctan(i)) = F. Y v(arctan()) = ( )i +( )1: %i j = F 3' 1 + (X/z 1 + (m2