Please answer all parts correctly and show all work. Thank you in advance!

Greens' Theorem Let f : R2 -> R2 be a vector field defined by zy sin(y? )i + 242 sin(y?)j y0 y = 0 (a) Compute curlf on all of R2. You may state any limits you use. (b) Is curlf continuous? Please explain. (c) Compute curlf dvol2 over D = (xER' : 0 0 such that & c [0, 1 - =] find a, b and c such that [ (8. t)ds = a+ be - = / 1-6 sin(1 - 1)2 2(1 - 1)2 dx. Hint: You need to parameterise the rest of the boundary Y yourself. (e) Suppose that sin(1 - >)- dx = c, ( 1 - 1) 2 d where c was found in part (d). Find K E R such that E-+0J lim (f, t)ds = K / curlfdvol2 YE