Question: Consider the 1-form defined on R2 {(0,0)}. (1) Show that dw = 0. (2) Let c: [0,1] 13 ydr+ady x + y R2 be

Consider the 1-form defined on R2 {(0,0)}. (1) Show that dw = 0. (2) Let c: [0,1] 13 ydr+ady x + y R2 be the curve defined by c(t) = (cos(2t), sin(2t)). Compute Lw. (3) Show that there does not exist C2 function f(x, y) such that df = w. Does this contradict Problem 4?

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