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...Math v calculus iv section spring solutions to practice midterm problem let c be the arc of parabola y x from evaluate following line integrals a r xds b cydx dy solution t dx dt tdt ds z ydx consider vector eld f yzcos xz i sin j xycos k find function such that ysin g yz h dh dz is constant integral dr where curve given by e use green s theorem oriented shown in figure union two semicircles and segments d zz dxdy rcos rsin rdrd drd xyzi yzj conservative explain no curl but curlf yi xy xzk xyz there curlg we have div for any divf torus with equation u cosu cosvi sinvj sinuk calculate ru rv sinucosvi sinusinvj cosuk sinv cosvj sinvi sinucosv sinusinv cosv cosucosvi cosusinvj an plane tangent at so surface area dudv sinu dv rrs zds upper hemisphere sincos sinsin cos sind cossind rr...