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...Math calculus may final exam i have neither given nor received aid on this name e kim am m daniel angel a gorokhovsky pm mishev if you question raise your hand and remain seated in order to receive full credit answer must be complete legible correct show all of work give adequate explanations donotwriteinthisbox problem points score pts total pt find the area region enclosed by curve x t y see picture below bygreen s theorem ydx with c above oriented counter clockwise thus z dt equation for plane tangent paraboloid that is also parallel write g so hx tells us normal vector our surface at point we need h will certainly happen when solving get ux f j k across portion rst octant unit normals positive components weknow rr nds let u v then r hu vi next da ida zz uhu ui idvdu udvdu evaluate integral cos dydx changing integration dxdy ydy sin wire cm long cut into three or fewer pieces each piece bent square what minimal squares justify denote lengths segments after it bending segment yields ...