MATH 0240 Final: MATH 240 Final Exam-53
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The curve is given parametrically by: find its curvature at the point (0, 1, 0), set up the integral representing the length of the curve from the point r(t) =< t3 + 1. 2 t2, 2t 1, t2 + t 5 > . (0, 1, 0) to the point (10, 3, 4 + 2 5). Find an equation of the plane tangent to the surface x2 + y2z2 = 8 at the point p = (2, 2, 1). Find all critical points of the function f (x, y) = x2 + 4xy 10x + y2 8y + 1. For each critical point determine if it is a local maximum, a local minimum or a saddle point. Find the work done by the force f(x, y) = 3yi + xj in moving a particle along the boundary of the trapeziod with the vertices (0, 0), (1, 1), (2, 1) and (3, 0) in the clockwise direction.
