MATH 0240 Final: MATH 240 Final Exam-36
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Find parametric equations of the line parallel to the planes x + y + z = 1 and x y + 2z = 5, and passing through the point (1, 2, 3). The curve is given parametrically as r(t) =< t + 1, t2 + 1, t3 + t2 > . Find its curvature at the point (0, 2, 0). Find and classify all critical points of f (x, y) = x2y 4y + x3 + 1. F dr, if f(x, y) = xyi + yj, and c is the path consisting of three line segments from (0, 0) to (1, 1), from (1, 1) to (1, 2), and from (1, 2) to (0, 0). The density of a circular lamina x2 + y2 4 is given by the formula (x, y) = 10 + xy2. , z ln x, y ln x : determine whether f is conservative, evaluate.
