MATH 0240 Final: MATH 240 Final Exam-38
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Find the unit tangent and unit normal vectors t and n to the curve r (t) = h3 cos t, 4t, 3 sin ti at the point p = (cid:18) . 2(cid:19). (b) find curvature of the curve at the point p . Use linear approximation to approximate the number 3. 04 + e 0. 08 . Find all critical points of the function f (x, y) = 4x 3x3 2xy2. For each critical point determine if it is a local maximum, local minimum or a saddle point. Find the volume of the solid e bounded by y = x2, x = y2, z = x+y+5, and z = 0. Evaluate the line integral hc e2x+y dx+e y dy along the negatively oriented closed curve c, where c is the boundary of the triangle with the vertices (0, 0), (0, 1), and (1, 0). 5 inside the cylinder x2 + y2 = 1. x2.
