MATH 0240 Final: Math 0240 m24final2121-294
Document Summary
Math 0240 - analytic geometry and calculus iii. Instructions: no tables, books, notes, headphones, calculators, or. If you need additional space, use the backs of the pages. 1: (a) (5 points) find the unit tangent and unit normal vectors t and n to the curve at the point p = (cid:18) . 2 r (t) = h3 cos t, 4t, 3 sin ti. 2(cid:19). (b) (5 points) find curvature of the curve at the point p . 2: (10 points) use linear approximation to approximate the number. 3: (10 points) 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. 4: (10 points) find the volume of the solid e bounded by y = x2, x = y2, z = x + y + 5, and z = 0. 6: (10 points) evaluate the integral ex 2y da.
