MATH 211 Final: MATH 211 NJIT M211 FinalExamF15

• School: New Jersey Institute of Technology
• Department: Mathematical Sciences
• Course: MATH 211
• Professor: All

Document Summary

1. (a) (15 points) find parametric equations for the line in which the planes 3x 6y . 2z = 3 and 2x + y 2z = 2 intersect. (b) (10 points) find the distance from the point (2, 3, 4) to the plane x+2y +2z = 2. (a) (10 points) find the length of the indicated portion of the curve r(t) = (t sin t + cos t)i + (t cos t sin t)j, 2 t 2. (b) (15 points) find z. 3. in the direction of v = 2i 3j + 6k. (b) (15 points) find equations for the tangent plane and normal lines at the point. P0 on the given surface. cos x x2y + exz + yz = 4, 5. (a) (15 points) sketch the region of integration, change to polar coordinates, and evaluate the integral. Show all your steps. (c) (5 points) evaluate the line integral z (2,1,1) (1,2,1)