MATH 230 Final: Final Spring 2015

• School: Northwestern University
• Department: Mathematics
• Course: MATH 230
• Professor: All

Document Summary

Find the equation of the plane through the point (1, 1, 2) parallel to the plane x + y + z = 5. Let w = f (x, y, z), and x = sin t, y = cos t, z = tan t. if fx = 2, fy = 3, fz = 4 nd f (t) for t = 0. Problem 3 (16 points) consider the following cube. (a) (12 points) given the coordinates e(2, 1, 5), f( 3, 1, 5), and h( 3, 2, 1), Nd an equation for the plane that contains the bottom face through. Problem 4 (16 points) a frontier airplane and a southwest airplane follow the paths and s(t) = h2t 2, t + 2, 4t 7i. Problem 5 (18 points) a surface is de ned by x2 = y2 + 4z2. (a) (12 points) sketch its traces in the following planes. z z x = 0.