MATH 226 Study Guide - Midterm Guide: Helen Baxendale, Tangent Space, Surface Integral
Document Summary
Circle the name of your instructor and your lecture time: You must show your work to obtain full credit. Points may be deducted if you do not justify your nal answer. Please indicate clearly whenever you continue your work on the back of the page. The exam is worth a total of 200 points. Problem 1: find an equation for the plane passing through the points (2, 3, 1), (1, 6, 4) and (3, 1, 0), let c be the curve parametrized by r(t) = ht2, t+3, 2t2+ti. Find parametric equations for the line which is tangent to this curve c at the point (4, 1, 6): find the point where the tangent line in part b meets the plane in part a. Use calculus to estimate the value of z. Find all critical points (x, y) of the function f (x, y) = 1 and classify each one as a local maximum, a local minimum or neither.
