MATH 2D Study Guide - Final Guide: Tangent Space, Lagrange Multiplier

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2D
• Professor: All

Document Summary

Instructions: this is it, your nal hurdle to freedom!!! You have 120 min- utes to take this exam, for a total of 100 points. This is a closed book and closed notes exam and calculators and/or portable electronic devices are not allowed. Remember that you are not only graded on your nal answer, but also on your work. If you need to continue your work on the back of the page, clearly indicate so, or else your work will be discarded. Math 2d final: (10 points) find parametric equations of the tangent line to the fol- lowing curve at (0, 1, 1), where 0 t 2 . Simplify your an- swer. r(t) = hcos(t), sin(t), cos(2t)i. 3: (10 points) find the (smallest) angle between the following two planes x + y = 2 and y z = 1. Math 2d final: (10 points) find grs, where g = g(r + s, r s)