MATH 2162.01 Study Guide - Final Guide: Divergence Theorem, Lagrange Multiplier, Spherical Coordinate System

• School: Ohio State University
• Department: Mathematics
• Course: MATH 2162.01
• Professor: All

Document Summary

We"ve covered a lot of materials in this course starting from the theory of sequences and series to stokes" theorem and the divergence theorem. Reviewing all of them thoroughly can be a very daunting task and one may easily lose sight of what"s more important and what"s less so. So here i prepare a short handout to help you prepare for the nal exam. Find the raidus and the interval of convergence: (1) (2) k=1 k=1 ( 1)k (10x 3)k. Let f (x) = ln (1 + x). Find the third-order taylor polynomial of f (x) centered at x = 0 and use it to estimate the value of ln (1. 07). Use lagrange"s method to nd the point on the plane 2x 3y + 5z = 20 closest to p (1, 2, 3). Let f (x, y) = h e x cos y, e x sin yi. Find (x, y) such that f = and then evaluate.