MATH 21A Study Guide - Midterm Guide: Heat Equation, The Tangent, Pac-Man
Document Summary
Answers which are illeg- ible for the grader cannot be given credit: show your work. Except for problems 1-2, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. Problem 1) true/false questions (20 points), no justi cations needed. Every function f (x, y) of two variables has either a global minimum or a global maximum. The linearization of the function f (x, y) = ex+3y at (0, 0) is l(x, y) = 1 + x + 3y. The function f (x, y, z) = x2 cos(z) + x3y2z + (y 2)3y5 satis es the partial di erential equation fxyxzxy = 12. If xez = y2z, then z/ x = ez/(y2 xez). The function cos(x2) cos(y2) has a local maximum at (0, 0). The value of the double integral r /4 (r 2. 0 x3 cos(y) dxdy is the same as.
