MATH 21A Study Guide - Midterm Guide: Directional Derivative, Multiple Integral, Quadratic Function
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Answers which are illeg- ible for the grader cannot be given credit: show your work. 2, and 8, we need to see the 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. If f (x, y) = 1 is a curve, and near (2, 3) one can write y as a function of x, then y = fy(2, 3)/fx(2, 3). If rrr f (x, y) da = 0, then the function f (x, y) is everywhere zero on r = The directional derivative in the direction of the gradient is | f|. The linearization of f (x, y) = x3 + y3 at (1, 1) is the quadratic function. The function f (x, y) = x2 + y2 satis es the partial di erential equation.
