2 Total differentials Question 1: What are the total differentials of the functions • f(x, y, z) = ¹e²²+y² f(r, 0) = r cos • f(x, t) = 2¹ √ Question 2: Which of the following expressions are total differentials, and if they are, what is the function whose differential it is? • df = ydx - xdy • df = xdx - ydy 2r • df = 2da + dy df = ¹ + Question 3: If we measure the position (x, y) of a point P in the plane, and there is a measurement error dr on the value of x, and a measurement error dy on the value of y, what is the measurement error on the distance from the origin to the point P?

2 Total differentials Question 1: What are the total differentials of the functions • f(x, y, z) = ¹e²²+y² f(r, 0) = r cos • f(x, t) = 2¹ √ Question 2: Which of the following expressions are total differentials, and if they are, what is the function whose differential it is? • df = ydx - xdy • df = xdx - ydy 2r • df = 2da + dy df = ¹ + Question 3: If we measure the position (x, y) of a point P in the plane, and there is a measurement error dr on the value of x, and a measurement error dy on the value of y, what is the measurement error on the distance from the origin to the point P?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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