Calculus II, Spring 2019 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 16

1. Section 16.4: Problems 10, 17, 19, 23, 27, 29, 38, 39.

2. Let F = \frac{x}{\sqrt{x^{2}+y^{2}}} i + \frac{y}{\sqrt{x^{2}+y^{2}}} j + 0k and G = \frac{−y}{x^{2}+y^{2}} i + \frac{x}{x^{2}+y^{2}} j + 0k.

(a) Show that both F and G satisfy the component test.

(b) The natural domain for both F and G is {(x, y, z), x^{2} + y^{2} ≠ 0} (that is where F and G are defined). Show that F is conservative in this domain by finding its potential function.

(c) Show that G is NOT conservative in this domain (see example 5 on p945).

(d) If given another H satisfying the component test in this domain, how do you determine whether H is conservative?