Solution Found!
Vector fields on regions Let S = {(x, y): /x/ 1, /y/ 1}(a
Chapter 14, Problem 38E(choose chapter or problem)
Vector fields on regions Let \(S=\{(x, y):|x| \leq 1 \text { and }|y| \leq 1\}\) la square cenleredat the origin), \(D=\{(x, y):|x|+|y| \leq 1\}\) (a diamond/ centered at the origin), and \(C=\left\{(x, y): x^{2}+y^{2} \leq 1\right\}\) (a disk centered at the origin). For each vector field F, draw pictures and analyze the vector field to answer the following questions.
a. At what points of S, D, and C does the vector field have its maximum magnitude?
b. At what points on the boundary of each region is the vector field directed out of the region?
\(\mathbf{F}=\langle x, y\rangle\)
Questions & Answers
QUESTION:
Vector fields on regions Let \(S=\{(x, y):|x| \leq 1 \text { and }|y| \leq 1\}\) la square cenleredat the origin), \(D=\{(x, y):|x|+|y| \leq 1\}\) (a diamond/ centered at the origin), and \(C=\left\{(x, y): x^{2}+y^{2} \leq 1\right\}\) (a disk centered at the origin). For each vector field F, draw pictures and analyze the vector field to answer the following questions.
a. At what points of S, D, and C does the vector field have its maximum magnitude?
b. At what points on the boundary of each region is the vector field directed out of the region?
\(\mathbf{F}=\langle x, y\rangle\)
ANSWER:Solution 38E
Step 1
