Chapter 14: Q. 17 (page 1132)

$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y) = {yx}^{2} i - x cosy j$

Short Answer

Expert verified

$div F = = 2 xy + x siny$

Step by step solution

Step 1. Given information is:

$F (x, y) = {yx}^{2} i - x cosy j$

Step 2. Divergence of vector field

$If F (x, y) = f_{1} (x, y) i + f_{2} (x, y) j, then div F = \frac{\partial f_{1}}{\partial x} + \frac{\partial f_{2}}{\partial y} Here, F (x, y) = {yx}^{2} i - x cosy j Compare this with, F (x, y) = f_{1} (x, y) i + f_{2} (x, y) j Then, f_{1} (x, y) = {yx}^{2}, f_{2} (x, y) = - x cosy div F = \frac{\partial f_{1}}{\partial x} + \frac{\partial f_{2}}{\partial y} = \frac{\partial ({yx}^{2})}{\partial x} + \frac{\partial (- x cosy)}{\partial y} = 2 xy + x siny$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y) = {yx}^{2} i - x cosy j$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

ComputethedivergenceofthevectorfieldsinExercises17–22.F(x,y)=yx2i−xcosyj

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y) = {yx}^{2} i - x cosy j$