Q. 21 Compute聽the聽divergence聽of聽th... [FREE SOLUTION]

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Chapter 14: Q. 21 (page 1132)

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . F (x, y, z) = \sin^{- 1} (xy) i + \ln (y + z) j + \frac{1}{2 x + 3 y + 5 z + 1} k$

Short Answer

Expert verified

$div F = \frac{y}{\sqrt{1 - {(xy)}^{2}}} + \frac{1}{y + z} - \frac{5}{{(2 x + 3 y + 5 z + 1)}^{2}}$

Step by step solution

Step 1. Given information is:

$F (x, y, z) = \sin^{- 1} (xy) i + \ln (y + z) j + \frac{1}{2 x + 3 y + 5 z + 1} k$

Step 2. Divergence of vector field

$If F (x, y, z) = f_{1} (x, y, z) i + f_{2} (x, y, z) j + f_{3} (x, y, z) k, then div F = \frac{鈭� f_{1}}{鈭� x} + \frac{鈭� f_{2}}{鈭� y} + \frac{鈭� f_{3}}{鈭� z} Here, F (x, y, z) = \sin^{- 1} (xy) i + \ln (y + z) j + \frac{1}{2 x + 3 y + 5 z + 1} k Compare this with, F (x, y, z) = f_{1} (x, y, z) i + f_{2} (x, y, z) j + f_{3} (x, y, z) k Then, f_{1} (x, y, z) = \sin^{- 1} (xy), f_{2} (x, y, z) = \ln (y + z), f_{3} (x, y, z) = \frac{1}{2 x + 3 y + 5 z + 1} div F = \frac{鈭� f_{1}}{鈭� x} + \frac{鈭� f_{2}}{鈭� y} + \frac{鈭� f_{3}}{鈭� z} = \frac{鈭� (\sin^{- 1} (xy))}{鈭� x} + \frac{鈭� (\ln (y + z))}{鈭� y} + \frac{鈭� (\frac{1}{2 x + 3 y + 5 z + 1})}{鈭� z} = \frac{y}{\sqrt{1 - {(xy)}^{2}}} + \frac{1}{y + z} - \frac{5}{{(2 x + 3 y + 5 z + 1)}^{2}}$

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91影视

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . F (x, y, z) = \sin^{- 1} (xy) i + \ln (y + z) j + \frac{1}{2 x + 3 y + 5 z + 1} k$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

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ComputethedivergenceofthevectorfieldsinExercises17鈥�22.F(x,y,z)=sin-1(xy)i+ln(y+z)j+12x+3y+5z+1k

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

Applied Mathematics

Logic and Functions

Decision Maths

Discrete Mathematics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

$Compute the divergence of the vector fields in Exercises 17 鈥� 22 . F (x, y, z) = \sin^{- 1} (xy) i + \ln (y + z) j + \frac{1}{2 x + 3 y + 5 z + 1} k$