Chapter 14: Q 3 (page 1153)

For multivariate functions $f$ in $R^{2}$ or $R^{3}$ with continuous second partial derivatives,
$c u r l \nabla f ==.$

Short Answer

Expert verified

The required answer is :-

For multivariate functions $f$ in $R^{2}$ or $R^{3}$ with continuous second partial derivatives,

c u r l \nabla f = \nabla \times (\nabla f) = 0 .

Step by step solution

Step 1. Given Information

For multivariate functions $f$ in role="math" localid="1651018325304" $R^{2}$ or $R^{3}$ with continuous second partial derivatives,

$c u r l \nabla f =______=______.$

Step 2. Complete the statement

For multivariate functions $f$ in $R^{2}$ or $R^{3}$ with continuous second partial derivatives,

$c u r l \nabla f =______=______.$

We know that :-

$c u r l F = \nabla \times F$

So that :-

$c u r l \nabla f = \nabla \times (\nabla f)$

Also we know that if $F$ is in $R^{2}$ or $R^{3}$ , then $\nabla \times F = 0$ .

So that :-

$\nabla \times (\nabla f) = 0$ .

So our final answer is :-

$c u r l \nabla f = \nabla \times (\nabla f) = 0 .$

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For multivariate functions $f$ in $R^{2}$ or $R^{3}$ with continuous second partial derivatives,
$c u r l \nabla f ==.$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

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For multivariate functions fin R2or R3with continuous second partial derivatives, curl∇f=______=______.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Complete the statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

For multivariate functions $f$ in $R^{2}$ or $R^{3}$ with continuous second partial derivatives,
$c u r l \nabla f ==.$