   Chapter 16, Problem 3RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.3. If f has continuous. partial derivatives of all orders on ℝ3, then div(curl ∇f) = 0.

To determine

Whether the statement “If f has continuous partial derivatives of all orders on 3 , then div(curl f)=0 ” is true or false.

Explanation

Given data:

div(curl f)=0 (1)

Formula used:

Write the expression for curl(f) .

curl(f)=0

Write the expression for div(0) .

div(0)=0

Consider left hand side (LHS) of equation (1).

LHS=div(curl f) (2)

Substitute 0 for curl f

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