Explanation Given: r ( t ) = 〈 t , 1 , 1 〉 Formula Used: For r ( t ) = 〈 x , y , z 〉 , ‖ r ( t ) ‖ = x 2 + y 2 + z 2 … ( 1 ) Proof: Here, we have r ( t ) = 〈 t , 1 , 1 〉 Now, from the equation (1), we get ‖ r ( t ) ‖ = ( t ) 2 + ( 1 ) 2 + ( 1 ) 2 = t 2 + 1 + 1 = t 2 + 2 Differentiating, we get ‖ r ( t ) ‖ ' = d d t ( t 2 + 2 )

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 14.2, Problem 39E

To determine

To proof:

The derivative of the norm is not equal to the norm of the derivative by verifying that $‖ r (t) ‖' \neq ‖ r (t)' ‖$ for $r (t) = 〈 t, 1, 1 〉$ .

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Chapter 14.2, Problem 38E

Chapter 14.2, Problem 40E

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Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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To proof: The derivative of the norm is not equal to the norm of the derivative by verifying that ‖ r ( t ) ‖ ' ≠ ‖ r ( t ) ' ‖ for r ( t ) = 〈 t , 1 , 1 〉 .

Solution Summary: The author proves that the derivative of the norm is not equal to the corresponding derivative by verifying that r ( t )'= d

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To proof:

The derivative of the norm is not equal to the norm of the derivative by verifying that $‖ r (t) ‖' \neq ‖ r (t)' ‖$ for $r (t) = 〈 t, 1, 1 〉$ .

Want to see the full answer?

Chapter 14 Solutions

To proof: The derivative of the norm is not equal to the norm of the derivative by verifying that ‖ r ( t ) ‖ ' ≠ ‖ r ( t ) ' ‖ for r ( t ) = 〈 t , 1 , 1 〉 .

Solution Summary: The author proves that the derivative of the norm is not equal to the corresponding derivative by verifying that r ( t )'= d

Concept explainers

Videos

To proof: The derivative of the norm is not equal to the norm of the derivative by verifying that ‖r(t)‖'≠‖r(t)'‖ for r(t)=〈t,1,1〉.

Want to see the full answer?

Chapter 14 Solutions

To proof:

The derivative of the norm is not equal to the norm of the derivative by verifying that $‖ r (t) ‖' \neq ‖ r (t)' ‖$ for $r (t) = 〈 t, 1, 1 〉$ .