Explanation Given: r ( t ) = 〈 t 2 2 , t 3 3 , t 〉 at t = 1 Formula used: N → ( t ) = v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ v ( t ) r ' ' ( t ) − v ' ( t ) r ' ( t ) ‖ r → ' ( t ) = d r → ( t ) d t v ( t ) = ‖ r → ' ( t ) ‖ r ' ' ( t ) = d 2 r → ( t ) d t 2 v ' ( t ) = d d t v → ( t ) Calculation: r → ( t ) = 〈 t 2 2 , t 3 3 , t 〉 r → ' ( t ) = d d t r → ( t ) = d d t 〈 t 2 2 , t 3 3 , t 〉 = d d t 〈 d d t t 2 2 , d d t t 3 3 , d d t t 〉 = 〈 1 2 × 2 t , 1 3 × 3 t 2 , 1 〉 = 〈 t , t 2 , 1 〉 ⋯ ⋯ ( 1 ) v ( t ) = ‖ r ' ( t ) ‖ = t 2 + t 4 + 1 ⋯ ⋯ ( 2 ) r → ' ' ( t ) = d d t ( r → ' ( t ) ) = d d t 〈 t , t 2 , 1 〉 = 〈 d d t t , d d t t 2 , d d t 1 〉 = 〈 1 , 2 t , 0 〉 ⋯ ⋯ ( 3 ) v ' ( t ) = 1 2 t 2 + t 4 + 1 × ( 2 t + 4 t 3 ) = 2 t 3 + t t 2 + t 4 + 1 ⋯ ⋯ ( 4 ) Substitute t = 1 in equation ( 1 ) , ( 2 ) , ( 3 ) , and ( 4 ) to find the value r → ' ( 1 ) , v → ( 1 ) , r → ' ' ( 1 ) and v → ' ' ( 1 ) r → ' ( 1 ) = 〈 1 , 1 , 1 〉 v ( 1 ) = 1 2 + 1 4 + 1

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.4, Problem 49E

To determine

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 \frac{t^{2}}{2}, \frac{t^{3}}{3}, t 〉 at t = 1$

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Chapter 14.4, Problem 48E

Chapter 14.4, Problem 50E

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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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Normal vector ( N → ) at the indicated point. 〈 t 2 2 , t 3 3 , t 〉 at t = 1

Solution Summary: The author explains how to calculate a normal vector (N ) at the indicated point.

Concept explainers

Videos

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 \frac{t^{2}}{2}, \frac{t^{3}}{3}, t 〉 at t = 1$

Want to see the full answer?

Chapter 14 Solutions

Normal vector ( N → ) at the indicated point. 〈 t 2 2 , t 3 3 , t 〉 at t = 1

Solution Summary: The author explains how to calculate a normal vector (N ) at the indicated point.

Concept explainers

Videos

To calculate: Normal vector (N→) at the indicated point. 〈t22,t33,t〉 at t=1

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Chapter 14 Solutions

To calculate:

Normal vector $(\vec{N})$ at the indicated point.

$〈 \frac{t^{2}}{2}, \frac{t^{3}}{3}, t 〉 at t = 1$