Explanation Given: r → ( t ) = 〈 t , 4 3 ( t ) 3 / 2 , t 2 〉 Formula used: T ∧ ( t ) = r → ( t ) ‖ r → ' ( t ) ‖ N ∧ ( t ) = T → ' ( t ) ‖ T → ' ( t ) ‖ B ∧ ( t ) = T ∧ ( t ) × N ∧ ( t ) Calculation: r → ( t ) = 〈 t , 4 3 t 3 / 2 , t 2 〉 r → ' ( t ) = d ( r → ( t ) ) d t = d d t 〈 t , 4 3 t 3 / 2 , t 2 〉 = 〈 d t d t , 4 d ( t ) 3 / 2 d t , d ( t ) 2 d t 〉 = 〈 1 , 2 t , 2 t 〉 ( d d t ( t n ) = n t n − 1 ) T ∧ ( t ) = r → ( t ) ‖ r ( t ) ‖ = 〈 1 , 2 t , 2 t 〉 ‖ 〈 1 , 2 t , 2 t 〉 ‖ = 〈 1 , 2 t , 2 t 〉 ( 1 ) 2 + ( 2 t ) 2 + ( 2 t ) 2 ( ‖ 〈 a , b , c 〉 ‖ = a 2 + b 2 + c 2 ) = 〈 1 , 2 t , 2 t 〉 1 + 4 t + 4 t 2 T ∧ ( t ) = 〈 1 , 2 t , 2 t 〉 1 + 4 t + 4 t 2 T ∧ ( 1 ) = 〈 1 , 2 , 2 〉 3 T ∧ ( 1 ) = 〈 1 3 , 2 3 , 2 3 〉 T → ( t ) = 〈 1 , 2 t , 2 t 〉 1 + 4 t + 4 t 2 T → ' ( t ) = d d t ( 〈 1 , 2 t , 2 t 〉 1 + 4 t + 4 t 2 ) 1 + 4 t + 4 t 2 = To determine (b) Find the equation of the osculating plane at the point corresponding to t = 1

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.4, Problem 53E

To determine

(a)

To calculate:

Find $\overset{\land}{T}, \overset{\land}{N} and \overset{\land}{B}$ at the points corresponding to $t = 1, where \vec{r} (t) = 〈 t, \frac{4}{3} t^{3 / 2}, t^{2} 〉$

To determine

(b)

Find the equation of the osculating plane at the point corresponding to $t = 1$

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Chapter 14.4, Problem 52E

Chapter 14.4, Problem 54E

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Chapter 14 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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

Knowledge Booster

(a) To calculate: Find T ∧ , N ∧ and B ∧ at the points corresponding to t = 1 , where r → ( t ) = 〈 t , 4 3 t 3 / 2 , t 2 〉

Solution Summary: The author explains the formula used to calculate the points corresponding to t = 1.

(a)

To calculate:

Find $\overset{\land}{T}, \overset{\land}{N} and \overset{\land}{B}$ at the points corresponding to $t = 1, where \vec{r} (t) = 〈 t, \frac{4}{3} t^{3 / 2}, t^{2} 〉$

(b)

Find the equation of the osculating plane at the point corresponding to $t = 1$

Want to see the full answer?

Chapter 14 Solutions

(a) To calculate: Find T ∧ , N ∧ and B ∧ at the points corresponding to t = 1 , where r → ( t ) = 〈 t , 4 3 t 3 / 2 , t 2 〉

Solution Summary: The author explains the formula used to calculate the points corresponding to t = 1.

(a) To calculate: Find T∧,N∧ and B∧ at the points corresponding to t=1, where r→(t)=〈t,43t3/2,t2〉

(b) Find the equation of the osculating plane at the point corresponding to t=1

Want to see the full answer?

Chapter 14 Solutions

(a)

To calculate:

Find $\overset{\land}{T}, \overset{\land}{N} and \overset{\land}{B}$ at the points corresponding to $t = 1, where \vec{r} (t) = 〈 t, \frac{4}{3} t^{3 / 2}, t^{2} 〉$

(b)

Find the equation of the osculating plane at the point corresponding to $t = 1$