Explanation Given: Curve = r ( t ) = 〈 1 − cos 2 t , t + sin t , t 2 〉 Formula used: cos θ = cos α ⇒ θ = 2 n π ± α Calculation: On yz-plane, x is equal to zero. So, x = 0. ⇒ 1 − cos 2 t = 0 ⇒ 1 = cos 2 t ⇒ cos 2 t = 1 ⇒ cos 2 t = cos 0 [ ∵ cos θ = cos α , ⇒ θ = 2 n π ± α ] ⇒ 2 t = 2 n π ± 0 ⇒ 2 t = 2 n π ⇒ t = n π Where, n = 0 , 1 , 2 , 3 , 4..... ∴ t = 0 , π , 2 π , 3 π , 4 π

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 13.1, Problem 11E

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Show that the space curve given by r(t)=〈1−cos2t,t+sint,t2〉 intersects the yz-plane in infinitely many points but does not cross through it.

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Chapter 13.1, Problem 10E

Chapter 13.1, Problem 12E

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ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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Show that the space curve given by r ( t ) = 〈 1 − cos 2 t , t + sin t , t 2 〉 intersects the yz-plane in infinitely many points but does not cross through it.

Solution Summary: The author explains that the space curve given by r(t)=langle 1-mathrmcos2t,t+

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Show that the space curve given by r(t)=〈1−cos2t,t+sint,t2〉 intersects the yz-plane in infinitely many points but does not cross through it.

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Chapter 13 Solutions