Explanation Given: The vector valued functions are r 1 ( t ) → = t i ^ + t 2 j ^ and r 2 ( t ) → = t 3 i ^ + t 6 j ^ where t = 1 Formula used: If r ( t ) → = x ( t ) i ^ + y ( t ) j ^ + z ( t ) k ^ is the given vector valued function, then the tangent vector to the given curve is d d t ( r ( t ) → ) t = a = [ d d t ( x ( t ) ) i ^ + d d t ( y ( t ) ) j ^ + d d t ( z ( t ) ) k ^ ] t = a Calculation: The vector valued functions are r 1 ( t ) → = t i ^ + t 2 j ^ and r 2 ( t ) → = t 3 i ^ + t 6 j ^ The tangent to the curve r 1 ( t ) → = t i ^ + t 2 j ^ is d d t ( r 1 ( t ) → ) t = a = [ d d t ( x ( t ) ) i ^ + d d t ( y ( t ) ) j ^ ] t = a ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ d d t ( t ) i ^ + d d t ( t 2 ) j ^ ] t = 1 ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ ( 1 ) i ^ + ( 2 t ) j ^ ] t = 1 ⇒ d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + ( 2 × 1 ) j ^ ] ∴ d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + 2 j ^ ] Thus, the tangent vector to the given curve at t = 1 is d d t ( r 1 ( t ) → ) t = 1 = [ i ^ + 2 j ^ ] ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 14.2, Problem 15E

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The curve associated with the given vector valued function and tangents of the given curve at given point.

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Chapter 14.2, Problem 14E

Chapter 14.2, Problem 16E

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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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The curve associated with the given vector valued function and tangents of the given curve at given point.

Solution Summary: The author calculates the curve associated with the given vector valued function and the tangents of it at a given point.

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The curve associated with the given vector valued function and tangents of the given curve at given point.

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Chapter 14 Solutions