Explanation Given: The equation is r ( t ) = < cos t , sin t , 2 3 t 3 2 > Calculation: The arc length parameterization of the r ( t ) = < cos t , sin t , 2 3 t 3 2 > If r (t) is a differentiable vector valued function, then the arc length function is defined by S ( t ) = ∫ 0 t | | r ′ ( t ) | | d t (I) So, for the equation r (t) is given by r ( t ) = < cos t , sin t , 2 3 t 3 2 > (II) Differentiating equation (II) with respect to t r ′ ( t ) = < − sin t , cos t , t 1 2 > (III) Calculating the magnitude | | r ′ ( t ) | | = sin 2 t + cos 2 t + t | | r ′ ( t ) | | = 1 + t (IV) Suppose C is a space curve defined by r ( t ) = < x ( t ) , y ( t ) , z ( t ) > , for a ≤ t ≤ b...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.3, Problem 33E

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Arc length parameterization of $r (t) = < \cos t, \sin t, \frac{2}{3} t^{\frac{3}{2}} >$

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Chapter 14.3, Problem 32E

Chapter 14.3, Problem 34E

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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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Arc length parameterization of r ( t ) = < cos t , sin t , 2 3 t 3 2 >

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Arc length parameterization of r ( t ) = < cos t , sin t , 2 3 t 3 2 >

Arc length parameterization of $r (t) = < \cos t, \sin t, \frac{2}{3} t^{\frac{3}{2}} >$