Explanation Given: r ( s ) = 4 s − 1 i − 8 3 s − 3 k s = 2 Formula used: a ( s ) = r ( s ) + s r ' ( s ) Calculation: The tangent line has the parametrization at given point: a ( s ) = r ( s ) + s r ' ( s ) ⇒ a ( s ) = r ( 2 ) + s r ' ( 2 ) r ( s ) = 4 s − 1 i − 8 3 s − 3 k Given, s = 2 ⇒ r ( 2 ) = 4 × ( 2 ) − 1 i − 8 3 × ( 2 ) − 3 k = 4 × 1 2 i − 8 3 × 1 2 3 k = 4 × 1 2 i − 8 3 × 1 8 k = 2 i − 1 3 k ⇒ r ' ( s ) = − 4 s − 2 i + 8 s − 4 k ⇒ r ' ( 2 ) = − 4 × ( 2 )

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Author: Jon Rogawski, Colin Adams, Robert Franzosa

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Chapter 13.2, Problem 35E

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Find a parametrization of the tangent line, r(s)=4s−1i−83s−3k at the point s=2.

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Chapter 13.2, Problem 34E

Chapter 13.2, Problem 36E

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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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Find a parametrization of the tangent line, r ( s ) = 4 s − 1 i − 8 3 s − 3 k at the point s = 2.

Solution Summary: The author calculates the tangent line's parametrization at the point s=2.

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Find a parametrization of the tangent line, r(s)=4s−1i−83s−3k at the point s=2.

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