Explanation Given: x ( t ) = a 0 ( 1 − t ) 3 + 3 a 1 t ( 1 − t ) 2 + 3 a 2 t 2 ( 1 − t ) + a 3 t 3 y ( t ) = b 0 ( 1 − t ) 3 + 3 b 1 t ( 1 − t ) 2 + 3 b 2 t 2 ( 1 − t ) + b 3 t 3 Formula used: Slope = d y d x = d y d t d x d t = y ' ( t ) x ' ( t ) Calculation: d y d x = d y d t d x d t d y d x = d d t ( b 0 ( 1 − t ) 3 + 3 b 1 t ( 1 − t ) 2 + 3 b 2 t 2 ( 1 − t ) + b 3 t 3 ) d d t ( a 0 ( 1 − t ) 3 + 3 a 1 t ( 1 − t ) 2 + 3 a 2 t 2 ( 1 − t ) + a 3 t 3 ) = b 0 d d t ( 1 − t ) 3 + b 1 d d t [ t ( 1 − t ) 2 ] + b 2 d d t [ t 2 ( 1 − t ) ] + b 3 d d t ( t 3 ) a 0 d d t ( 1 − t ) 3 + a 1 d d t [ t ( 1 − t ) 2 ] + a 2 d d t [ t 2 ( 1 − t ) ] + a 3 d d t ( t 3 ) = b 0 × 3 ( 1 − t ) 2 d d t ( 1 − t ) + b 1 [ t d d t ( 1 − t ) 2 + ( 1 − t ) 2 d d t t ] + b 2 d d t [ t 2 d d t ( 1 − t ) + ( 1 − t ) d d t t 2 ] + b 3 d d t ( t 3 ) a 0 × 3 ( 1 − t ) 2 d d t ( 1 − t ) + a 1 [ t d d t ( 1 − t ) 2 + ( 1 − t

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12.1, Problem 70E

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To show:The cubic Bezier curve is tangent to the segment $\bar{p_{2} p_{3}}$ at $p_{3}$ .

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Chapter 12.1, Problem 69E

Chapter 12.1, Problem 71E

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(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the above

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Chapter 12 Solutions

Calculus - Standalone book

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The cubic Bezier curve is tangent to the segment p 2 p 3 ¯ at p 3 .

Solution Summary: The author illustrates how the cubic Bezier curve is tangent to the segment p 2

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To show:The cubic Bezier curve is tangent to the segment $\bar{p_{2} p_{3}}$ at $p_{3}$ .

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Chapter 12 Solutions

The cubic Bezier curve is tangent to the segment p 2 p 3 ¯ at p 3 .

Solution Summary: The author illustrates how the cubic Bezier curve is tangent to the segment p 2

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To show:The cubic Bezier curve is tangent to the segment p2p3¯ at p3.

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Chapter 12 Solutions

To show:The cubic Bezier curve is tangent to the segment $\bar{p_{2} p_{3}}$ at $p_{3}$ .