Explanation Given info: r → ( t ) = ( Sin t , Cos t , Sin t . Cos 2 t ) Concept used: Projection of point ( x , y , z ) on x z plane is ( x , 0 , z ) Calculation: Equation of curve r → ( t ) = ( Sin t , Cos t , Sin t . Cos 2 t ) So general point on the curve is ( x , y , z ) = ( Sin t , Cos t , Sin t . Cos 2 t ) The projection of this general point on x z plane is ( Sin t , 0 , Sin t . Cos 2 t ) , Thus equation of curve is r → ( t ) = ( Sin t , Cos t , Sin t . Cos 2 t ) If general point on this curve is ( x , y , z ) , then x = Sin t y = 0 z = Sin t ...

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Chapter 14.1, Problem 28E

To determine

Show that the projection of $\vec{r} (t)$ onto the $x z$ plane is the curve.

$z = x - 2 x^{3} for - 1 \leq x \leq 1$

$\vec{r} (t) = (Sin t, Cos t, Sin t . Cos 2 t)$

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Chapter 14.1, Problem 27E

Chapter 14.1, Problem 29E

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Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Chapter 14 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

Show that the projection of r → ( t ) onto the x z plane is the curve. z = x − 2 x 3 for − 1 ≤ x ≤ 1 r → ( t ) = ( Sin t , Cos t , Sin t . Cos 2 t )

Solution Summary: The author explains that the projection of r ( t ) onto the x z plane is the curve.

Concept explainers

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Show that the projection of $\vec{r} (t)$ onto the $x z$ plane is the curve.

$z = x - 2 x^{3} for - 1 \leq x \leq 1$

$\vec{r} (t) = (Sin t, Cos t, Sin t . Cos 2 t)$

Want to see the full answer?

Chapter 14 Solutions

Show that the projection of r → ( t ) onto the x z plane is the curve. z = x − 2 x 3 for − 1 ≤ x ≤ 1 r → ( t ) = ( Sin t , Cos t , Sin t . Cos 2 t )

Solution Summary: The author explains that the projection of r ( t ) onto the x z plane is the curve.

Concept explainers

Videos

Show that the projection of r→(t) onto the xz plane is the curve. z=x−2x3 for −1≤x≤1 r→(t)=(Sint,Cost,Sint.Cos2t)

Want to see the full answer?

Chapter 14 Solutions

Show that the projection of $\vec{r} (t)$ onto the $x z$ plane is the curve.

$z = x - 2 x^{3} for - 1 \leq x \leq 1$

$\vec{r} (t) = (Sin t, Cos t, Sin t . Cos 2 t)$