Question

Consider the curve formed by the intersection of the surfaces $x^2 + y^2 = 9$ and $z = 2xy^2$. This curve is parametrized by equations $x(t)$, $y(t)$, $z(t)$ where $x(t)$ is given by $x(t) = 3 \cos(t)$ After finishing this parametrization, what is the value of $z$ when $t = \frac{\pi}{3}$?

          Consider the curve formed by the intersection of the surfaces $x^2 + y^2 = 9$ and $z = 2xy^2$.
This curve is parametrized by equations $x(t)$, $y(t)$, $z(t)$ where $x(t)$ is given by
$x(t) = 3 \cos(t)$
After finishing this parametrization, what is the value of $z$ when $t = \frac{\pi}{3}$?

Consider the curve formed by the intersection of the surfaces x^2 + y^2 = 9 and z = 2xy^2.
This curve is parametrized by equations x(t), y(t), z(t) where x(t) is given by
x(t) = 3 cos(t)
After finishing this parametrization, what is the value of z when t = (π)/(3)?

Added by Eric S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

08/20/2023

Step 1

Step 1: We are given the equation z = 2xy^2 and we need to parametrize it using x(t) = 3cos(t). Show more…

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Help with calculus z = 2xy2 This curve is parametrized by equations (t), y(t), z(t) where (t) is given by x(t) = 3 cos(t) After finishing this parametrization, what is the value of z when t = iH 3