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Multivariable Calculus

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Moderate

Find Parameterization of Spherical Cap Lying Above xy-plane

MVCALC-ZA463I

Find a parameterization of the spherical cap lying above the $x$-$y$ plane created by the intersection of the sphere $x^2 + y^2 + z^2 = 4$ and the cylinder $x^2 + y^2 = 1$.

A

$\vec{G}(\theta,z) = (2\cos\theta, 2\sin\theta, z)$ for $0 \leq \theta \leq 2\pi$ and $\sqrt{3} \leq z \leq 2$

B

$\vec{G}(\theta,z) = (z\cos\theta, z\sin\theta, z)$ for $0 \leq \theta \leq 2\pi$ and $\sqrt{3} \leq z \leq 2$

C

$\vec{G}(\theta, \phi) = (\cos \theta \sin \phi, \sin \theta \sin \phi, \sin \phi)$ for $0 \leq \theta \leq 2\pi$ and $0 \leq \phi \leq \pi/6$

D

$\vec{G}(\theta, \phi) = (2 \cos \theta \sin \phi, 2 \sin \theta \sin \phi, 2 \cos \phi)$ for $0 \leq \theta \leq 2\pi$ and $0 \leq \phi \leq \pi/6$

E

None of the Above