Problem 1. Parametrize the following surfaces:(a) 2x + 3y + z = 6.(b) z = 9 – Vr2 + y?.(c) x² + 22 = 4.%3D(d) z == y?.Problem 2. Find the equation of the tangent plane to a given surface at the specified point.(a) Parametric surface given by x = u +vy = 3u? z = u – v, at (2,3,0).(b) The cylinder x² + z² = 4, at (0,3, 2).

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Problem 1. Parametrize the following surfaces: (a) 2x + 3y + z = 6. (b) z = 9 – Vx² + y?. - (c) x² + 22 = 4.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Problem 1. Parametrize the following surfaces:
(a) 2x + 3y + z = 6.
(b) z = 9 – Vr2 + y?.
(c) x² + 22 = 4.
%3D
(d) z =
= y?.
Problem 2. Find the equation of the tangent plane to a given surface at the specified point.
(a) Parametric surface given by x = u +v
y = 3u? z = u – v, at (2,3,0).
(b) The cylinder x² + z² = 4, at (0,3, 2).

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