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(4) Consider the following set: S = {(x, y, z) = R³ | (3+ y²) (x² + z²) = 1}. (a) Show that S is a surface. (b) Sketch S. (c) Give a parametrisation of S such that (-2√21, 2√2) lies in the image of S. 1 (d) Compute the tangent plane to S at (-2√2, 1, 2√2).

(4) Consider the following set: S = {(x, y, z) = R³ | (3+ y²) (x² + z²) = 1}. (a) Show that S is a surface. (b) Sketch S. (c) Give a parametrisation of S such that (-2√21, 2√2) lies in the image of S. 1 (d) Compute the tangent plane to S at (-2√2, 1, 2√2).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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(4) Consider the following set: S = {(x, y, z) = R³ | (3+ y²) (x² + z²) = 1}. (a) Show that S is a surface. (b) Sketch S. (c) Give a parametrisation of S such that (-2√21, 2√2) lies in the image of S. 1 (d) Compute the tangent plane to S at (-2√2, 1, 2√2).
Transcribed Image Text:(4) Consider the following set: S = {(x, y, z) = R³ | (3+ y²) (x² + z²) = 1}. (a) Show that S is a surface. (b) Sketch S. (c) Give a parametrisation of S such that (-2√21, 2√2) lies in the image of S. 1 (d) Compute the tangent plane to S at (-2√2, 1, 2√2).
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