Chapter 14: Q. 12 (page 1119)

Given a smooth parametrization for a “generalized cylinder” S, given by extending the curve y = x² upwards and downwards from z =−2 to z = 3.

Short Answer

Expert verified

$Therefore, the required smooth parametrization is r (u, v) = <u, u^{2}, v>$

Step by step solution

Step 1. Given

The equation of smooth parametrization for a “generalized cylinder” S, given by extending the curve y = x^2.

Step 2. Finding the equation

$The parametrization of the curve y = x^{2} . Let x = u then, y = x^{2} = u^{2} Hence, The parametrization of the curve y = x^{2} is, \{\begin{cases} x = u \\ y = u^{2} \end{cases} Let = v, then the parametrization of a " generalized cylinder " S, defined by extending the curve y = x ² upwards and downwards from = = - 2 to z = 3 is, \{\begin{cases} x = u \\ y = u^{2} \\ z = v \end{cases} Where, - 2 \leq v \leq 3 Therefore, the required smooth parametrization is r (u, v) = <u, u^{2}, v>$

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Given a smooth parametrization for a “generalized cylinder” S, given by extending the curve y = x² upwards and downwards from z =−2 to z = 3.

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding the equation

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Given a smooth parametrization for a “generalized cylinder” S, given by extending the curve y = x2 upwards and downwards from z =−2 to z = 3.

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Logic and Functions

Geometry

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Given a smooth parametrization for a “generalized cylinder” S, given by extending the curve y = x² upwards and downwards from z =−2 to z = 3.