/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 12 Given a smooth parametrization f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q. 12 (page 1119)

Given a smooth parametrization for a 鈥済eneralized cylinder鈥� S, given by extending the curve y = x2 upwards and downwards from z =鈭�2 to z = 3.

Short Answer

Expert verified

Therefore,therequiredsmoothparametrizationisr(u,v)=u,u2,v

Step by step solution

01

Step 1. Given

The equation of smooth parametrization for a 鈥済eneralized cylinder鈥� S, given by extending the curve y = x2.

02

Step 2.  Finding the equation

Theparametrizationofthecurvey=x2.Letx=uthen,y=x2=u2Hence,Theparametrizationofthecurvey=x2is,x=uy=u2Let=v,thentheparametrizationofa"generalizedcylinder"S,definedbyextendingthecurvey=x虏upwardsanddownwardsfrom==-2toz=3is,x=uy=u2z=vWhere,-2鈮�v鈮�3Therefore,therequiredsmoothparametrizationisr(u,v)=u,u2,v

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the masses of the lamina:

The lamina occupies the region of the hyperboloid with equation z2+4=x2+y2 that lies above and/or below the disk of radius 5 about the origin in the XY-plane, and the density function, 蟻(x, y,z), is proportional to the distance from the origin.

Calculus of vector-valued functions: Calculate each of the following.

ddt(r(t)),wherer(t)=3cos2ti+5tj+tt2+1k

What are the inputs of a vector field in 鈩�3?

What are the outputs of a vector field in the Cartesian plane?

Find the area of S is the portion of the plane with equation x = y + z that lies above the region in the xy-plane that is bounded by y = x, y = 5, y = 10, and the y-axis.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.