Chapter 14: Q. 17 (page 1119)

If S is parametrized by r(u, v), why is $d S = r_{u} \times r_{v}$ the correct factor to use to account for distortion of area?

Short Answer

Expert verified

$Hence, the correct factor to use to account for distortion of area is dS = ||r_{u} and r_{v}|| dudv$

Step by step solution

Step 1. Given

The r(u, v) is parametrized

Step 2. Finding area of parallelogram

$The area of the parallelogram with sides r_{u} and r_{v} is, The arear, ||r_{u} and r_{v}||, of this parallelogram approximates the area of the portion of the tangent plane used to approximate the area of S; in the limit, the analogy is exact . Hence, the correct factor to use to account for distortion of area is dS = ||r_{u} and r_{v}|| dudv$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If S is parametrized by r(u, v), why is $d S = r_{u} \times r_{v}$ the correct factor to use to account for distortion of area?

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding area of parallelogram

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

If S is parametrized by r(u, v), why is dS=ru×rvthe correct factor to use to account for distortion of area?

Short Answer

Step by step solution

Step 1. Given

Step 2. Finding area of parallelogram

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

If S is parametrized by r(u, v), why is $d S = r_{u} \times r_{v}$ the correct factor to use to account for distortion of area?