considerGlu,v)= cuo v, uv)しtvsCompute Tus Tvofsalso Compute the surlace areu

Name: considerGlu,v)= cuo v, uv)しtvsCompute Tus Tvofsalso Compute the surla
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Description: considerGlu,v)= cuo v, uv)しtvsCompute Tus Tvofsalso Compute the surlace areu

Answered: consider surface s with parami Glusv) =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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consider
Glu,v)
= cuo v, uv)
しtvs
Compute Tus Tv
ofs
also Compute the surlace areu

Expert Solution

Step 1

Given surface is,

$G (u, v) = (u, v, u v)$

Step 2

To find: $T_{u}, T_{v}, N (u, v)$ .

Surface area of surface S.

To find $T_{u}$ :

Use the formula $T_{u} = \frac{\partial G}{\partial u}$ .

Here $G (u, v) = (u, v, u v)$

Differentiate $G (u, v) = (u, v, u v)$ partially with respect to u,

$\frac{\partial G}{\partial u} = \frac{\partial}{\partial u} (u, v, u v) = (1, 0, v)$

$\Rightarrow T_{u} = (1, 0, v)$

To find $T_{v}$ :

Use the formula $T_{v} = \frac{\partial G}{\partial v}$ .

Here $G (u, v) = (u, v, u v)$

Differentiate $G (u, v) = (u, v, u v)$ partially with respect to v,

$\frac{\partial G}{\partial v} = \frac{\partial}{\partial v} (u, v, u v) = (0, 1, u)$

$\Rightarrow T_{v} = (0, 1, u)$ .

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