   Chapter 16, Problem 11RCC

Chapter
Section
Textbook Problem

(a) What is a parametric surface? What arc its grid curves?(b) Write an expression for the area of a parametric surface.(c) What is the area of a surface given by an equation z = g(x, y)?

(a)

To determine

To explain: The parametric surface and its grid curves.

Explanation

The surface S of vector function of two parameters u and v (r(u,v)) is expressed as,

r(u,v)=x(u,v)i+y(u,v)j+z(u,v)k

Here,

x, y, and z are component functions of r .

Consider the vector function r(u,v) as real-valued with region D on 3 in uv-plane

(b)

To determine

To write: The expression for area of parametric surface.

(c)

To determine

The area of surface of equation z=g(x,y) .

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