   Chapter 15.5, Problem 21E

Chapter
Section
Textbook Problem

Show that the area of the part ol the plane z = ax + by + c that projects onto a region D in the xy-plane with area A(D) is a 2   +   b 2   +   1     A ( D ) .

To determine

To show: The area of the part of the plane that projects onto a region D in the xy-plane is equal to A(D)a2+b2+1.

Explanation

Given:

The function is the part of the plane, z=ax+by+c.

The area of the given region D is denoted by A(D).

Formula used:

The surface area with equation z=f(x,y),(x,y)D where fx and fy are continuous, is A(S)=D[fx(x,y)]2+[fy(x,y)]2+1dA.

Here, D is the given region.

Calculation:

Obtain the partial derivatives of the function with respect to x and y

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