   Chapter 15.5, Problem 2E

Chapter
Section
Textbook Problem

Find the area of the surface.2. The part of the plane 6x + 4y + 2z = 1 that lies inside the cylinder x2 + y2 = 25

To determine

To find: The area of given surface.

Explanation

Given:

The part of the plane, 6x+4y+2z=1 .

The region D lies inside the cylinder x2+y2=25 .

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:

Express the given equation as follows.

6x+4y+2z=12z=16x4yz=16x4y2z=123x2y

The partial derivatives fx and

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