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Chapter 12: Q 37. (page 917)

In Exercise, sketch the surface of revolution formed when the given function on the specified interval is revolved around the z-axis and find a function of two variables with the surface as its graph.

fx=x,0,3

Short Answer

Expert verified

fx,y=x2+y2

Step by step solution

01

Step 1. Given information

Function isfx=x.

02

Step 2. Explanation

Function is fx=x

The function represents a line with slope 1 that passes through the origin of the xy plane.

This line generates a conical funnel shape when rotated around the z-axis.

The shape formed will be simply a section of this conical shape because the interval is just across the first quadrant of the xy-plane.

Replace x by x2+y2to get a function of two variables that denotes the surface of revolution

So,

f(x,y)=x2+y2

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