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Chapter 12: Q. 40. (page 917)

In Exercises 37鈥�42, 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.

f(x)=x3/2,0,1

Short Answer

Expert verified

The required surface formed is as shown below:

The function of two variables to represent the surface of revolution is determined by replacing 'x'by x2+y2is (x2+y2)34

Step by step solution

01

Given information 

The function is f(x)=x3/2over an interval of [0,1]

The z-axis is the center of this function.

02

The objective is to sketch the surface of the revolution

The function represents a parabola that passes through the xy-origin plane and along the x-axis.

When the z-axis of this parabolic form is rotated,

The surface formed is as shown below:

03

The objective is to find a function of two variables to represent this surface. 

By replacing xby x2+y2the function of two variables to represent the surface of revolution is determined

f(x,y)=(x2+y2)32 =(x2+y2)34

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