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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find and sketch the domain of the function.

2. f ( x , y ) = 4 x 2 y 2 + 1 x 2

To determine

To find: The domain of the function f(x,y)=4x2y2+1x2 and sketch its graph.

Explanation

Given:

The function is, f(x,y)=4x2y2+1x2 .

Calculation:

Consider the expression, 1x2 .

Since the radicand cannot take negative values, 1x20 . That is 1x1 .

Similarly for the expression, 4x2y2 .

Since the radicand cannot take negative values the expression, 4x2y20 .

Simplify the inequality as follows.

4x2y204x2y24x2y4x2

That is, 4x2y4x2 . Also notice that x2+y24 is a circle

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Chapter 14 Solutions

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