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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Consider the function

f ( x , y ) = 9 x 2 y 2

a. Find the domain of f.

b. Find the range of f.

(a)

To determine

To calculate: The domain of the function f(x,y)=9x2y2.

Explanation

Given Information:

The function f(x,y)=9x2y2.

Calculation:

Consider the provided function.

f(x,y)=9x2y2

As the function has no restrictions on the points, the domain is considered to be the set of all points which makes the function to be true.

The expression inside the radical can never be negative. Hence, the expression inside the radical must be greater than or equal to zero. So,

9x2y20

Subtract 9 from both the sides of the inequality and simplify

(b)

To determine

To calculate: The range of the function f(x,y)=9x2y2.

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