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Expert-verified Found in: Page 623 ### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280 # Find and sketch the domain of the function $$f(x,y) = ln(9 - {x^2} - 9{y^2})$$

The domain of the function is $$\left\{ {\left( {x,y} \right)/{x^2} + 9{y^2} < 3} \right\}$$

See the step by step solution

## Step 1:- Consideration:

Let $$f(x,y) = \ln (9 - {x^2} - 9{y^2})$$ is the function

## Step 2:- Finding relation

For the function f(x,y) to be exist $$\ln (9 - {x^2} - 9{y^2})$$ must be real

If $$9 - {x^2} - 9{y^2} > 0$$ the f exists

Therefore the domain of the function of $$\left\{ {\left( {x,y} \right)/{x^2} + 9{y^2} < 3} \right\}$$ I.e. set of all points inside the ellipse $${x^2} + 9{y^2} = {(3)^2}$$ but the ellipse is not included

## Step 3:- Graph Hence the domain of f is $$\left\{ {\left( {x,y} \right)/{x^2} + 9{y^2} < 3} \right\}$$ ### Want to see more solutions like these? 