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Chapter 12: Problem 2

What is the domain of \(f(x, y)=x^{2} y-x y^{2} ?\)

Short Answer

Expert verified
Answer: The domain of the function is all real values of \(x\) and \(y\), which can be represented as the set of all ordered pairs \((x, y)\) such that \(x\) and \(y\) are real numbers. In interval notation, the domain is: $$(-\infty, \infty) \times (-\infty, \infty)$$

Step by step solution

01

Identify any restrictions on x and y

There are no square roots, logarithms, or divisions in the function \(f(x, y) = x^2y - xy^2\), so there are no restrictions on the values for \(x\) and \(y\).
02

Determine the domain of the function

Since there are no restrictions on the values of \(x\) and \(y\), the domain of \(f(x, y)\) includes all real values of \(x\) and \(y\). We can write the domain as the set of all ordered pairs \((x, y)\) such that \(x\) and \(y\) are real numbers. In interval notation, the domain is: $$(-\infty, \infty) \times (-\infty, \infty)$$

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