Chapter 12: Q 22. (page 916)

In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y) = x^{2} y^{3}, (\frac{1}{2}, \frac{4}{3}), (0, π)$

Short Answer

Expert verified

$\begin{array}{rcl} f (\frac{1}{2}, \frac{4}{3}) & = & \frac{16}{27} \\ f (0, π) & = & 0 \end{array}$

Domain is $R^{2}$ and range is R.

Step by step solution

Step 1. Given information

Function is $f (x, y) = x^{2} y^{3}$

Step 2. Explanation

$\begin{array}{rcl} f (\frac{1}{2}, \frac{4}{3}) & = & {(\frac{1}{2})}^{2} {(\frac{4}{3})}^{3} \\ = & (\frac{1}{4}) (\frac{64}{27}) \\ = & \frac{16}{27} \\ f (0, π) & = & (0)^{2} (π)^{3} \\ = & (0) (π^{3}) \\ = & 0 \end{array}$

Domain of the function is $R^{2}$ and range is R.

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In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y) = x^{2} y^{3}, (\frac{1}{2}, \frac{4}{3}), (0, π)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.fx,y=x2y3,12,43,0,π

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.
$f (x, y) = x^{2} y^{3}, (\frac{1}{2}, \frac{4}{3}), (0, π)$