# Difference between revisions of "Math 22 Functions of Several Variables"

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'''Example:''' Find the domain of <math>f(x,y)=\sqrt{9-x^2-y^2}</math> | '''Example:''' Find the domain of <math>f(x,y)=\sqrt{9-x^2-y^2}</math> | ||

− | Notice that : The radicand should be non-negative. So, <math>9-x^2-y^2\ge 0</math>, hence the domain is <math>x^2+y^2\le 9</math>. | + | Notice that : The radicand should be non-negative. So, <math>9-x^2-y^2\ge 0</math>, hence the domain is <math>x^2+y^2\le 9</math> (or the set of all point that lie inside the circle). |

Notice: <math>x^2+y^2= 9</math> is the circle center at <math>(0,0)</math>, radius 3. | Notice: <math>x^2+y^2= 9</math> is the circle center at <math>(0,0)</math>, radius 3. |

## Latest revision as of 07:06, 18 August 2020

## Definition of a Function of Two Variables

Let be a set of ordered pairs of real numbers. If to each ordered pair in there corresponds a unique real number , then is a function of and . The set is the domain of , and the corresponding set of values for is the range of . Functions of three, four, or more variables are defined similarly.

**Exercises 1** Given . Evaluate:

**1)**

Solution: |
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So, |

**2)**

Solution: |
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So, |

**3)**

Solution: |
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So, |

**4)**

Solution: |
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So, |

## The Domain and Range of a Function of Two Variables

**Example:** Find the domain of

Notice that : The radicand should be non-negative. So, , hence the domain is (or the set of all point that lie inside the circle).

Notice: is the circle center at , radius 3.

Since the point satisfies the inequality . Hence the range is

**This page were made by Tri Phan**