Provide notes on a real-valued function of two independent variables and three independent variables with example.

Question

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Answer 1

Question

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

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Answer 2

Question

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

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Answer 3

Question

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

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Answer 4

Question

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

Answer 6

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.

If f is a function of two independent variables, that is the independent variables x and y and the dependent variable z.

Example:

The dependent variable z as a function of two variables is z=y−x2.

If f is a function of three independent variables, that is the independent variables x, y, and z and the dependent variable w.

Example:

The dependent variable w as a function of three variables is w=x2+y2+z2.

Answer 7

Chapter 13, Problem 1GYR

To determine

Provide notes on a real-valued function of two independent variables and three independent variables with example.

Answer 8

Expert Solution & Answer

Explanation of Solution

Suppose D is a set of n-tuples of real numbers (x1, x2,…,xn).

A real-valued function f on D is a rule that assigns a real number w=f(x1, x2,…,xn) to each element in D. The set D is the function’s range. The symbol w is the dependent variable of f, and f is said to be a function of the n independent variables x1 to xn. We also call the xj's the function’s input variables and call w the function’s output variable.