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 14, 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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Students have asked these similar questions

Is the function f(x) continuous at x = 1? (x) 7 6 5 4 3 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -71 Select the correct answer below: The function f(x) is continuous at x = 1. The right limit does not equal the left limit. Therefore, the function is not continuous. The function f(x) is discontinuous at x = 1. We cannot tell if the function is continuous or discontinuous.

Question Is the function f(x) shown in the graph below continuous at x = -5? f(z) 7 6 5 4 2 1 0 -10 -6 -5 -4 1 0 2 3 5 7 10 -1 -2 -3 -4 -5 Select the correct answer below: The function f(x) is continuous. The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. We cannot tell if the function is continuous or discontinuous.

The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = -1. 654 -2- -7-6-5-4- 2-1 1 2 5 6 7 02. Select all that apply: ☐ f(x) is not continuous at x = -1 because f(-1) is not defined. ☐ f(x) is not continuous at x = −1 because lim f(x) does not exist. x-1 ☐ f(x) is not continuous at x = −1 because lim ƒ(x) ‡ ƒ(−1). ☐ f(x) is continuous at x = -1 J-←台

Answer 2

Question

Chapter 14, 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 14, 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 4

Question

Chapter 14, 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 14, 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 14, 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 14, 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.