# Applications Of Multivariable Derivatives

10 Questions | Total Attempts: 131  Settings  Multi variable calculus are an extension of calculus in 1 variable to calculus with functions of several variables, like for instance, the differentiation and integration of functions involving multiple variables rather than just one. Test your knowledge about those types of applications by completing our small quiz.

• 1.
What are the typical operations involved in multivariable calculus?
• A.

Limits and continuity.

• B.

With limits exclusively.

• C.

With continuity exclusively.

• D.

None of the above.

• 2.
What does the partial derivative do?
• A.

It generalizes the notion of the derivative to higher dimensions.

• B.

It partially solves equations.

• C.

It only helps decipher the first steps into solving an equation.

• D.

It helps find exact results.

• 3.
What's the use of the del operator in vector calculus?
• A.

To define concepts of numbers, divergence and curl in terms of partial derivatives.

• B.

To define concepts of values, divergence and curl in terms of partial derivatives.

• C.

To define concepts of gradiant, divergence and curl in terms of partial derivatives.

• D.

To define concepts of functions, divergence and curl in terms of partial derivatives.

• 4.
How is a matrix of partial derivatives called?
• A.

• B.

Newton matrix

• C.

Jacobian matrix

• D.

Leibniz matrix

• 5.
What is the Jacobian matrix used for?
• A.

To represent the derivative of a function between 2 spaces or arbitrary dimensions.

• B.

To represent the derivative of a function between 2 spaces or arbitrary axis.

• C.

To represent the solution of a function between 2 spaces or arbitrary dimensions.

• D.

To represent the shaded area of a function between 2 spaces or arbitrary dimensions.

• 6.
How are differential equations containing partial derivatives called?
• A.

A Jacobian matrix.

• B.

A Newton Matrix

• C.

A calculus matrix

• D.

A Pythagorean matrix.

• 7.
What's the logic behind the Fubini theorem?
• A.

It guarantees that a multiple integral is evaluated as a repeated function.

• B.

It guarantees that a multiple integral is evaluated as a repeated formula.

• C.

It guarantees that a single integral is evaluated as a repeated integral.

• D.

It guarantees that a multiple integral is evaluated as a repeated integral.

• 8.
What are the surface and line integrals used for?
• A.

To change over curved manifolds such as surfaces and curves.

• B.

To integrate over straight manifolds such as surfaces and curves.

• C.

To integrate over curved manifolds such as surfaces and curves.

• D.

To integrate over curves uch as surfaces and curves.

• 9.
How many theorems of calculus are found in multiple dimension?
• A.

4

• B.

3

• C.

5

• D.

6

• 10.
What is the purpose of multivariate calculus?
• A.

They are used in optimal control of continuous time dynamic systems.

• B.

They are used in optimal control of continuous time dynamic measures.

• C.

They are used in optimal control of continuous time dynamic formula.

• D.

They are used in optimal control of continuous time dynamic values.

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