Multivariable Calculus Quizzes, Questions & Answers

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Partial Derivatives Quizzes

Are you familiar with the mathematical rule, which wants that when all other variables are held constant, then the partial derivative rules for dealing with coefficients, simple po...

Questions: 10 | Attempts: 182 | Last updated: Mar 18, 2025

Sample Question
What's the particularity of the function f(x,y) = x^2(y)/ ((x^4) +( y^2))?

It is that it approaches "100" along any line through the origin.

It is that it approaches "1" along any line through the origin.

It is that it approaches "0" along any line through the origin.

It is that it approaches "-1" along any line through the origin.

Partial Derivatives Made Simple: Definitions, Tables & Mixed Partials

Partial derivatives reveal how multivariable functions change when one variable varies while the others remain fixed. This quiz deepens your understanding of first-order and higher...

Questions: 15 | Attempts: 11 | Last updated: Dec 17, 2025

Sample Question
For the function f(x,y) = 3x²y + 5xy³, find the partial derivative with respect to x.

6xy + 5y³

3x² + 15xy²

6xy + 15xy²

3x²*y + 5y³

Partial Derivatives Basics: First-Order Derivatives & Rate-of-Change Interpretation

Partial derivatives allow us to study how a multivariable function changes when one variable varies while the others remain fixed. They play a central role in multivariable calculu...

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
What is the partial derivative of f(x, y) = 3x²y + 4y³ with respect to x?

6xy

6xy + 12y²

3x² + 12y²

3x² + 4y³

All Partial Derivatives Quizzes

Gradient Vectors Quizzes

Vector Quiz Questions and answers

Let us find out how much you know or understand through these vector quiz questions and answers. Vector is an element of vector space in math and physics. There are many other name...

Questions: 10 | Attempts: 11905 | Last updated: Mar 22, 2025

Sample Question
Which of these expresses a vector quantity?

10kg

10kg to the north

10 m/s

10 m/s to the east

persamaan garis lurus 2

This quiz titled 'persamaan garis lurus 2' focuses on the calculation of gradients and coordinates in linear equations, testing understanding through various problem-solving questi...

Questions: 10 | Attempts: 2236 | Last updated: Mar 22, 2025

Sample Question
gradien garis yang memiliki persamaan y = 6 - 2x adalah ....

6

- 6

2

- 2

X IPA MATEMATIKA MINAT

This advanced mathematics quiz focuses on vector calculus, exploring concepts like orthogonal projections, vector operations, and angle measurements between vectors.

Questions: 20 | Attempts: 558 | Last updated: Mar 22, 2025

Sample Question
Diketahui vektor a = pi + 2j – k, b = 4i – 3j + 6k, dan c = 2i – j + 3k. Jika a tegak lurus b, maka hasil dari (a – 2b) . (3c) adalah….

171

63

-63

-111

All Gradient Vectors Quizzes

Vector Fields Quizzes

GK Questions For Math

Explore advanced mathematical concepts in this GK quiz tailored for enthusiasts. Dive into Euclidean geometry, harmonic functions, exponential derivatives, tensor analysis, statist...

Questions: 15 | Attempts: 235 | Last updated: Mar 17, 2025

Sample Question
Which of Euclid's postulates dealt with parallel lines and led to developing non-Euclidean geometry?

Third

Fourth

First

Fifth

All Vector Fields Quizzes

Line Integrals Quizzes

Line Integrals: Scalar Integrals & Arc Length Fundamentals

This quiz focuses on evaluating line integrals—both scalar line integrals involving arc length and vector line integrals representing work done by force fields. You will prac...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Compute the line integral ∫_C 2(x+y) ds, where C is the straight line segment from (0, 0) to (3, 4).

15

25

35

45

Line Integrals: Applications in Physics, Work, Energy & Geometry

This quiz explores essential concepts in line integrals, conservative vector fields, and the Fundamental Theorem of Line Integrals. You’ll work with scalar and vector fields,...

Questions: 13 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
A particle moves along the curve defined by x² + y² = 25. If the force field acting on the particle is F(x, y) = <2x, 2y>, what is the total work done by the force field as the particle moves from (5, 0) to (0, 5) along the arc?

25

50

5

Line Integrals: Work, Vector Fields & Parametric Paths

This quiz explores the core techniques and interpretations of line integrals in both scalar fields and vector fields. You will practice parameterizing curves—including straig...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Which of the following represents the correct setup for the scalar line integral of the function f(x, y) = x + y over the curve C, where C is the line segment from (0, 0) to (1, 1)?

∫₀¹ (t + t) dt

∫₀¹ (t + t) * √(2) dt

∫₀¹ (t² + t²) dt

∫₀¹ (x + y) dx dy

All Line Integrals Quizzes

Divergence And Curl Quizzes

Divergence & Curl: Computing Operators for Common 2D & 3D Vector Fields

Divergence and curl are central tools in vector calculus, revealing how vector fields behave in physical and mathematical systems. Divergence measures how much a field spreads outw...

Questions: 15 | Attempts: 12 | Last updated: Dec 16, 2025

Sample Question
Let F = < 3x, 5y, -2z > be a vector field representing the velocity of a fluid. Calculate the divergence of F.

6

< 3, 5, -2 >

10

Divergence & Curl: Core Definitions, Notation & Geometric Insight

Divergence and curl are two of the most fundamental operators in vector calculus, revealing how vector fields behave in space. Divergence measures how much a field spreads out from...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
What is the divergence of a vector field F = P i + Q j + R k in three dimensions?

∂P/∂x + ∂Q/∂y + ∂R/∂z

∂R/∂y - ∂Q/∂z, ∂P/∂z - ∂R/∂x, ∂Q/∂x - ∂P/∂y

∂P/∂y + ∂Q/∂z + ∂R/∂x

∂P/∂z + ∂Q/∂x + ∂R/∂y

Divergence & Curl: Fluid Flow, Sources, Sinks & Rotational Motion

Divergence and curl are fundamental tools in vector calculus, used to describe how vector fields behave in space. Divergence measures how much a field spreads outward from a point,...

Questions: 15 | Attempts: 10 | Last updated: Dec 16, 2025

Sample Question
Using the Del (nabla) operator ∇ = < ∂/∂x, ∂/∂y, ∂/∂z >, how is the divergence of a vector field F represented symbolically?

∇ × F

∇ · F

∇ F

|∇ F|

All Divergence And Curl Quizzes

Top Trending Multivariable Calculus Quizzes

Thinking About Multivariable Functions

Multivariable calculus is defined as the extension of calculus in 1 variable to calculus with function of several variables: the differentiation and integration of functions involving multiple variables, rather than just 1. If...

Questions: 10 | Attempts: 266 | Last updated: Mar 20, 2025

Sample Question 1
What is the advantage that comes with multivariable calculus?

They yield many counter-intuitive results not demonstrated by single-variable function.

They yield many results not demonstrated by single-variable function.

They yield many counter-intuitive results not demonstrated by the f(x) function.

They reveal many counter-intuitive results not demonstrated by single-variable function.

Sample Question 2
What are the main points of study in multivariable calculus?

Continuity

Limits

Limits and continuity.

F(x)

Applications Of Multivariable Derivatives

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...

Questions: 10 | Attempts: 189 | Last updated: Mar 20, 2025

Sample Question 1
What are the typical operations involved in multivariable calculus?

Limits and continuity.

With limits exclusively.

With continuity exclusively.

None of the above.

Sample Question 2
What does the partial derivative do?

It generalizes the notion of the derivative to higher dimensions.

It partially solves equations.

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

It helps find exact results.

Multivariable Calculus Quizzes, Questions & Answers

Popular Multivariable Calculus Topics

Partial Derivatives Quizzes

Gradient Vectors Quizzes

Vector Fields Quizzes

Line Integrals Quizzes

Divergence And Curl Quizzes

Top Trending Multivariable Calculus Quizzes

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