MAT 1052 • Final • Calculus II

Distance Between Points

Vectors: Arithmetic, Parallelism and Unit Vector

Angles between Vectors: Dot Product

Cross Product of Vectors

Plane Equations

Planes Equations 2

Line Equations

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Exam like Question 6

Exam like Question 7

Exam like Question 8

Exam like Question 9

Exam like Question 10

Domain of Multivariable Functions

Level Curves

Level Curves and Level Surfaces

Graphs of Surfaces

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Exam like Question 5

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

Continuity of Multivariable Functions

Exam like Question 1

Exam like Question 2

Limit Definition of Partial Derivative

Partial Differentiation Rules 1

Partial Differentiation Rules 2

Higher Order Partial Differentiation

Chain Rule 1

Chain Rule 2

Chain Rule 3

Implicit Differentiation I

Implicit Differentiation II

Implicit Differentiation III

Implicit Higher Differentiation

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

Linear Approximation

Extreme Values

Exam like Question 1

Exam like Question 2

Exam like Question 3

Exam like Question 4

Extreme Values on Closed Regions

Lagrange Multipliers I

Lagrange Multipliers II

Lagrange Multipliers Using Gradient

Optimization with Lagrange Multipliers 1

Optimization with Lagrange Multipliers 2

Lagrange Multipliers with Two Constraints

Introduction to Double Integrals

Sketching the Area of Integration I

Sketching the Area of Integration II

Reversing the Order of Integration I

Reversing the Order of Integration II

Reversing the Order of Integration III

Volume Calculation by Double Integrals

Exam like Question 1

Exam like Question 2

Cartesian to Polar Coordinates

Double Integrals in Polar Coordinates I

Double Integrals in Polar Coordinates II

Double Integrals in Polar Coordinates III

Volume Calculation using Polar Coordinates

Area Calculation using Polar Coordinates

Introduction to Triple Integrals

Triple Integration over Regions

Graphs of Important Surfaces

Volume by Triple or Double Integrals

Volume between Two Surfaces

Triple Integrals: Reversing the Order

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Arc Length

Arc Length Parametrization

Line Integral 1

Line Integral 2

Line Integral 3

Line Integral 4

Line Integral 5

Vector Fields and Field Lines

Conservative Fields

Potential Function

Line Integrals of Vector Fields

Limit of Multivariable Functions 1

Limit of Multivariable Functions 2

Limit of Multivariable Functions 3

Limit of Multivariable Functions 4

Limit of Multivariable Functions 5

Limit of Multivariable Functions 6

Limit of Multivariable Functions 7

Limit of Multivariable Functions 8

Limit of Multivariable Functions 9

Limit of Multivariable Functions 10

Continuity 1

Continuity 2

Partial Derivative 1

Partial Derivative 2

Partial Derivative 3

Partial Derivative 4

Partial Derivative 5

Partial Derivative 6

Higher Order Differentiation 1

Higher Order Differentiation 2

Higher Order Differentiation 3

Higher Order Differentiation 4

Higher Order Differentiation 5

Tangent Plane 1

Tangent Plane 2

Tangent Plane 3

Tangent Plane 4

Tangent Plane and Normal Line 1

Tangent Plane and Normal Line 2

Tangent Plane and Normal Line 3

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule 4

Chain Rule 5

Chain Rule 6

Chain Rule and Tangent Plane

Gradient and Tangent Plane 1

Gradient and Tangent Plane 2

Gradient and Tangent Plane 3

Gradient and Directional Derivative 1

Gradient and Directional Derivative 2

Gradient and Directional Derivative 3

Gradient and Directional Derivative 4

Gradient and Directional Derivative 5

Gradient and Directional Derivative 6

Gradient and Directional Derivative 7

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values 4

Extreme Values 5

Extreme Values 6

Extreme Values on Closed Region 1

Extreme Values on Closed Region 2

Extreme Values on Closed Region 3

Extreme Values on Closed Region 4

Extreme Values on Closed Region 5

Extreme Values on Closed Region 6

Lagrange Multipliers 1

Lagrange Multipliers 2

Lagrange Multipliers 3

Lagrange Multipliers 4

Lagrange Multipliers 5

Lagrange Multipliers 6

Lagrange Multiplier 7

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Reversing the Order of Integration 4

Double Integral in Polar Coordinate 1

Double Integral in Polar Coordinate 2

Double Integral in Polar Coordinate 3

Double Integral in Polar Coordinate 4

Double Integral in Polar Coordinate 5

Double Integral in Polar Coordinate 6

Double Integral in Polar Coordinate 7

Double Integral in Polar Coordinate 8

Double Integral in Polar Coordinate 9

Double Integral in Polar Coordinate 10

Equation of Planes

Critical Points: Max-Min & Saddle Point

Lagrange Multipliers

The Chain Rule

Gradient & Directional Derivative

Double Integrals: Reversing the Order

Double Integrals: Polar Coordinates

Double Integrals & Volume

Convergence of Series

Convergence of Series