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

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 1

Extreme Values on Closed Regions 2

Lagrange Multipliers I

Lagrange Multipliers II

Optimization with Lagrange Multipliers 1

Optimization with Lagrange Multipliers 2

Lagrange Multipliers with Two Constraints

Intuition: Double Integrals

Volume Calculation with Double Integration

Area Calculation with Double Integral

Sketching the Area of Integration 1

Sketching the Area of Integration 2

Sketching the Area of Integration 3

Reversing the Order of Integration 1

Reversing the Order of Integration 2

Reversing the Order of Integration 3

Cartesian to Polar Coordinates 1

Cartesian to Polar Coordinates 2

Polar to Cartesian Coordinates

Double Integrals in Polar Coordinates 1

Double Integrals in Polar Coordinates 2

Double Integrals in Polar Coordinates 3

Double Integrals in Polar Coordinates 4

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