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

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Exam like Question 4

Exam like Question 5

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Exam like Question 10

Domain of Multivariable Functions

Level Curves

Level Curves and Level Surfaces

Graphs of Surfaces

Exam like Question 1

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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

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

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

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

Problem 1a) Convergence of Series

Problem 1b) Root Test

Problem 1c) Comparison Test

Problem 1d) The N-th Term Test

Problem 2) Power Series & Limit of a Sequence

Problem 3) Radius and Interval of Convergence

Problem 4) Vectors & Planes

Problem 5a) Equation of a Plane

Problem 5b) Equation of a Plane

Problem 6) Gradient, Tangent Plane and Directional Derivative

Problem 6) Gradient and Tangent Plane

Problem 7a) Domain of Multivariable Functions

Problem 7b) & 8a) Gradient and Applications

Problem 8) Directional Derivatives

Problem 9) Linear Approximation (Tangent Plane)

Problem 10) Extreme Values on Closed Region

Problem 11) Extremum Values on Closed Region

Problem 12) Chain Rule

Problem 13) Chain Rule

Problem 14a) Double Integrals in Rectangular Coordinates

Problem 14b) Volume by Double Integral

Problem 15a) Sketching & Reversing Order of Integration

Problem 15b) Sketching & Reversing Order of Integration

Problem 15c) Sketching & Reversing Order of Integration

Problem 15d) Double Integrals: Polar Coordinates

Problem 16) Double Integrals in Polar Coordinates

Problem 17) Theory Problems