MATH 132 • Final • Calculus II

Domain of Functions

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

The Squeeze Theorem

Continuity of Multivariable Functions

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

Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

Tangent Plane Approximation

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

Definition of Partial Derivative 1

Definition of Partial Derivative 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 Vector

Directional Derivative

Gradient and Directional Derivative

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 Using Gradient

Lagrange Multipliers with Two Constraints

Maxima-Minima and Saddle Points 1

Maxima-Minima and Saddle Points 2

Maxima-Minima and Saddle Points 3

Maxima-Minima and Saddle Points 4

Maxima-Minima and Saddle Points 5

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

Extreme Values on Closed Region 7

Lagrange Multipliers 1

Lagrange Multiplier 2

Lagrange Multiplier 3

Lagrange Multiplier 4

Lagrange Multiplier 5

Lagrange Multipliers 6

Gradient & Tangent Plane

Gradient & Tangent Plane

Gradient & Tangent Plane

Gradient ,Tangent Plane and Normal Lines

Gradient ,Tangent Plane and Normal Lines

Gradient & Directional Derivative

Directional Derivatives

Gradient and Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

Gradient & Directional Derivative

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

Double Integrals: Reversing the Order of Integration

Double Integrals: Reversing the Order of Integration

Double Integrals: Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Reversing the Order of Integration

Double Integral on Cartesian Coordinates

Double Integral on Cartesian Coordinates

Double Integrals in Rectangular Coordinates

Critical Points

Gradient and Directional Derivative

Double Integrals: Reversing the Order

Double Integral - Volume

Double Integral - Area

Double Integral - Polar Coordinates

Maclaurin Series

Limits of Multivariable Functions

Critical Points & Extreme Values

Directional Derivative

Equation of a Tangent Plane

Double Integral: Reversing the Order

Double Integral - Polar Coordinates

Convergence of Series : Alternating Series Test

Limits of Multivariable Functions

Gradient, Directional Derivative, Tangent Plane

Criticial Points, Max-Min-Saddle Points

Polar Coordinates & Reversing the Order

Limit using Taylor Series

Limit of Multivariable Functions

Continuity of Multivariable Functions

Extreme Values on Closed Region

Implicit Differentiation

Polar Coordinates & Reversing the Order

Lines & Planes Equations

Limits of Multivariable Functions

Linear (Tangent Plane) Approximation

The Chain Rule

Gradient & Directional Derivatives

Criticial Points, Max-Min-Saddle Points

Lagrange Multipliers

Double Integral : Cartesian Coordinates

Double Integral : Reversing the Order