MATH 102 • Midterm II • Multivariable Calculus

Vector Functions and Curves

Domain of a Vector Function

Limit of a Vector Function

Derivative of a Vector Function

Integral of a Vector Function

Position, Velocity, Acceleration

Position, Velocity, Acceleration 2

Arc Length

Arc Length Parametrization

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

Equation of a Tangent Plane 1

Equation of a Tangent Plane 2

Horizontal Tangent Plane

Normal Vector to a Multivariable Function

Tangent Plane Approximation

Gradient Vector

Directional Derivative

Gradient and Directional Derivative

Extreme Values

Exam like Question 1

Exam like Question 2

Exam like Question 3

Extreme Values on Closed Regions 1

Extreme Values on Closed Regions 2

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

Limit and Continuity of Multivariable Functions

Directional Derivative and Tangent Plane

Vector Functions - Tangent Lines and Arclength

Partial Differentiation

Critical Points

Extreme Values

Intersection of Plane and Sphere

Applications of Maclaurin Series

Lines and Planes

Lines and Planes

Vector Valued Functions 1

Vector Valued Functions 2

Vector Valued Functions 3

Vector Valued Functions 4

Unit Tangent 1

Unit Tanget 2

Unit Tangent 3

Unit Tangent, Normal, Binormal

Arc Length 1

Arc Length 2

Arc Length 3

Arc Length 4

Arc Length 5

Curvature 1

Curvature 2

Arc Length, Curvature, Tangent

Integral of Vector Valued Functions

Position Vectors 1: Velocity, Speed, Acceleration

Position Vectors 2: Velocity, Speed, Acceleration

Position Vectors 3: Velocity, Speed, Acceleration

Position Vectors 4: Velocity, Speed, Acceleration

Parametric Equation for Tangent Line

Parameterization of the Curves 1

Parameterization of the Curves 2

Parameterization of the Curves 3

Parameterization of the Curves 4

Parameterization of the Curves 5

Position Vectors 5: Velocity, Speed, Acceleration

Position Vectors 6: Velocity, Speed, Acceleration

Length of the Curves 1

Length of the Curves 2

Length of the Curve 3

Length of the Curve 4

Length of the Curves 5

Length of the Curves 6

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

Continuity 1

Continuity 2

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Continuity and Partial Derivative

Partial Derivative 1

Partial Derivative 2

Partial Derivative 3

Higher Order Derivative 1

Higher Order Derivative 2

Chain Rule 1

Chain Rule 2

Chain Rule 3

Chain Rule and Higher Order Derivative 1

Chain Rule and Higher Order Derivative 2

Tangent Plane 1

Tangent Plane 2

Tangent Plane and Normal Line

Approximation 1

Approximation 2

Gradient and Tangent Plane 1

Gradient and Tangent Plane 2

Gradient and Directional Derivative 1

Gradient and Directional Derivative 2

Chain Rule and Tangent Plane

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values 4

Extreme Values on Closed Region 1

Extreme Values on Closed Region 2

Extreme Values on Closed Region 3

Extreme Values on Closed Region 4

Lagrange Multipliers 1

Lagrange Multipliers 2