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

Lines and Planes

Vectors and Planes

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