MATH 114 • Midterm II • Mathematics II

Distance Between Points

Cosine Theorem in 3D & Euclidean N-Space

Vectors: Arithmetic, Parallelism and Unit Vector

Angles between Vectors : Dot Product

Vector Projection

Cross Product of Vectors

Applications of Cross Product

Plane Equations

Line Equations 1

Line Equations 2

Intersection of Planes

Intersection of Planes and Lines

Distance of a Point to Lines & Planes

Domain of Multivariable Functions

Level Curves

Level Curves and Level Surfaces

Graphs of Surfaces

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

Multivariable Squeeze Theorem

Continuity of Multivariable Functions

Limits with Polar Coordinates

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

Extreme Values

Extreme Values on Restricted Regions 1

Extreme Values on Restricted Regions 2

Optimization With Lagrange Multipliers

Lagrange Multipliers Example-1

Lagrange Multipliers Example-2

Lagrange Multipliers Example-3

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Functions

Limit of Multivariable Function

Limit of Multivariable Function

Limit of Multivariable Function

Limit of Multivariable Function

Limit of Multivariable Function

Limit of Multivariable Function

Continuity

Continuity

Definition of Partial Derivative

Definition of Partial Derivative

Partial Derivative

Partial Derivative

Partial Derivative

Partial Derivative

Partial Derivative

Partial Derivative

Higher Order Differentiation

Higher Order Differentiation

Higher Order Differentiation

Higher Order Differentiation

Higher Order Differentiation

Partial Derivative - Implicit

Partial Derivative - Implicit - Formula

Chain Rule

Chain Rule

Chain Rule

Chain Rule

Chain Rule

Chain Rule

Chain Rule and Tangent Plane

Tangent Plane

Tangent Plane

Tangent Plane

Tangent Plane

Tangent Plane and Normal Line

Tangent Plane and Normal Line

Tangent Plane and Normal Line

Tangent Plane Approximation

Tangent Plane Approximation

Tangent Plane Approximation

Tangent Plane Approximation

Gradient and Tangent Plane

Gradient and Tangent Plane

Gradient and Tangent Plane

Gradient and Directional Derivative

Gradient and Directional Derivative

Gradient and Directional Derivative

Gradient and Directional Derivative

Gradient and Directional Derivative

Gradient and Directional Derivative

Gradient and Directional Derivative

Extreme Values

Extreme Values

Extreme Values

Extreme Values

Extreme Values

Extreme Values

Extreme Values on Closed Region

Extreme Values on Closed Region

Extreme Values on Closed Region

Extreme Values on Closed Region

Extreme Values on Closed Region

Extreme Values on Closed Region

Lagrange Multipliers

Lagrange Multipliers

Lagrange Multipliers

Lagrange Multipliers

Lagrange Multipliers

Lagrange Multipliers

Lagrange Multipliers

Domain of Multivariable Functions

Equation of Tangent Plane

Lagrange Multipliers

Extreme Values & Saddle Points