MATH 102 • Midterm II • Calculus II

Distance Between Points 1

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

Parametric Equations 1

Parametric Equations 2

Parametric Equations 3

Calculus with Parametric Equations

Length of a Curve

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

Tangent, Normal, Binormal Vectors and Curvature, Torsion

Calculation of Tangent, Normal, Binormal Vectors and Curvature, Torsion

Domain of Functions

Level Curves

Limits of Multivariable Functions 1

Limits of Multivariable Functions 2

Limits of Multivariable Functions 3

The Squeeze Theorem

Continuity of Multivariable Functions

Exam like Question 1

Exam like Question 2

Sertoz Theorem

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

Linear Approximation

Implicit Differentiation

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

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 Function 8

Limit of Multivariable Functions 9

Limit of Multivariable Functions 10

Limit of Multivariable Function 11

Continuity 1

Continuity 2

Bonus Problem: Limit & Continuity

Definition of Partial Derivative 1

Definition of Partial Derivative 2

Definition of Partial Derivative 3

Tangent Plane 1

Tangent Plane 2

Tangent Plane 3

Tangent Plane and Normal Line 1

Tangent Plane and Normal Line 2

Approximation 1

Approximation 2

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

Higher Order Derivative 1

Higher Order Derivative 2

Higher Order Derivative 3

Chain Rule 1

Chain Rule 2

Chain Rule and Tangent Plane

Chain Rule and Higher Order Derivative

Extreme Values 1

Extreme Values 2

Extreme Values 3

Extreme Values (Spring 2021)

Extreme Values (Spring 2018)

Tangent Plane (Spring 2013)

Chain Rule (Spring 2020)

Chain Rule (Spring 2011)

Tangent Plane & Chain Rule (Spring 2016)

Tangent Plane & Chain Rule (Spring 2014)

Gradient and Tangent Plane (Spring 2019)

Directional Derivative (Spring 2018)

Directional Derivative (Spring 2011)

Directional Derivative (Spring 2022)

Directional Derivative (Spring 2020)

Directional Derivative (Spring 2019)

Directional Derivative (Spring 2017)

Directional Derivative (Spring 2016)

Directional Derivative (Spring 2014)

Directional Derivative (Spring 2013)

Higher Order Differentiation (Spring 2016)

Higher Order Differentiation (Spring 2017)

Higher Order Differentiation (Spring 2015)

Higher Order Differentiation (Spring 2019)

Higher Order Differentiation (Spring 2018)

Higher Order Differentiation (Spring 2013)

Higher Order Differentiation (Spring 2010)

Higher Order Differentiation (Spring 2011)

Parametric Equations (2D)

Parametric Equations (2D)

Vector Valued Functions - Limit

Vector Valued Functions - Derivative

Tangent Line to Vector Functions

Integral of Vector Valued Functions

Integral of Vector Valued Functions

Position Vectors: Velocity, Speed, Acceleration

Position Vectors: Velocity, Speed, Acceleration

Position Vectors: Velocity, Speed, Acceleration

Arc Length

Arc Length

Unit Tangent Vector

Unit Tangent Vector, Curvature, Arc Length

Cross Product Applications

Equation of a Plane

Equation of a Plane

Equation of a Plane

Equation of a Plane

Equation of a Plane

Coplanarity

Intersection of Planes

Intersection of Planes

Intersection of Lines

Planes and Lines

Planes and Lines

Plane and Lines

Planes and Lines

Plane and Lines

Planes and Lines

Angle between Planes

Angle between Lines

Distance of a Point to Lines & Planes

Distance of a Point to Lines & Planes

Distance of a Point to Lines & Planes

Distance of a Point to Lines & Planes

Planes and Lines (Spring 2023)

Vector Functions (Spring 2023)

Tangent Plane (Spring 2023)

Tangent Plane (Spring 2021)

Vector Functions and Planes (Spring 2019)

Vector Functions,Planes and Lines (Spring 2020)

Vector Functions (Spring 2015)

Spring 2022: Limits of Multivariable Functions

Spring 2020: Limits of Multivariable Functions

Spring 2022: Extreme Values

Spring 2019 : Extreme Values

Spring 2023: Extreme Values

Spring 2023: Gradient - Directional Derivatives

Spring 2024: Sertoz Theorem

Spring 2024: Sertoz Theorem

Spring 2024: Limits of Multivariable Functions

Spring 2023: Gradient - Directional Derivatives

Spring 2024: Gradient - Directional Derivatives

Spring 2024: Vector Functions