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Calculus II & III Study Guide: Vectors, Multivariable Functions, Sequences, Series, and Taylor Expansions

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Properties of Functions

  • Guided course
    Properties of Functions
    06:21

Properties of Functions

  • Guided course
    Properties of Functions
    06:21

Basic Rules of Differentiation

  • The Power Rule: Negative & Rational Exponents
    04:09
  • The Power Rule: Negative & Rational Exponents Example 1
    03:37
  • The Power Rule
    04:02

Introduction to Limits

  • Cases Where Limits Do Not Exist Example 2
    03:33
  • Finding Limits Numerically and Graphically
    6:47
  • Cases Where Limits Do Not Exist
    03:07

Continuity

  • Intro to Continuity
    05:34
  • Intro to Continuity Example 2
    00:57
  • Determine Continuity Algebraically
    05:25

Derivatives as Functions

  • Guided course
    Derivatives
    05:44

The Chain Rule

  • Intro to the Chain Rule Example 2
    07:39
  • Intro to the Chain Rule Example 3
    03:52
  • Intro to the Chain Rule Example 1
    07:01

The First Derivative Test

  • The First Derivative Test: Finding Local Extrema Example 3
    11:22
  • The First Derivative Test: Finding Local Extrema Example 2
    04:00
  • The First Derivative Test: Finding Local Extrema Example 4
    05:00

Concavity

  • Determining Concavity Given a Function Example 3
    02:33
  • Determining Concavity from the Graph of f' or f''
    03:56
  • Determining Concavity Given A Function Example 2
    6:08

The Second Derivative Test

  • The Second Derivative Test: Finding Local Extrema
    06:02
  • The Second Derivative Test: Finding Local Extrema Example 1
    05:34

Curve Sketching

  • Summary of Curve Sketching
    11:41
  • Summary of Curve Sketching Example 3
    06:22
  • Summary of Curve Sketching Example 1
    13:20

Sequences

  • Recursive Formulas
    5:59
  • Arithmetic Sequences - General Formula Example 2
    7:00
  • Geometric Sequences - Recursive Formula
    04:18

Series

  • Guided course
    Intro to Series: Partial Sums
    06:45
  • Guided course
    Intro to Series: Partial Sums Example 1
    04:33
  • Guided course
    Geometric Series
    06:00

Convergence Tests

  • Guided course
    Ratio Test
    05:35
  • Guided course
    Direct Comparison Test
    09:25
  • Guided course
    Ratio Test Example 1
    10:07

Introduction to Power Series

  • Intro to Power Series Example 1
    03:17
  • Representing Functions as Power Series Example 8
    07:19
  • Intro to Power Series
    05:58

Taylor Series & Taylor Polynomials

  • Taylor Polynomials
    07:00
  • Taylor Series
    08:42
  • Convergence of Taylor & Maclaurin Series
    08:26

Properties of Functions

  • Guided course
    Properties of Functions
    06:21