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ap calculus - mid-year review: limits & derivatives

originally streamed in 2019 with Jenni DurostTeacher
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Review limits, derivatives, and integrals for your AP Calculus mid-year exam. This 80-minute session walks through practice problems and key concepts from first semester calculus to help you prepare for your assessment. This review covers the major ...more

covered in this stream

units
Unit 1 – Limits and ContinuityUnit 2 – Fundamentals of DifferentiationUnit 3 – Composite, Implicit, and Inverse FunctionsUnit 5 – Analytical Applications of Differentiation
topics
What is a Limit?1.11 Defining Continuity at a Point1.6 Determining Limits Using Algebraic Manipulation1.14 Connecting Infinite Limits and Vertical Asymptotes1.15 Connecting Limits at Infinity and Horizontal Asymptotes1.8 Determining Limits Using the Squeeze Theorem1.9 Connecting Multiple Representations of LimitsAlgebraic Limits2.5 Applying the Power Rule2.6 Derivative Rules2.7 Derivatives of cos x, sinx, e^x, and ln x2.8 The Product Rule2.9 The Quotient Rule3.1 The Chain Rule3.2 Implicit Differentiation5.2 Extreme Value Theorem, Global vs Local Extrema, and Critical Points5.3 Determining Intervals on Which a Function is Increasing or Decreasing5.4 Using the First Derivative Test to Determine Relative (Local) Extrema5.6 Determining Concavity5.7 Using the Second Derivative Test to Determine Extrema5.8 Sketching Graphs of Functions and Their Derivatives5.9 Connecting a Function, Its First Derivative, and its Second Derivative

timestamps

  • 0:00

    Introduction to Review

  • 0:30

    Session Overview

  • 1:31

    Topics and Approach

  • 2:03

    Limits Basics

  • 3:05

    Limit Definition

  • 4:06

    Continuity Criteria

  • 5:07

    Proving Continuity

  • 6:12

    Asymptotes with Limits

  • 7:33

    Vertical Asymptote Example

  • 9:06

    Infinite Limits

  • 10:09

    Horizontal Asymptotes

  • 11:41

    Evaluating Limits

  • 12:42

    Limit Example Positive Side

  • 15:26

    Determining Infinity Direction

  • 17:35

    Indeterminate Forms

  • 18:07

    Conjugate Method

  • 20:22

    Limits at Infinity

  • 24:30

    Sin x over x Limit

  • 26:07

    Composition of Limits

  • 30:17

    Direction in Compositions

  • 31:19

    Composition Example

  • 33:27

    Introduction to Derivatives

  • 35:00

    Basic Derivative Rules

  • 37:50

    Product Quotient Chain Rules

  • 38:22

    Product Rule Example

  • 40:28

    Quotient Rule Example

  • 42:10

    Chain Rule Example

  • 47:28

    Implicit Differentiation

  • 52:12

    Derivative Applications

  • 53:44

    First Derivative Test

  • 54:17

    Second Derivative Concavity

  • 54:48

    Function Analysis Example

  • 1:00:22

    Resuming Critical Points

  • 1:03:00

    Solving for Theta

  • 1:04:36

    Sign Chart Analysis

  • 1:06:46

    Increase Decrease Intervals

  • 1:08:21

    Min Max Identification

  • 1:09:59

    Second Derivative Test

  • 1:10:29

    Concavity Sign Chart

  • 1:12:04

    Concavity Intervals

  • 1:12:35

    Graph Sketching

  • 1:15:50

    Wrapping Up Session

  • 1:16:52

    Feedback and Resources

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history

šŸŒŽ ap world historyšŸ‡ŗšŸ‡ø ap us historyšŸ‡ŖšŸ‡ŗ ap european history

social science

āœŠšŸæ ap african american studiesšŸ—³ļø ap comparative government🚜 ap human geographyšŸ’¶ ap macroeconomicsšŸ¤‘ ap microeconomics🧠 ap psychologyšŸ‘©šŸ¾ā€āš–ļø ap us government

english & capstone

āœšŸ½ ap english languagešŸ“š ap english literaturešŸ” ap researchšŸ’¬ ap seminar

arts

šŸŽØ ap art & designšŸ–¼ļø ap art historyšŸŽµ ap music theory

science

🧬 ap biology🧪 ap chemistryā™»ļø ap environmental sciencešŸŽ” ap physics 1🧲 ap physics 2šŸ’” ap physics c: e&māš™ļø ap physics c: mechanics

math & computer science

🧮 ap calculus abā™¾ļø ap calculus bcšŸ“ ap precalculusšŸ“Š ap statisticsšŸ’» ap computer science aāŒØļø ap computer science p

world languages

šŸ‡ØšŸ‡³ ap chinesešŸ‡«šŸ‡· ap frenchšŸ‡©šŸ‡Ŗ ap germanšŸ‡®šŸ‡¹ ap italianšŸ‡ÆšŸ‡µ ap japanesešŸ›ļø ap latinšŸ‡ŖšŸ‡ø ap spanish languagešŸ’ƒšŸ½ ap spanish literature

go beyond AP

high school exams

āœļø PSATšŸŽ“ Digital SATšŸŽ’ ACT

honors classes

šŸ¬ honors algebra IIšŸ«€ honors anatomyšŸ‡ honors biologyšŸ‘©šŸ½ā€šŸ”¬ honors chemistryšŸ’² honors economicsšŸ“ honors geometryāš¾ļø honors physicsšŸ“ honors pre-calculusšŸ“Š honors statisticsšŸ—³ļø honors us governmentšŸ‡ŗšŸ‡ø honors us historyšŸŒŽ honors world history

college classes

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APĀ® and SATĀ® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.