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site_name: AP Calculus Notes

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repo_name: Pagius5/AP Calc

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nav:
  - "Home": index.md
  - "I. Limits & Continuity":
    - "Unit 01 - Limits & Continuity": unit01/limits.md
  - "II. Differential Calculus":
    - "Unit 02 - Basic Differentiation": unit02/deriv_basic.md
    - "Unit 03 - Advanced Differentiation": unit03/deriv_advanced.md
    - "Unit 04 - Contextual Applications": unit04/apps_context.md
    - "Unit 05 - Analytical Applications": unit05/apps_analytic.md
  - "III. Integral Calculus":
    - "Unit 06 - Integration": unit06/integration.md
    - "Unit 07 - Differential Equations": unit07/diff_eq.md
    - "Unit 08 - Applications of Integration": unit08/apps_int.md
  - "IV. Miscellaneous (BC only)":
    - "Unit 09 - Parametric & Polar": unit09/parametric_polar.md
    - "Unit 10 - Infinite Series": unit10/series.md

  # - "I. Limits & Continuity":
  #   - "Unit 01 - Limits & Continuity":
  #       - "1.1 Introducing Calculus: Can Change Occur at an Instant?": unit01/1_1.md
  #       - "1.2 Defining Limits and Using Limit Notation": unit01/1_2.md
  #       - "1.3 Estimating Limit Values from Graphs": unit01/1_3.md
  #       - "1.4 Estimating Limit Values from Tables": unit01/1_4.md
  #       - "1.5 Determining Limits Using Algebraic Properties of Limits": unit01/1_5.md
  #       - "1.6 Determining Limits Using Algebraic Manipulation": unit01/1_6.md
  #       - "1.7 Selecting Procedures for Determining Limits": unit01/1_7.md
  #       - "1.8 Determining Limits Using the Squeeze Theorem": unit01/1_8.md
  #       - "1.9 Connecting Multiple Representations of Limits": unit01/1_9.md
  #       - "1.10 Exploring Types of Discontinuities": unit01/1_10.md
  #       - "1.11 Defining Continuity at a Point": unit01/1_11.md
  #       - "1.12 Confirming Continuity over an Interval": unit01/1_12.md
  #       - "1.13 Removing Discontinuities": unit01/1_13.md
  #       - "1.14 Connecting Infinite Limits and Vertical Asymptotes": unit01/1_14.md
  #       - "1.15 Connecting Limits at Infinity and Horizontal Asymptotes": unit01/1_15.md
  #       - "1.16 Working with the Intermediate Value Theorem (IVT)": unit01/1_16.md

  # - "II. Differential Calculus":
  #   - "Unit 02 - Basic Differentiation":
  #       - "2.1 Defining Average and Instantaneous Rates of Change": unit02/2_1.md
  #       - "2.2 Defining the Derivative of a Function": unit02/2_2.md
  #       - "2.3 Estimating Derivatives at a Point": unit02/2_3.md
  #       - "2.4 Connecting Differentiability and Continuity": unit02/2_4.md
  #       - "2.5 Applying the Power Rule": unit02/2_5.md
  #       - "2.6 Derivative Rules: Constant, Sum, Difference, and Multiple": unit02/2_6.md
  #       - "2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)": unit02/2_7.md
  #       - "2.8 The Product Rule": unit02/2_8.md
  #       - "2.9 The Quotient Rule": unit02/2_9.md
  #       - "2.10 Derivatives of Tangent, Cotangent, Secant, and Cosecant": unit02/2_10.md
  #   - "Unit 03 - Advanced Differentiation":
  #       - "3.1 The Chain Rule": unit03/3_1.md
  #       - "3.2 Implicit Differentiation": unit03/3_2.md
  #       - "3.3 Differentiating Inverse Functions": unit03/3_3.md
  #       - "3.4 Differentiating Inverse Trigonometric Functions": unit03/3_4.md
  #       - "3.5 Selecting Procedures for Calculating Derivatives": unit03/3_5.md
  #       - "3.6 Calculating Higher-Order Derivatives": unit03/3_6.md
  #   - "Unit 04 - Contextual Applications":
  #       - "4.1 Interpreting the Meaning of the Derivative in Context": unit04/4_1.md
  #       - "4.2 Straight-Line Motion: Position, Velocity, and Acceleration": unit04/4_2.md
  #       - "4.3 Rates of Change in Applied Contexts (Non-Motion)": unit04/4_3.md
  #       - "4.4 Introduction to Related Rates": unit04/4_4.md
  #       - "4.5 Solving Related Rates Problems": unit04/4_5.md
  #       - "4.6 Linearization and Local Linearity": unit04/4_6.md
  #       - "4.7 Using L'Hospital's Rule for Indeterminate Forms": unit04/4_7.md
  #   - "Unit 05 - Analytical Applications":
  #       - "5.1 Using the Mean Value Theorem": unit05/5_1.md
  #       - "5.2 Extreme Value Theorem, Global vs Local Extrema": unit05/5_2.md
  #       - "5.3 Determining Intervals of Increase or Decrease": unit05/5_3.md
  #       - "5.4 The First Derivative Test for Extrema": unit05/5_4.md
  #       - "5.5 Using the Candidates Test for Absolute Extrema": unit05/5_5.md
  #       - "5.6 Determining Concavity of Functions": unit05/5_6.md
  #       - "5.7 Using the Second Derivative Test for Extrema": unit05/5_7.md
  #       - "5.8 Sketching Graphs of Functions and Their Derivatives": unit05/5_8.md
  #       - "5.9 Connecting a Function, Its First, and Second Derivative": unit05/5_9.md
  #       - "5.10 Introduction to Optimization Problems": unit05/5_10.md
  #       - "5.11 Solving Optimization Problems": unit05/5_11.md
  #       - "5.12 Exploring Behaviors of Implicit Relations": unit05/5_12.md

  # - "III. Integral Calculus":
  #   - "Unit 06 - Integration":
  #       - "6.1 Exploring Accumulations of Change": unit06/6_1.md
  #       - "6.2 Approximating Areas with Riemann Sums": unit06/6_2.md
  #       - "6.3 Definite Integral Notation": unit06/6_3.md
  #       - "6.4 FTC and Accumulation Functions": unit06/6_4.md
  #       - "6.5 Interpreting Accumulation Functions": unit06/6_5.md
  #       - "6.6 Properties of Definite Integrals": unit06/6_6.md
  #       - "6.7 FTC and Definite Integrals": unit06/6_7.md
  #       - "6.8 Finding Antiderivatives and Indefinite Integrals": unit06/6_8.md
  #       - "6.9 Integrating Using Substitution": unit06/6_9.md
  #       - "6.10 Integrating Functions Using Long Division & Square": unit06/6_10.md
  #       - "6.11 Integrating Using Integration by Parts (BC Only)": unit06/6_11.md
  #       - "6.12 Using Linear Partial Fractions (BC Only)": unit06/6_12.md
  #       - "6.13 Evaluating Improper Integrals (BC Only)": unit06/6_13.md
  #       - "6.14 Selecting Techniques for Antidifferentiation": unit06/6_14.md
  #   - "Unit 07 - Differential Equations":
  #       - "7.1 Modeling Situations with Differential Equations": unit07/7_1.md
  #       - "7.2 Verifying Solutions for Differential Equations": unit07/7_2.md
  #       - "7.3 Sketching Slope Fields": unit07/7_3.md
  #       - "7.4 Reasoning Using Slope Fields": unit07/7_4.md
  #       - "7.5 Approximating Solutions Using Euler's Method (BC Only)": unit07/7_5.md
  #       - "7.6 General Solutions Using Separation of Variables": unit07/7_6.md
  #       - "7.7 Particular Solutions and Separation of Variables": unit07/7_7.md
  #       - "7.8 Exponential Models with Differential Equations": unit07/7_8.md
  #       - "7.9 Logistic Models with Differential Equations (BC Only)": unit07/7_9.md
  #   - "Unit 08 - Applications of Integration":
  #       - "8.1 Average Value of a Function on an Interval": unit08/8_1.md
  #       - "8.2 Connecting Position, Velocity, and Acceleration": unit08/8_2.md
  #       - "8.3 Accumulation Functions in Applied Contexts": unit08/8_3.md
  #       - "8.4 Finding Area Between Curves (f(x))": unit08/8_4.md
  #       - "8.5 Finding Area Between Curves (f(y))": unit08/8_5.md
  #       - "8.6 Finding Area Between Curves with Intersections": unit08/8_6.md
  #       - "8.7 Volumes with Cross Sections: Squares & Rectangles": unit08/8_7.md
  #       - "8.8 Volumes with Cross Sections: Triangles & Semicircles": unit08/8_8.md
  #       - "8.9 Volume with Disc Method: Revolving Around Axis": unit08/8_9.md
  #       - "8.10 Volume with Disc Method: Revolving Around Other Axes": unit08/8_10.md
  #       - "8.11 Volume with Washer Method: Revolving Around Axis": unit08/8_11.md
  #       - "8.12 Volume with Washer Method: Revolving Around Other Axes": unit08/8_12.md
  #       - "8.13 Arc Length of a Curve and Distance Traveled (BC Only)": unit08/8_13.md

  # - "IV. Miscellaneous (BC only)":
  #   - "Unit 09 - Parametric & Polar":
  #       - "9.1 Defining and Differentiating Parametric Equations": unit09/9_1.md
  #       - "9.2 Second Derivatives of Parametric Equations": unit09/9_2.md
  #       - "9.3 Finding Arc Lengths of Parametric Curves": unit09/9_3.md
  #       - "9.4 Defining and Differentiating Vector-Valued Functions": unit09/9_4.md
  #       - "9.5 Integrating Vector-Valued Functions": unit09/9_5.md
  #       - "9.6 Solving Motion Problems (Parametric & Vector)": unit09/9_6.md
  #       - "9.7 Defining Polar Coordinates and Polar Differentiation": unit09/9_7.md
  #       - "9.8 Finding the Area of a Polar Region": unit09/9_8.md
  #       - "9.9 Finding the Area Bounded by Two Polar Curves": unit09/9_9.md
  #   - "Unit 10 - Infinite Series":
  #       - "Overview": unit10/series.md
  #       - "10.1 Defining Convergent and Divergent Infinite Series": unit10/10_1.md
  #       - "10.2 Working with Geometric Series": unit10/10_2.md
  #       - "10.3 The nth Term Test for Divergence": unit10/10_3.md
  #       - "10.4 Integral Test for Convergence": unit10/10_4.md
  #       - "10.5 Harmonic Series and p-Series": unit10/10_5.md
  #       - "10.6 Comparison Tests for Convergence": unit10/10_6.md
  #       - "10.7 Alternating Series Test for Convergence": unit10/10_7.md
  #       - "10.8 Ratio Test for Convergence": unit10/10_8.md
  #       - "10.9 Determining Absolute or Conditional Convergence": unit10/10_9.md
  #       - "10.10 Alternating Series Error Bound": unit10/10_10.md
  #       - "10.11 Taylor Polynomial Approximations": unit10/10_11.md
  #       - "10.12 Lagrange Error Bound": unit10/10_12.md
  #       - "10.13 Radius and Interval of Convergence of Power Series": unit10/10_13.md
  #       - "10.14 Finding Taylor or Maclaurin Series for a Function": unit10/10_14.md
  #       - "10.15 Representing Functions as Power Series": unit10/10_15.md
  
  # - "I. Limits & Continuity":
  #     - "Unit 01 - Limits": unit01/limits.md

  # - "II. Differential Calculus":
  #     - "Unit 02 - Basic Differentiation": unit02/deriv_basic.md
  #     - "Unit 03 - Advanced Differentiation": unit03/deriv_advanced.md
  #     - "Unit 04 - Contextual Applications": unit04/apps_context.md
  #     - "Unit 05 - Analytical Applications": unit05/apps_analytic.md

  # - "III. Integral Calculus":
  #     - "Unit 06 - Integration": unit06/integration.md
  #     - "Unit 07 - Differential Equations": unit07/diff_eq.md
  #     - "Unit 08 - Applications of Integration": unit08/apps_int.md

  # - "IV. Miscellaneous (BC only)":
  #     - "Unit 09 - Parametric & Polar": unit09/parametric_polar.md
  #     - "Unit 10 - Infinite Series":
  #         - "Overview": unit10/series.md
  #         - "10.1 Defining Series": unit10/10_1.md
  #         - "10.2 Geometric Series": unit10/10_2.md
  #         - "10.3 nth Term Test": unit10/10_3.md
  #         - "10.4 Integral Test": unit10/10_4.md
  #         - "10.5 p-Series": unit10/10_5.md
  #         - "10.6 Comparison Tests": unit10/10_6.md
  #         - "10.7 Alternating Series": unit10/10_7.md
  #         - "10.8 Ratio Test": unit10/10_8.md
  #         - "10.9 Absolute/Conditional": unit10/10_9.md
  #         - "10.10 Taylor & Error Bound": unit10/10_10.md