Mr. Valsa's Math Page
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  • AP Calculus AB
    • Course Intro
    • Unit 01: Limits & Continuity >
      • 1.1 Intro to Calculus
      • 1.2 Defining Limits & Using Limit Notation
      • 1.3 Estimating Limit Values from a Graph
      • 1.4 Estimating Limit Values from a Table
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Squeeze Theorem
      • 1.9 Multiple Representations of Limits
      • 1.10 Exploring Types of Discontinuities
      • 1.11 Defining Continuity
      • 1.12 Confirming Continuity over an Interval
      • 1.13 Removing Discontinuity
      • 1.14 Infinite Limits & Vertical Asymptotes
      • 1.15 Connecting Limits at Infinity & Horizontal Asymptotes
      • 1.16 Intermediate Values Theorem (IVT)
    • Unit 02: Intro to the Derivative >
      • 2.1 Defining Average & Instantaneous Rates of Change
      • 2.2 Defining the Derivative of a Function
      • 2.3 Estimating the Derivative at a Point
      • 2.4 Determining When Derivatives Exist
      • 2.5 Applying the Power Rule
      • 2.6 Derivative Rules
      • 2.7: Derivatives of sin, cos, e^x, ln(x)
      • 2.8 Product Rule
      • 2.9 Quotient Rule
      • 2.10 Derivative of tan/cot/sec/csc
  • PreCalculus
    • Course Intro
    • Unit 01: Function Analysis >
      • 1.1 Set & Interval Notation
      • 1.2 Function Review
      • 1.3 Domain & Range
      • 1.4 End Behavior & Extrema
      • 1.5 Inc/Dec/Const
      • 1.6 Symmetry
      • 1.7 Function Transformations
      • 1.8 Function Operations
      • 1.9 Inverses
      • 1.10 Piecewise Functions
      • Unit 01 Review Material
    • Unit 02: Polynomial & Rational Functions >
      • 2.1 Solving Polynomials
      • 2.2 Classifying Polynomials
      • 2.3 Complex Numbers
      • 2.4 End Behavior
      • 2.5 Writing Equations of Polynomials
      • 2.6 Solving Rational Equations
      • 2.7 Rational Inequalities
      • 2.8 Types of Discontinuity
      • 2.9 Graphing Rational Functions
  • Integrated Math 3
    • Course Intro
    • Unit 01: Analytic Geometry >
      • 1.1 Graphing Lines
      • 1.2 Parallel & Perpendicular
      • 1.3 Distance & Pythagorean Theorem
      • 1.4 Classifying Quadrilaterals
      • Unit 01 Review
    • Unit 02: Geometric Proofs & Modeling >
      • 2.1 Surface Area & Volume
      • 2.2 Density
      • 2.3 Cross Sections
      • Unit 02 Review
    • Unit 03: Circles & Parabolas >
      • 3.1 Circles Review
      • 3.2 Arc Length & Sector Area
      • 3.3 Writing & Graphing Circles
      • 3.4 Completing the Square
      • 3.5 Parabolas
    • SAT Practice
  • Math Team
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​9.9 Applications

9.9_applications.pdf
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9.9_completed_notes.pdf
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9.9_worksheet.pdf
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9.9_worksheet_ans.pdf
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9.9_worksheet_worked_out_solutions.pdf
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  • Home
  • AP Calculus AB
    • Course Intro
    • Unit 01: Limits & Continuity >
      • 1.1 Intro to Calculus
      • 1.2 Defining Limits & Using Limit Notation
      • 1.3 Estimating Limit Values from a Graph
      • 1.4 Estimating Limit Values from a Table
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Squeeze Theorem
      • 1.9 Multiple Representations of Limits
      • 1.10 Exploring Types of Discontinuities
      • 1.11 Defining Continuity
      • 1.12 Confirming Continuity over an Interval
      • 1.13 Removing Discontinuity
      • 1.14 Infinite Limits & Vertical Asymptotes
      • 1.15 Connecting Limits at Infinity & Horizontal Asymptotes
      • 1.16 Intermediate Values Theorem (IVT)
    • Unit 02: Intro to the Derivative >
      • 2.1 Defining Average & Instantaneous Rates of Change
      • 2.2 Defining the Derivative of a Function
      • 2.3 Estimating the Derivative at a Point
      • 2.4 Determining When Derivatives Exist
      • 2.5 Applying the Power Rule
      • 2.6 Derivative Rules
      • 2.7: Derivatives of sin, cos, e^x, ln(x)
      • 2.8 Product Rule
      • 2.9 Quotient Rule
      • 2.10 Derivative of tan/cot/sec/csc
  • PreCalculus
    • Course Intro
    • Unit 01: Function Analysis >
      • 1.1 Set & Interval Notation
      • 1.2 Function Review
      • 1.3 Domain & Range
      • 1.4 End Behavior & Extrema
      • 1.5 Inc/Dec/Const
      • 1.6 Symmetry
      • 1.7 Function Transformations
      • 1.8 Function Operations
      • 1.9 Inverses
      • 1.10 Piecewise Functions
      • Unit 01 Review Material
    • Unit 02: Polynomial & Rational Functions >
      • 2.1 Solving Polynomials
      • 2.2 Classifying Polynomials
      • 2.3 Complex Numbers
      • 2.4 End Behavior
      • 2.5 Writing Equations of Polynomials
      • 2.6 Solving Rational Equations
      • 2.7 Rational Inequalities
      • 2.8 Types of Discontinuity
      • 2.9 Graphing Rational Functions
  • Integrated Math 3
    • Course Intro
    • Unit 01: Analytic Geometry >
      • 1.1 Graphing Lines
      • 1.2 Parallel & Perpendicular
      • 1.3 Distance & Pythagorean Theorem
      • 1.4 Classifying Quadrilaterals
      • Unit 01 Review
    • Unit 02: Geometric Proofs & Modeling >
      • 2.1 Surface Area & Volume
      • 2.2 Density
      • 2.3 Cross Sections
      • Unit 02 Review
    • Unit 03: Circles & Parabolas >
      • 3.1 Circles Review
      • 3.2 Arc Length & Sector Area
      • 3.3 Writing & Graphing Circles
      • 3.4 Completing the Square
      • 3.5 Parabolas
    • SAT Practice
  • Math Team
  • Contact