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Lacamu's Calculus BC
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Unit 1
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid Unit Review
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
End of Unit Review
Unit 1 Test
Test Answers
Unit 2
2.1 Average and Instantaneous Rate of Change
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 The Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos(x), sin(x), e, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
End of Unit Review
Unit 2 Test
Unit 2 Test Answers
Unit 3
3.1 The Chain Rule
3.6 Calculating Higher-Order Derivatives
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Derivatives
End of Unit Review
Unit 3 Test
Unit 3 Test Answers
Unit 4
4.1 Interpreting the Derivative in Context
4.2 Position, Velocity, and Acceleration
4.3 Rates of Change Other Than Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates
4.6 Approximating with Local Linearity
4.7 L'Hospital's Rule
End of Unit 4 Review
Unit 4 Test
Unit 4 Test Answers
Unit 5
5.1 The Mean Value Theorem
5.2 Critical Points
5.3 Increasing and Decreasing Intervals
5.4 The First Derivative Test
5.5 Determine Absolute Extrema from Candidates
5.6 Determining Concavity
5.7 The Second Derivative Test
Unit 5 Mid Unit Review
5.8 Sketching Graphs of Derivatives
5.9 Connecting f, f', and f''
5.10 Introduction to Optimization
5.11 Solving Optimization Problems
5.12 Behaviors of Implicit Relations
Unit 5 End of Unit Review
Unit 5 Test
Unit 5 Test Answers
Unit 6
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral N
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
Unit 6 Mid Unit Review
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Nota
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.11 Integrating Using Integration by Parts
6.12 Linear Partial Fractions
6.13 Evaluating Improper Integrals
6.14 Selecting Techniques for Antidifferentiation
Integration Cheat Sheet
Unit 6 End of Unit Review
Unit 6 Test
Unit 7
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Approximating Solutions Using Euler’s Method
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and Separation of Varia
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations
Unit 7 End of Unit Review
Unit 7 Test
Unit 9
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Arc Lengths of Curves (Parametric Equations)
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Unit 9 End of Unit Review
Unit 9 Test
Unit 10
10.1 Defining Convergent and Divergent Infinite Series
10.2 Geometric Series
10.3 The Nth Term Test
10.4 Integral Test
10.5 Harmonic Series and p-series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
Unit 10 Mid Unit Review
Practice Tests
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as a Power Series
Unit 10 End of Unit Review
Unit 8
8.1 Average Value of a Function
8.2 Connecting P,V,A of Functions Using Inte
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
Unit 8 Mid-Unit Review
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-axis
8.12 Volume with Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
Yearly Grades
1st Nine Weeks
2nd Nine Weeks
3rd Nine Weeks
Lacamu's Calculus BC
Home
Unit 1
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid Unit Review
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
End of Unit Review
Unit 1 Test
Test Answers
Unit 2
2.1 Average and Instantaneous Rate of Change
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 The Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos(x), sin(x), e, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
End of Unit Review
Unit 2 Test
Unit 2 Test Answers
Unit 3
3.1 The Chain Rule
3.6 Calculating Higher-Order Derivatives
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Derivatives
End of Unit Review
Unit 3 Test
Unit 3 Test Answers
Unit 4
4.1 Interpreting the Derivative in Context
4.2 Position, Velocity, and Acceleration
4.3 Rates of Change Other Than Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates
4.6 Approximating with Local Linearity
4.7 L'Hospital's Rule
End of Unit 4 Review
Unit 4 Test
Unit 4 Test Answers
Unit 5
5.1 The Mean Value Theorem
5.2 Critical Points
5.3 Increasing and Decreasing Intervals
5.4 The First Derivative Test
5.5 Determine Absolute Extrema from Candidates
5.6 Determining Concavity
5.7 The Second Derivative Test
Unit 5 Mid Unit Review
5.8 Sketching Graphs of Derivatives
5.9 Connecting f, f', and f''
5.10 Introduction to Optimization
5.11 Solving Optimization Problems
5.12 Behaviors of Implicit Relations
Unit 5 End of Unit Review
Unit 5 Test
Unit 5 Test Answers
Unit 6
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral N
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
Unit 6 Mid Unit Review
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Nota
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.11 Integrating Using Integration by Parts
6.12 Linear Partial Fractions
6.13 Evaluating Improper Integrals
6.14 Selecting Techniques for Antidifferentiation
Integration Cheat Sheet
Unit 6 End of Unit Review
Unit 6 Test
Unit 7
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Approximating Solutions Using Euler’s Method
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and Separation of Varia
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations
Unit 7 End of Unit Review
Unit 7 Test
Unit 9
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Arc Lengths of Curves (Parametric Equations)
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Unit 9 End of Unit Review
Unit 9 Test
Unit 10
10.1 Defining Convergent and Divergent Infinite Series
10.2 Geometric Series
10.3 The Nth Term Test
10.4 Integral Test
10.5 Harmonic Series and p-series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
Unit 10 Mid Unit Review
Practice Tests
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as a Power Series
Unit 10 End of Unit Review
Unit 8
8.1 Average Value of a Function
8.2 Connecting P,V,A of Functions Using Inte
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
Unit 8 Mid-Unit Review
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-axis
8.12 Volume with Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
Yearly Grades
1st Nine Weeks
2nd Nine Weeks
3rd Nine Weeks
More
Home
Unit 1
1.1 Can Change Occur at an Instant?
1.2 Defining Limits and Using Limit Notation
1.3 Estimating Limit Values from Graphs
1.4 Estimating Limit Values from Tables
1.5 Determining Limits Using Algebraic Properties
1.6 Determining Limits Using Algebraic Manipulation
1.7 Selecting Procedures for Determining Limits
1.8 Determining Limits Using the Squeeze Theorem
1.9 Connecting Multiple Representations of Limits
Mid Unit Review
1.10 Exploring Types of Discontinuities
1.11 Defining Continuity at a Point
1.12 Confirming Continuity Over an Interval
1.13 Removing Discontinuities
1.14 Infinite Limits and Vertical Asymptotes
1.15 Limits at Infinity and Horizontal Asymptotes
1.16 Intermediate Value Theorem (IVT)
End of Unit Review
Unit 1 Test
Test Answers
Unit 2
2.1 Average and Instantaneous Rate of Change
2.2 Defining the Derivative of a Function and Using Derivative Notation
2.3 Estimating Derivatives of a Function at a Point
2.4 Connecting Differentiability and Continuity
2.5 The Power Rule
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
2.7 Derivatives of cos(x), sin(x), e, and ln(x)
2.8 The Product Rule
2.9 The Quotient Rule
2.10 Derivatives of tan(x), cot(x), sec(x), and csc(x)
End of Unit Review
Unit 2 Test
Unit 2 Test Answers
Unit 3
3.1 The Chain Rule
3.6 Calculating Higher-Order Derivatives
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Inverse Trigonometric Functions
3.5 Selecting Procedures for Derivatives
End of Unit Review
Unit 3 Test
Unit 3 Test Answers
Unit 4
4.1 Interpreting the Derivative in Context
4.2 Position, Velocity, and Acceleration
4.3 Rates of Change Other Than Motion
4.4 Introduction to Related Rates
4.5 Solving Related Rates
4.6 Approximating with Local Linearity
4.7 L'Hospital's Rule
End of Unit 4 Review
Unit 4 Test
Unit 4 Test Answers
Unit 5
5.1 The Mean Value Theorem
5.2 Critical Points
5.3 Increasing and Decreasing Intervals
5.4 The First Derivative Test
5.5 Determine Absolute Extrema from Candidates
5.6 Determining Concavity
5.7 The Second Derivative Test
Unit 5 Mid Unit Review
5.8 Sketching Graphs of Derivatives
5.9 Connecting f, f', and f''
5.10 Introduction to Optimization
5.11 Solving Optimization Problems
5.12 Behaviors of Implicit Relations
Unit 5 End of Unit Review
Unit 5 Test
Unit 5 Test Answers
Unit 6
6.1 Exploring Accumulation of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral N
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
Unit 6 Mid Unit Review
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Nota
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.11 Integrating Using Integration by Parts
6.12 Linear Partial Fractions
6.13 Evaluating Improper Integrals
6.14 Selecting Techniques for Antidifferentiation
Integration Cheat Sheet
Unit 6 End of Unit Review
Unit 6 Test
Unit 7
7.1 Modeling Situations with Differential Equations
7.2 Verifying Solutions for Differential Equations
7.3 Sketching Slope Fields
7.4 Reasoning Using Slope Fields
7.5 Approximating Solutions Using Euler’s Method
7.6 General Solutions Using Separation of Variables
7.7 Particular Solutions using Initial Conditions and Separation of Varia
7.8 Exponential Models with Differential Equations
7.9 Logistic Models with Differential Equations
Unit 7 End of Unit Review
Unit 7 Test
Unit 9
9.1 Defining and Differentiating Parametric Equations
9.2 Second Derivatives of Parametric Equations
9.3 Arc Lengths of Curves (Parametric Equations)
9.4 Defining and Differentiating Vector-Valued Functions
9.5 Integrating Vector-Valued Functions
9.6 Solving Motion Problems Using Parametric and Vector-Valued Functions
9.7 Defining Polar Coordinates and Differentiating in Polar Form
9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar
9.9 Finding the Area of the Region Bounded by Two Polar Curves
Unit 9 End of Unit Review
Unit 9 Test
Unit 10
10.1 Defining Convergent and Divergent Infinite Series
10.2 Geometric Series
10.3 The Nth Term Test
10.4 Integral Test
10.5 Harmonic Series and p-series
10.6 Comparison Tests for Convergence
10.7 Alternating Series Test for Convergence
10.8 Ratio Test for Convergence
10.9 Determining Absolute or Conditional Convergence
Unit 10 Mid Unit Review
Practice Tests
10.10 Alternating Series Error Bound
10.11 Finding Taylor Polynomial Approximations of Functions
10.12 Lagrange Error Bound
10.13 Radius and Interval of Convergence of Power Series
10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as a Power Series
Unit 10 End of Unit Review
Unit 8
8.1 Average Value of a Function
8.2 Connecting P,V,A of Functions Using Inte
8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4 Finding the Area Between Curves Expressed as Functions of x
8.5 Finding Area Between Curves Expressed as Functions of y
8.6 Finding the Area Between Curves That Intersect at More Than Two Points
Unit 8 Mid-Unit Review
8.7 Volumes with Cross Sections: Squares and Rectangles
8.8 Volumes with Cross Sections: Triangles and Semicircles
8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
8.10 Volume with Disc Method: Revolving Around Other Axes
8.11 Volume with Washer Method: Revolving Around the x- or y-axis
8.12 Volume with Washer Method: Revolving Around Other Axes
8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
Yearly Grades
1st Nine Weeks
2nd Nine Weeks
3rd Nine Weeks
8.12 Volume with Washer Method:
Revolving Around Other Axes
Blank Notes
Lacamu Notes
8.12.pdf
calc_8.12_solutions.pdf
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