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ap calc study guides

✍️  Free Response Questions (FRQ)

Calculus Free Response Questions

👑  Unit 1: Limits & Continuity

1.0Unit 1 Overview: Limits and Continuity

1.1Introducing Calculus: Can Change Occur at An Instant?

1.2Defining Limits and Using Limit Notation

1.3Estimating Limit Values from Graphs

1.4Estimating Limit Values from Tables

1.5Determining Limits Using Algebraic Properties of Limits

1.6Determining Limits Using Algebraic Manipulation

1.7Selecting Procedures for Determining Limits

1.8Determining Limits Using the Squeeze Theorem

1.10Exploring Types of Discontinuities

1.11Defining Continuity at a Point

1.12Confirming Continuity over an Interval

1.13Removing Discontinuities

1.14Connecting Infinite Limits and Vertical Asymptotes

1.15Connecting Limits at Infinity and Horizontal Asymptotes

1.16Working with the Intermediate Value Theorem (IVT)

🤓  Unit 2: Differentiation: Definition & Fundamental Properties

2.0Unit 2 Overview: Differentiation

2.1Defining Average and Instantaneous Rates of Change at a Point

2.2Defining the Derivative of a Function and Using Derivative Notation

2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

2.6Derivative Rules: Constant, Sum, Difference, and Constant Multiple

2.7Derivatives of cos x, sinx, e^x, and ln x

2.8The Product Rule

2.9The Quotient Rule

2.10Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

🤙🏽  Unit 3: Differentiation: Composite, Implicit & Inverse Functions

3.0Unit 3 Overview: Differentiation: Composite, Implicit, and Inverse Functions

3.1The Chain Rule

3.2Implicit Differentiation

3.3Differentiating Inverse Functions

3.4Differentiating Inverse Trigonometric Functions

3.5Selecting Procedures for Calculating Derivatives

3.6Calculating Higher-Order Derivatives

👀  Unit 4: Contextual Applications of the Differentiation

4.0Unit 4 Overview: Contextual Applications of Differentiation

4.1Interpreting the Meaning of the Derivative in Context

4.2Straight-Line Motion: Connecting Position, Velocity, and Acceleration

4.3Rates of Change in Applied Contexts other than Motion

4.4Intro to Related Rates

4.5Solving Related Rates Problems

4.6Approximating Values of a Function Using Local Linearity and Linearization

4.7Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

✨  Unit 5: Analytical Applications of Differentiation

5.0Unit 5 Overview: Analytical Applications of Differentiation

5.1Using the Mean Value Theorem

5.2Extreme Value Theorem, Global vs Local Extrema, and Critical Points

5.3Determining Intervals on Which a Function is Increasing or Decreasing

5.4Using the First Derivative Test to Determine Relative (Local) Extrema

5.6Determining Concavity

5.7Using the Second Derivative Test to Determine Extrema

5.11Solving Optimization Problems

🔥  Unit 6: Integration and Accumulation of Change

6.11Integrating Using Integration by Parts

6.12Using Linear Partial Fractions

💎  Unit 7: Differential Equations

7.0Unit 7 Overview: Differential Equations

7.2Verifying Solutions for Differential Equations

7.4Reasoning Using Slope Fields

7.5Approximating Solutions Using Euler’s Method

7.7Finding Particular Solutions Using Initial Conditions and Separation of Variables

7.9Logistic Models with Differential Equations

🐶  Unit 8: Applications of Integration

8.0Unit 8 Overview: Applications of Integration

8.1Finding the Average Value of a Function on an Interval

8.2Connecting Position, Velocity, and Acceleration of Functions Using Integrals

8.3Using Accumulation Functions and Definite Integrals in Applied Contexts

8.4Finding the Area Between Curves Expressed as Functions of x

8.5Finding the Area Between Curves Expressed as Functions of y

8.6Finding the Area Between Curves That Intersect at More Than Two Points

8.7Volumes with Cross Sections: Squares and Rectangles

8.8Volumes with Cross Sections: Triangles and Semicircles

8.9Volume with Disc Method: Revolving Around the x- or y-Axis

8.10Volume with Disc Method: Revolving Around Other Axes

8.11Volume with Washer Method: Revolving Around the x- or y-Axis

8.12Volume with Washer Method: Revolving Around Other Axes

🦖  Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

9.0Unit 9 Overview: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

9.1Defining and Differentiating Parametric Equations

9.4Defining and Differentiating Vector-Valued Functions

9.7Defining Polar Coordinates and Differentiating in Polar Form

9.9Finding the Area of the Region Bounded by Two Polar Curves

♾  Unit 10: Infinite Sequences and Series (BC Only)

10.0Unit 10 Overview: Infinite Series and Sequences

10.1Defining Convergent and Divergent Infinite Series

10.2Working with Geometric Series

10.3The nth Term Test for Divergence

10.4Integral Test for Convergence

10.5Harmonic Series and p-Series

10.6Comparison Tests for Convergence

10.7Alternating Series Test for Convergence

10.8Ratio Test for Convergence

10.9Determining Absolute or Conditional Convergence

10.10Alternating Series Error Bound

10.1110.11 Finding Taylor Polynomial Approximations of Functions

10.12Lagrange Error Bound

10.13Radius and Interval of Convergence of Power Series

10.14Finding Taylor or Maclaurin Series for a Function

10.15Representing Functions as Power Series

🧐  Multiple Choice Questions (MCQ)

AP Calculus AB/BC Multiple Choice Help (MCQ)

Calculus Multiple Choice Questions

♾️ ap calc

👑  jump to Unit 1 library

1.15 Connecting Limits at Infinity and Horizontal Asymptotes

#infinitelimits

#asymptotes

⏱️  1 min read

written by

Anusha Tekumulla

anusha tekumulla

June 7, 2020

available on hyper typer

Asymptotes, Continued

🎥Watch: AP Calculus AB/BC - Limits at Infinity and Horizontal Asymptotes

The other type of asymptote is a horizontal asymptote. They are lines parallel to the x-axis. 🚂

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(428).png?alt=media&token=e20cf2b8-66dd-4196-81fe-bc37ece0311f

Therefore, to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity. A function can have at most two horizontal asymptotes, one in each direction. ♾️

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