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Calculus Study Guide

Table of Contents

Click any heading in the study guide to return to TOC

👉 I - Foundational Geometry

1 - Lines and Slopes

2 - Secant Lines and Tangent Lines

3 - Intersection of Lines

4 - Polygons and Areas

👉 II - Limits of Functions

1 - Definition and Basic Techniques

2 - Indeterminate Forms

👉 III - Derivative Rules and Applications

1 - Basic Derivative Rules

2 - Implicit Differentiation

3 - Derivatives of Common Functions

4 - Geometric Interpretation

5 - Related Rates

👉 IV - Curve Analysis

1 - Critical Points

2 - Maxima and Minima

3 - Inflection Points

4 - Sketching and Labeling

👉 V - Trig Functions

1 - Basic Graphs: sin(x) & cos(x)

2 - Other Trig Functions: tan, cot, sec, csc

3 - Trig Identities

4 - Derivatives and Integrals of Trig Functions

👉 VI - Integration

1 - Indefinite Integrals

2 - Definite Integrals

3 - "u" Substitution

4 - Integration by Parts

5 - Volume of Revolution

👉 VII - Exponential and Logarithmic Functions

1 - Properties of e^x and ln(x)

2 - Graphing e^x and ln(x)

3 - Solving Exponential and Logarithmic Equations

4 - Derivatives and Integrals

👉 VIII - Putting it All Together

1 - Combining Geometry and Calculus

2 - Problem-Solving Strategies

3 - Technical Jargon & Communication

4 - Troubleshooting and Decision Making

👉 I - Foundational Geometry

1 - Lines and Slopes

2 - Secant Lines and Tangent Lines

3 - Intersection of Lines

4 - Polygons and Areas

👉 II - Limits of Functions

1 - Definition and Basic Techniques

2 - Indeterminate Forms

3 - Continuity

4 - Summary

👉 III - Derivative Rules and Applications

1 - Basic Derivative Rules

2 - Implicit Differentiation

3 - Derivatives of Common Functions

4 - Geometric Interpretation

5 - Related Rates

6 - Summary

👉 IV - Curve Analysis

1 - Critical Points

2 - Maxima and Minima

3 - Inflection Points

4 - Sketching and Labeling

5 - Summary

👉 V - Trig Functions

1 - Basic Graphs: sin(x) & cos(x)

2 - Other Trig Functions: tan, cot, sec, csc

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3 - Trig Identities

4 - Derivatives and Integrals of Trig Functions

5 - Summary

👉 VI - Integration

1 - Indefinite Integrals

2 - Definite Integrals

3 - "u" Substitution

4 - Integration by Parts

5 - Volume of Revolution

6 - Summary

👉 VII - Exponential and Logarithmic Functions

1 - Properties of e^x and ln(x)

2 - Graphing e^x and ln(x)

3 - Solving Exponential and Logarithmic Equations

4 - Derivatives and Integrals

5 - Summary

👉 VIII - Putting it All Together

1 - Combining Geometry and Calculus

2 - Problem-Solving Strategies

3 - Technical Jargon & Communication

4 - Troubleshooting and Decision Making

5 - Summary

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