The Calculus I Flashcard has seven chapters containing 110 flashcards. It covers the first-semester of calculus including limits, differentiation, application of differentiation, continuity, and integration. Below is the chapter summary.

----Calculus I Flashcard Summary
Chapter 1 Limits and Their Properties
• Definition of Limit
• Basic Limits
• Properties of Limits
• Limits of a Polynomial Function
• Limits of a Rational Function
• The Limit of Radical Functions
• The Limit of a Composite Function
• Limits of Trigonometric functions
...

Chapter 2 Limits and Continuity
• Definition of Continuity
• Continuity on a Closed Interval
• Properties of Continuity
• Continuity of a Composite Function

Chapter 3 Differentiation
• Tangent Line with Slope m
• Derivative of a Function
• Differentiability Implies Continuity
• The Constant Rule
• The Power Rule
• The Constant Multiple Rule
• The Sum and Difference Rules
• Derivatives of Sine and Cosine Functions
• The Product Rule
• The Quotient Rule
...

Chapter 4 Applications of Differentiation
• Extrema
• The Extreme Value Theorem
• Relative Extrema
• Critical Number
• Relative Extrema Occur at Critical Numbers
• Rolle’sTheorem
• The Mean Value Theorem
• Increasing and Decreasing Functions
• Test for Increasing and Decreasing Functions
• The First Derivative Test
• Concavity
• Test for Concavity
• Points of Inflection
• Second Derivative Test
• Definition of Limits at Infinity
• Horizontal Asymptote
• Theorem of Limits at Infinity
• Definition of Differentials
• Differential Formulas

Chapter 5 Integration
• Representation of antiderivatives
• Summation Formulas
• Definition of the Area of a Region in the Plane
• Riemann Sum
•The Definite Integral as the Area of a Region
• Two Special Definite Integrals
• Additive Interval Property
• Presentation of Inequality
• Properties of Definite Integrals
• The Fundamental Theorem of Calculus
• Mean Value Theorem for Integrals
• Average Value of a Function on an Interval
• The Second Fundamental Theorem of Calculus
• Antidifferentiation of a Composite Function
• The General Power Rule for Integration
• Change of Variables for Definite Integrals
• Integration of Even and Odd Functions
• Integral of p(x) = Ax2 + Bx + C
• The Trapezoidal Rule
• Errors in the Trapezoidal Rule
• Simpson’s Rule (n is even)
• Errors in the Simpson’s Rule

Chapter 6 Derivatives and Integrals of Logarithmic, Exponential, Trigonometric, and Inverse Functions
• The Natural Logarithmic Function
• Definition e
• Definition of e Involving Limits
• Derivative of the Natural Logarithmic Functions
• Derivative Involving Absolute Value
• Log Rule for Integration
• Integrals of the Six Basic Trigonometric Functions
• Reflective Property of Inverse Functions
• The Existence of an Inverse Function
• Continuity and Differentiability of Inverse Functions
• The Derivative of an Inverse Function
• The Derivative of the Natural Exponential Function
• Derivatives for Base of Any Number
• The Power Rule for Real Exponents
...

Chapter 7 Derivatives and Integrals of Hyperbolic Functions

• The Hyperbolic Functions
• Hyperbolic Identities (Unity)
• Hyperbolic Identities (Double Angle)
• Hyperbolic Identities (Sinh and Cosh Squared)
• Hyperbolic Identities (Sum and Difference of Angles)
• Differentiation of Hyperbolic Function
...
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