Calculus Notecard Checklist

You should have the following concepts organized with definitions and/or examples.

Keep in mind, the words "Show", "Verify", or "Prove" mean you must state the definition.

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Chapter 1	Chapter 2	Chapter 3	Chapter 4	Chapter 5	Chapter 6
Chapter 7	Chapter 8


Chapter 1	Chapter 2
Rules for Rounding	How to Evaluate a Limit ... 5 ways
Trig Identities	Properties of Limits
Transformations (Parent Functions)	Definition of a Limit at x = c
Odd/Even Functions ... graphically & algebraically	When Limits Fail ... 3 ways
Inverse Functions ... graphically & algebraically	Limits You Should Know
	Definition of a Vertical Asymptote
	End Behavior
	End Behavior Models

	Definition of a Horizontal Asymptote
	Finding Horizontal Asymptotes
	Slant "Oblique" Asymptotes
	Definition of Continuity at x = c
	Types of Discontinuities
	Intermediate Value Theorem
	Definition of Average Rate of Change
	Definition of Instantaneous Rate of Change

Chapter 3	Chapter 4
Definition of a Derivative ... 3 ways	Where to find Extrema
Definition of the existence of a derivative at x = c and at an endpoint.	Mean Value Theorem
Where does a derivative NOT exist	Relationship of f ' to Increasing/Decreasing
Slope Fields	1st Derivative Test for Extrema
Power Rule	Relationship of f '' to Concavity
Product Rule	2nd Derivative Test for Extrema
Quotient Rule	Relationship of f '' to Inflection Points
Velocity vs. Speed	Linearization
Relationships between Position, Velocity, and Acceleration	Differentials
Derivatives of 6 Trig Functions	Absolute vs Relative vs Percentage Change
	Related Rates
Chain Rule Derivatives of Inverse Trig Functions	Optimization
Derivative of an Inverse Function at a Point (p, q)
Derivatives of Exponential Functions
Derivatives of Logarithmic Functions
Logarithmic Differentiation


Chapter 5	Chapter 6
LRAM, RRAM, and MRAM	Slope Fields (Revisited)
Trapezoidal Rule	Indefinite Integrals
Riemann Sum	U - Substitution
Definition of Definite Integral	Integration by Parts (LIPET) ... no longer in AB
Properties of Definite Integral	Special Cases of LIPET ... no longer in AB
Average Value of f(x)	Derivation of an Exponential Function
Relationship between Average Value of f(x) and Average Rate of Change	Separate and Integrate
Fundamental Theorem of Calculus Part (Derivative of an Integral Part)	Integral of TRIG functions
Fundamental Theorem of Calculus Part (Evaluation)	Integral of (TRIG)^2 functions




Chapter 7	Chapter 8
Total Distance implies	L'Hopitals Rule
Displacement implies	Rate of Growth
Area between curves ... dx ... dy	Improper Integral
Volume of a Solid with known Perpendicular Cross Sections
Disc Method
Washer Method
Shell Method