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.

The files on this page are .pdf files. You will need Adobe Acrobat (6.0 or newer). If you do not have Acrobat Reader version 6.0 or higher, click here

and download the latest version of the completely free Acrobat Reader.


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 Horizontal Asymptote
	Definition of a Vertical Asymptote
	End Behavior

	End Behavior Models
	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
Chain Rule	Linearization
Derivatives of 6 Trig Functions	Differentials
Relationships between Position, Velocity, and Acceleration	Absolute vs Relative vs Percentage Change
Velocity vs. Speed	Related Rates
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	Slope Fields (Revisited)
RRAM	Indefinite Integrals
MRAM	U - Substitution
Trapezoidal Rule	Integration by Parts (LIPET)
Riemann Sum	Special Cases of LIPET
Definition of Definite Integral	Derivation of an Exponential Function
Properties of Definite Integral	Separate and Integrate
Average Value of f(x)	Integral of TRIG functions
Relationship between Average Value of f(x) and Average Rate of Change	Integral of (TRIG)^2 functions
Fundamental Theorem of Calculus Part 1 (Extended)
Fundamental Theorem of Calculus Part 2 (Evaluation)


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