Final Exam Review Sheet

Definitions: Be prepared to explain *’d definitions with a diagram or an example which clarifies all notation and technical language.

Q1)  * The calculus method

Q1)  Increasing and decreasing functions

Q1)  Rational function

 Q2) * The precise definition of a limit

Q2) * Continuity at a point


Q2) Continuity on an open or closed interval


Q2) * The precise definition of limit at infinity

Mid) *The definition of the derivative of a function at a point

Q3) * Unit circle definition of sinx and cosx

Q4) Inverse function

Q4) Velocity, acceleration, jerk

Q5) Absolute maximum and minimum

Q5) Local maximum and minimum

Q5) Critical number

Q5) Antiderivative

Fin) * Area

Fin) * Partition, mesh of a partition

Fin) Riemann sum

Fin) Riemann integral

Theorems: Be prepared to explain *’d theorems with a diagram or example that clarifies all notation and technical language.

Q2) The Squeeze Theorem

Q2) * The Intermediate Value Theorem

Mid) If f(x) is differentiable at a then it is continuous at a, but continuity does not guarantee a derivative.

Q3) All derivative rules

Q5) Extreme Value Theorem

Q5) Fermat's Theorem

Q5) Closed Interval Method

Q5) Mean Value Theorem

Q5) Increasing/Decreasing test

Q5) L'Hopital's Rule

Q5) First Derivative test for absolute extreme values (p. 334)

Q5) Antiderivative theorem (Thm 1, p. 353)

Fin) Properties of antiderivatives (from class)

Fin) Properties of definite integral 1-8 section 5.2

Fin) Fundamental Theorem of Calculus, version 1

Fin) Fundamental Theorem of Calculus, version 2