Quiz and Miterm Review Sheet

Calc 140, Fall 2005

Hunsicker

This review sheet gives the definitions and theorems you should be learning for quizzes and exams. The quizzes will cover only the material indicated as pertaining to that quiz. Each quiz has one theory question and one problem. You will have 20 minutes to complete each quiz.

The first midterm will cover material from the beginning of the course, including subjects already covered on quizzes. The second midterm will cover material since the first midterm, including any material already covered on quizzes. The final will be cumulative, but will consist 50% on material since the second midterm, and only 25% on material from each midterm.

Definitions: Definitions indicated with a * you should be able to explain using a diagram or an example. Your diagram or example and explanation should clarify all notation and technical terms. Other definitions you only need to state.

Q1) Function

Q1) * The graph of a function

Q1) * The calculus method

Q1) * Even and odd functions

Q1) Increasing and decreasing functions

Q1) Polynomial

Q1) Rational function

Q1) Composition of functions

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 infinite limit
Q2) * The precise definition of limit at infinity

For the midterm, learn all of the above, plus:

Mid) * The definition of tangent line

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

Q3) Euler's constant, the number e

Q3) * Marginal cost

Q3) Unit circle definition of sinx and cosx

Q4) * One-to-one function

Q4) Inverse function

Q4) Velocity, acceleration, jerk

Q5) Absolute maximum and minimum

Q5) Local maximum and minimum

Q5) Critical number

Q5) Antiderivative

Theorems/explanations: Theorems indicated with a * you should be able to explain using a diagram or an example. Your diagram or example and explanation should clarify all notation and technical terms. Other theorems you only need to state.

Q1) Laws of exponents

Q2) * The Squeeze Theorem

Q2) The Direct Substitution Property

Q2) * The Intermediate Value Theorem

For the midterm, learn all of the above, plus

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

Q3) Power rule for derivatives (general version on p. 185)

Q3) Exponential rule for derivatives

Q3) Sum rule * know how to prove this!

Q3) constant multiple rule * know how to prove this!

Q3) Product rule for derivatives

Q3) Quotient rule for derivatives

Q3) Chain rule for derivatives

Q3) Derivatives of sinx and cosx

Q3) limit of sinx/x as x goes to 0, limit of (1-cosx)/x as x goes to 0

Q4) The chain rule together with the power rule

Q4) The chain rule together with the exponential rule

Q4) Laws of logarithms (p. 68)

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)