Download review sheet

Math 132, Spring 2003
Test 1 Review Sheet
Test 1 covers sections 0.1–0.5, 1.1–1.4, 1.6–1.8, 2.1, 2.2, and 2.5.
1. Graphs, Equations and Functions
(a) Basics
• Coordinate Geometry (how graphs and equations mix)
• Domain and range of functions
• Combination of functions (especially composition)
(b) Polynomials and factoring
•
•
•
•
situations where factoring is useful
polynomials can always be factored into linear and quadratic pieces
for a polynomial p, if p(a) = 0 then (x − a) will factor out
quadratic formula
(c) Other important functions (rational functions, power functions)
• algebraic manipulations involving fractions and rational functions
• rules for working with exponents (page 43, for example)
• compound interest and annual percentage yield
2. Limits
(a) What limits mean
(b) The Limit Blah Law, and how to use it to evaluate limits
3. Derivatives
(a) Foundation
•
•
•
•
•
•
Graphical interpretation: slope of tangent line, steepness of curve
Functional interpretation: rate of change
Relationship between slope of secant line and slope of tangent line
Relationship between average rate of change and instantaneous rates of change
Relationship between graphs of f and f 0
Units for derivatives
(b) Computation
•
•
•
•
Different kinds of notation: f 0 (x), dy
dt , etc.
Using definition (limits) to evaluate a derivative
Computing derivatives using differentiation rules
Second derivatives, too.
(c) Applications
•
•
•
•
Finding equations of tangent lines
Position, velocity and acceleration
Marginal cost, marginal profit, etc.
Optimization problems