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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