My summary of principal subject matter for the
first exam in Math 151, fall 2007
- Analytic geometry: coordinates, points, distance, lines,
circles. Functions: domains; ranges; graphs.
- Common sorts of functions: polynomial, rational, algebraic
(roots), trig, inverse trig, exp, ln, with corresponding domain
- Plugging in (cite "Continuity").
- Algebraic transformation to a form which is recognized by a).
- Use of one of the complicated results or special limits (such as
- Continuity: no breaks, etc.: its specific definition. Recognition
of the graph of a continuous function.
- Intermediate Value Theorem (bisection for location of a root).
- The derivative
- Instantaneous rate of change using approximation by average rate
- Slope of a tangent line.
- The actual definition with a limit.
- Computation of derivative from the definition using limit
- Computation of derivative formulas or values for functions defined
by formulas or tabular information using the differentiation
- Graph of a derivative from graphical information (or the
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