BASIC CALCULUS REFRESHER
1. BASIC CALCULUS REFRESHER . Ismor Fischer, Dept. of Statistics UW-Madison 1. Introduction. This is a very condensed and simplified version of BASIC CALCULUS , which is a prerequisite for many courses in Mathematics, Statistics, Engineering, Pharmacy, etc. It is not comprehensive, and absolutely not intended to be a substitute for a one-year freshman course in differential and integral CALCULUS . You are strongly encouraged to do the included Exercises to reinforce the ideas. Important mathematical terms are in boldface; key formulas and concepts are boxed and highlighted . To (). view a color .pdf version of this document (recommended), see ~ifischer. 2. Exponents BASIC Definitions and Properties For any real number base x, we define powers of x: x0 = 1, x1 = x, x2 = x x, x3 = x x x, etc. (The exception is 00, which is considered indeterminate.)
5 p < 0 0 < p < 1 p = 1 y = x p p = 0 p > 1 NOTE: The preceding examples are special cases of power functions, which have the general form y = x p, for any real value of p, for x > 0. If p > 0, then the graph starts at the origin and continues to rise to infinity. (In particular, if p > 1, then the graph is concave up, such as the parabola y = x2.If p = 1, the graph is the straight line y = x.
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