Transcription of BASIC CALCULUS REFRESHER
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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.) Powers are also called exponents. Examples: 50 = 1, ( )1 = , ( )2 = = , 103 = 10 10 10 = 1000, ( 3)4 = ( 3) ( 3) ( 3) ( 3) = 81.
p = 1, the graph is the straight line y = x. And if 0 < p < 1, then the graph is concave down, such as the parabola y = x1/2 = x.) However, if p < 0, such as y = x 1 = 1 x, or y = x 2 = 1 x2, then the Y-axis acts as a vertical asymptote for the graph, and the X-axis is a horizontal asymptote. Exercise: Why is y = xx not a power function? Sketch ...
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