MAT 212- Midterm Exam Guide - Comprehensive Notes for the exam ( 242 pages long!)
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= x x + ln (1 x) d2 dx2 (ln(1 x))(0) 5. 2 the natural logarithmic function notes: sterling. This would be towards base a with the following: a > 0 a 6= 1 y = logax. Domain y is the logarithm to the base, a, of x y = logax x = ay x > 0. 0 < a < 1 a > 1 (1, 0) (a, 1) (cid:18) 1 a. 5. 3 the natural exponential function notes: sterling. Initial value a : base a : p ositive real n umber (a > 0) a 6= 1. All real n umbers a : growth f actor f (0) = ca0 = c (1) = c. Then f (x) = c ax a > 0 a 6= 1 x : any real n umber f (x + 1) f (x) = a f (x + 1) = af (x) Range f (x) = ax a > 1.
