MATH-160 Final: MATH 160 Boise State Final review
15 Feb 2019
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Exponentials/logarithms overview september 5, 2014: de nition (a) e is a real number (about 2. 7). (b) e3 = e e e, and e0. 5 = e. So e3/2 = e3. (c) ex can be similarly de ned for all rational numbers, and lled in for irrational numbers by taking limits. (d) ln x is the inverse function of ex. Note: ln x is not de ned for x 0: change of base (a) 2x = (eln 2)x = ex ln 2 (b) log2 x = ln x ln 2. In both formulas, 2 can be replaced by any positive number: derivatives and integrals d ex dx. Z ex dx = ex + c d dx ln x = Z 1 x dx = ln|x| + c: derivatives in other bases: We consider ex and ln x rather than, say, 2x and log2 x because their derivatives and integrals have these natural forms.
