Mathematics 1560 Lecture Notes - Lecture 5: Irrational Number, Exponential Growth, Exponential Function
Document Summary
In chapter 7 we will use calculus to de ne logarithmic and expo- nential functions. In this section and the next, we informally deal with these functions, as you did in highschool. If a 6= 1 is a positive constant, the function f (x) = ax is the exponential function with base a. If x = n is an integer, then ax = an = a a a a n factors. If x = p/q is a rational number (a ratio of integers), then ax = ap/q = q ap. If x is irrational, then the decimal representation of x has no terminating or repeating pattern. We could use rational approximations of x to approxi- For example, 3 1. 732050808, and we could approximate 2. 2 by using more and more decimals of 3: We would then look for the limit of the sequence.
