Maclaurin Polynomials It can be shown using calculus that the function e" can be approximated by what are known as Maclaurin polynomials as follows. e = 1-x e=1-x- 2 ! er =1+x+ 2! 4! e=1+x+ I' 2! 3! 4! 5! By adding more and more terms, you get the general Maclaurin polynomial 12 13 2! ! 4! 5! When x = 1, these polynomials can be used to approximate e or e to the thousandths place. Remember e = 2.718. el = 1+1=2 12 el = 1 +1 + = 2.5 2! 12 el =1 +1+ - 2 2.6667 2! 3! 12 13 ex 1+1+ 2! 3! 4! ~ 2.7083 13 14 e =1+1- 2.7166 2! 3! 41 51 12 13 14 15 10 e =1+1+ 3! 41 5! 61 2.7181 2! Exercises Use the Maclaurin polynomials to approximate each of the following powers of e to the hundredths place. 1. e15 2. e2 3. 21 4. 22