Question

7. For a Taylor series generated by a function f(x) at a point x = a, what information do you need about the function f to construct the series? Give an example of a function f(x) and the Taylor series generated by it.

Answer 1

Since fla) = 1 a= 0 1-a f(o)= 1 f'(a)- 1 a f'(o)=I, (1-2) f (a) 1.2 I f'(o)= 21 (1-2)3 I fu (n) 1.2.3 f" (o)= 31 (1-2) - th (n)- = 1.2.3.- n fl(o)=nl (1-n)+) fin)= En n! (2-0) ho hi fln)= α η { ho a flu)= ltata2 ta 3t-a. tant - which is very important power sules, which used many in binomial expensions.