Use the definition of Taylor series to find the first three
nonzero terms of the Taylor series (centered at c) for the
function f.
f(x) = 7 tan x, c = 9π
Find the Taylor series for f ( x ) centered at the given value
of a . (Assume that f has a power series expansion. Do not show
that R n ( x ) → 0 . f ( x ) = 2 /x , a = − 4
use the definition of the Taylor series to find the first four
nonzero terms of the series for f(x) centered at x = a
a) f(x) = xe^x, a = 0
b) f(x) = sin (x), a = π/6
Find the Taylor series or polynomial generated by the following
functions
a. )f(x) √ x centred at x=4 , of order 3
b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0
c.) f(x) = x tan^-1x^2 , centred at x=0
d.) f(x) = 1/(√1+x^3) , centred at x=0 , of order 4
e.) f(x) = cos(2x+pie/2) centred at x= pie/4
What are the different methods used to show a function is equal
to its Taylor series near its center. In particular discuss
Taylor’s inequality and how it can be used. Give a detailed
example.