1. Find Taylor series centered at 1 for f(x) = e^ (x^2). Then
determine interval of convergence.
2. Find the coeffiecient on x^4 in the Maclaurin Series
representation of the function g(x) = 1/ (1-2x)^2
1. Find a closed form expression for the MacLaurin series for
f(x) = sinh(3x)
2. Find a closed form expression for the Taylor series for f(x)
= 4e2x expanded at a=3
1) Find the Taylor series (to second order terms) of the
function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y =
−1.
2)Explain why the corresponding Taylor Series (to third order
terms) will be the same as the second-order series.
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
The function f(x)= x^−5 has a Taylor series at a=1 . Find the
first 4 nonzero terms in the series, that is write down the Taylor
polynomial with 4 nonzero terms.
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