Find a power series for the following function, centered at c =
0, and determine the interval of convergent
f(x)=(3x−8)/(3x^2+5x−2)
(show all the works please)
(a) Determine the Taylor Series centered at a = 1 for the
function f(x) = ln x.
(b) Determine the interval of convergence for this Taylor
Series.
(c) Determine the number n of terms required to estimate the
value of ln(2) to within Epsilon = 0.0001.
Can you please help me solve it step by step.
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
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
Find the Taylor polynomial of degree 2 centered at a = 1 for the
function f(x) = e^(2x) . Use Taylor’s Inequality to estimate the
accuracy of the approximation e^(2x) ≈ T2(x) when 0.7 ≤
x ≤ 1.3