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
Using the function f(x)=ln(1+x)
a. Find the 8 degree taylor polynomial centered at 0 and
simplify.
b. using your 8th degree taylor polynomial and taylors
inequality, find the magnitude of the maximum possible error on
[0,0.1]
c.approximate ln(1.1) using your 8th degree taylor polynomial.
what is the actual error? is it smaller than your estimated
error?Round answer to enough decimal places so you can
determine.
d. create a plot of the function f(x)=ln(1+x) along with your
taylor polynomial. Based on...
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
a) Find the Taylor series for sinh(x) (centered at x=0), for e^x
(centered at x=0) and hyperbolic sine and hyperbolic cosine.
b) same as a but cosh(x) instead
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
Let f(x) = 1 + x − x2 +ex-1.
(a) Find the second Taylor polynomial T2(x) for f(x)
based at b = 1.
b) Find (and justify) an error bound for |f(x) − T2(x)| on the
interval
[0.9, 1.1]. The f(x) - T2(x) is absolute value.
Please answer both questions cause it will be hard to post them
separately.