Compute the Taylor series at x = 0 for ln(1+x) and for x cos x
by repeatedly differentiating the function. Find the radii of
convergence of the associated series.
P1.
Write the Taylor series for f(x) = cos
x about x = 0.
State the Taylor polynomials T2(x),
T4(x), and T6(x) (note that
T3(x)
will be the same as T2(x), and
T5(x) will be the same as
T4(x)).
Plot f(x), T2(x), T4(x), and T6(x), together on one graph,
using demos
or similar (cut-and-paste or reproduce
below).
f(x) = x ln x
(a) Write the Taylor polynomial T3(x) for f(x) at center a =
1.
(b) Use Taylor’s inequality to give an upper bound for |R3| =
|f(x) − T3(x)| for |x − 1| ≤ 0.1. You don’t need to simplify the
number.
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...
Use matlab to plot Taylor approximation for f(x) for x near 0
Given f(x) = exp(x)
Use subpots to plot and its absolute and realative erros for N=
1,2,3
PLease give matlab code for Taylor and explain in detail, Thank
you