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...
consider f(x) = ln(x)
a) Approximate f(0.9) and f(1.1)
b) Use Taylor remainder to find an error formula for Taylor
polynomial.
Give error bounds for each of the two approximations in (a).
Which of the two approximations in part (a) is closer to correct
value?
c) Compare an actual error in each case with error bound in part
(b).
consider f(x) = ln(x)
a) Approximate f(0.9) and f(1.1)
b) Use Taylor remainder to find an error formula for Taylor
polynomial.
Give error bounds for each of the two approximations in (a).
Which of the two approximations in part (a) is closer to correct
value?
c) Compare an actual error in each case with error bound in part
(b).
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.
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