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...
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
Compute the Taylor polynomial indicated. f(x) = cos(x), a =
0
T5(x) =
Use the error bound to find the maximum possible size of the
error. Round your answer to nine decimal places.
cos(0.4) − T5(0.4) ≤
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