Taylor series
f(xi+1)=f(xi)+f'(xi)h+(f''(xi)/2!)h2+(f'''(xi)/3!)h3+.....
given
f''(xi)=(-f(xi+3)+4f(xi+2)-5f(xi+1)+2f(xi))/h2
what is the order of error o(h2)
Taylor series
f(xi+1)=f(xi)+f'(xi)h+(f''(xi)/2!)h2+(f'''(xi)/3!)h3+.....
given
f''(xi)=(-f(xi+3)+4f(xi+2)-5f(xi+1)+2f(xi))/h2
1) Find the Taylor series (to second order terms) of the
function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y =
−1.
2)Explain why the corresponding Taylor Series (to third order
terms) will be the same as the second-order series.
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 f(1), f(2), f(3) and f(4) if f(n) is defined recursively by
f(0)=4f(0)=4 and for n=0,1,2,…n=0,1,2,… by:
(a) f(n+1)=−2f(n)
f(1)=
f(2)=
f(3)=
f(4)=
(b) f(n+1)=4f(n)+5
f(1)=
f(2)=
f(3)=
f(4)=
(b) f(n+1)=f(n)2−4f(n)−2
f(1)=
f(2)=
f(3)=
f(4)=
Given are five observations for two variables,
xi
yi
1
3
2
8
3
5
4
11
5
14
Round your answers to two decimal places.
a. Estimate the standard deviation of ŷ* when x = 4. 2
b. Develop a 95% confidence interval for the expected value of y
when x = 4.
c. Estimate the standard deviation of an individual value of y
when x = 4.
d. Develop a 95% prediction interval for y when x =...