The question asks to derive the leading order term. I expand both to 4 terms (up to third derivative) and get identical answers which are just the second derivative divided by delta x. I'm not to...

f(μ)+1/2*f''(x)var(f(x)) =f(x)+b{f'(x)+1/2*x f"(x)} where μ=x+b var(f(x))=xb+b^2   how bold and Italic part is derived????

Use zero- through fourth-order Taylor series expansions to predict f(2.5) for: f(x) = ln x using a base point at x = 1. Compute the true percent relative error E% for each approximation. Discuss the...

I am being asked to evaluate the first four nonzero terms using Taylor expansion about x=0. I am told the initial value problem is y'=e^y; y(0)=1 and y'(0)=-1.  I am not sure how to utilize...

Consider the following function values   http://oi61.tinypic.com/msoiuc.jpg   also given http://oi57.tinypic.com/2cxux5h.jpg   a ) Set up a system of equations...

A function has an nth derivative evaluated at x = a that is proportional to n. What is the radius of convergence of the Taylor series of this function expanded about the point x = a?

I have had to calculate the limits for the fraction 1-cos(x) over xsin(pi x) and found the answer to be 1 over 2pi. However, now i have to apply taylor series to the numerator and the denominator...

Find the Taylor Series of g(x) = cos(x2)/x, c=¶/4   ¶ = pi X

Note that (c) is independent component a) Find the 3rd Taylor polynomial for f(x)=x^3+2x^2+x-2 in vicinty of a=1 b) Talk about the error approach in (a) and how it could...