how would you find the power series representation of x2ln(3-x) using term by term differentiation or integration?

how would you find the power series representation of x2ln(3-x) using term by term differentiation or integration?

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...

For this equation is the Taylor Series the best approach to wstimate numerically? I am also using Euler’s to compare. Trying to find y(1) given y(x) is a solution to the equation...

Let f(x)=sqrt(x+1); Compute T1,T2 at 0. And by that I mean Taylor . I know how to compute a Taylor polynomial for f(x,y) but how do I compute for f(x)? Please help I have...

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?

use formal multiplication to find the taylor series for the following function g(x)=x^3e^(x^2/2).

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...

The answer requires the replacement of the numerator and denominator with a taylor series that will produce the same limit as when lhospitals is applied to the original fraction/equation

Find the Taylor series for f(x)=sin x expanded at about x=(pi/2) and prove that the series converges to sin x for all x

I have already found out the Taylor polynomial of degree 3 f(x) = x³ + 2x² + x − 2 ----> f(1) = 2 f'(x) = 3x² + 4x + 1 -------> f'(1) = 8 f''(x) = 6x...

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...