9. copts Find the taylor series of fl) se e-2x with Xo=0 use any method! show...
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
(1 point) Use sigma notation to write the Taylor series about x = Xo for the function. e-Sx, xo = -5. Taylor series = ((-5)^k/k!)(k+1/5)^k KO
2. Use the definition of Taylor series to find the Taylor series of f(x)=sin(2x), centered at ca. You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. 4
Use power series operations to find the Taylor series at x = 0 for the following function. 9xex The Taylor series for e* is a commonly known series. What is the Taylor series at x = 0 for e? 00 Σ (Type an exact answer.) n=0 नि
3) Find the Taylor series centered at 1 for x3 - 2x + 7 4) Find the Maclaurin series for sin X. By using it, show that lim sinx as X + 0 equals 1. X (sing
Use power series operations to find the Taylor series atx 0 for the following function 7x 2 7+7cosx t is the Taylor se Σ □(Type an exact answer) Find the binomial series for the function (1+6x) The binomial series is Using a Taylor series, find the polynomial of least degree that will approximate F(x) throughout the given interval with an error of magnitude less than 10-5 F(x)=| cost dt, [0.1] F(x) A
Use power series operations to find the Taylor...
5. (a) (10) Write down the Taylor series for3) and find the 6th Taylor polynomial p() (b) (10) Find the Taylor series about 0 for f(a) 3 cos, and use the Lagrange Remainder Formula toshow that for any z, nlim。m(z) = 0. em t
5. (a) (10) Write down the Taylor series for3) and find the 6th Taylor polynomial p() (b) (10) Find the Taylor series about 0 for f(a) 3 cos, and use the Lagrange Remainder Formula toshow that...
-a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D.
-a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D.
find a taylor series for f(x) = e^2x centered at a=3. give the first four nonzero terms and the general term for each series
QUESTION 6 Compute the Taylor series of f(x)= sin 2x at Then show for the series above that linck; f(x) = 0 for each r QUESTION 7 Let f (x) =-x + 3, x E [0, 1] and let P be a partition of [0,1] given by 1 2 n-1 Calculate L(P) and U(P) and prove using these summations that f is Riemann integrable on [0, 1]. Also evaluate o f(x)dx.