0.1 11) Use a Taylor series to approximate ſ sin(x*)dx with error less than 10-15 0...
0.1 Use a Taylor series to approximate ſ sin (x“)dr with error less than 10-15
Please answer all, be explanatory but concise. Thanks. Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
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...
6) Use a Taylor series to estimate the integral's value to within an error of magnitude less than 10-3 0.7 In(x2 + 1)dx 6) Use a Taylor series to estimate the integral's value to within an error of magnitude less than 10-3 0.7 In(x2 + 1)dx
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T. 15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
need answer for #2, which is about arctan #1 Suppose we want to estimate sin (0.1) using the Taylor series of sin x at x = 0. (a) Find roughly a number of nonzero terms which are required to compute sin(0.1) to n decimals (you do not need to find the minimum number.) (b) Find such a number more accurately, i.e. find a smaller one, using any mathematical tech niques. You may want to use the fact related to Stirling's...
Setup a program that will solve for sin x using the Taylor series expansion of x. Make sure the number of terms is some type of input. Calculate approximate 1. error Setup a program that will solve for sin x using the Taylor series expansion of x. Make sure the number of terms is some type of input. Calculate approximate 1. error
Use substitution to find the Taylor series at x = 0 of the function 16 sin(-x). What is the general expression for the nth term in the Taylor series at x = 0 for 16 sin (-x)? 00 (Type an exact answer.) no
Use a series to estimate the following integral's value with an error of magnitude less than 105 0.2 sin x dx
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...