If f(x) has the following Taylor series, Σ 5" (x + 2)", (n + 1)(n+2) P=0...
Solve the Taylor Series.
1. (a) Use the root test to find the interval of convergence of-1)* に0 (b) Demonstrate that the above is the taylor series of f()- by writing a formula for f via taylor's theorem at α-0. That is write f(x)-P(z) + R(x) where P(r) is the nth order taylor polynomial centered at a point a and the remainder term R(x) = ((r - a)n+1 for some c between z and a where here a 0. Show...
7. (-/5 Points) DETAILS MY NOTES Find the Taylor series for f(x) centered at the given value of a, assuming that f(x) has a power series expansion about a. f(x) = x - x3 = --3 Submit Answer Find the Taylor series for f(x) centered at the given value of a, assuming that f(x) has a power series expansion about a. 1 f(x) a = 2 х 20 8( (-1)". „n+1(x - 2) n=0 Find the Maclaurin series for f(x),...
point) Consider a function f(x) that has a Taylor Series centred at x = 5 given by ſan(x – 5)" n=0 he radius of convergence for this Taylor series is R= 4, then what can we say about the radius of convergence of the Power Series an ( 5)"? nons A. R= 20 B.R= 8 C. R=4 D. R= E. R= 2 F. It is impossible to know what R is given this information. point) Consider the function f(x) =...
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...
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
5. A function f has Taylor series (at 0) f(x)=0+2x+ 4x2/2! + 3x3/3!+... Assume f−1 exists. Find as much of the Taylor series of f−1 (at 0) as you can. (Since you only know the first few terms of the Taylor series for f, you can only figure out f−1. (Hint: There are two ways of doing this problem. One is get the derivatives of f−1 from knowing the derivatives of f; we talked about the first derivative in January...
(1 point) Determine the Taylor Series of the function f(x) = - 8x2 (1 − x)2 centred at x = 0. Α. (-8)" x2η. n=1 ΧΟ 8 Β. r743 η + 1 n=0 0 c. Σ 8" x2η. n=1 ΧΟ 8x2n+2 n=1 Ε. Σ 8nx+1. n=1
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...
2 1. The Taylor series for a function f about x =0 is given by k=1 Ikitt (a) Find f(")(). Show the work that leads to your answer. (b) Use the ratio test to find the radius of convergence of the Taylor series for f about x=0. c) Find the interval of convergence of the Taylor series of f. (a) Use the second-degree Taylor polynomial for f about x = 0 to approximate s(4)
(1 point) The Taylor series for f(x) = e' at a = -2 is Cr(x + 2)" n=0 Find the first few coefficients. Co = C1 = C2 = C3 = C4 = x 5 (1 point) Find the first four terms of the Taylor series for the function - about the point a = 1. (Your answers should include the variable x when appropriate and be listed in increasing degree, starting with the constant term) 5 II + +...