Applied Engineering Analysis II
Only answer 5(c).
Applied Engineering Analysis II Only answer 5(c). Find the Taylor series about the point indicated of...
9,17,33 and ill like cos 22 14. 2+1 In Exercises 1-26 find the Taylor series for the function about the given point. In each case determine values of z for which the series converges to the function. 3 1. + about zo = 0 2. 1+2 about = 1 3. (1 - 2)2 about 20 = 0 4. e* about 20 = 1+i 5. sin z about 20 = i 6. cos z about zo = 2 - 7. sinh...
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...
= 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4 = 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about r y" - (sin )y=cos y(0) 3, y'(0)-4 +0(*) y=3-4
(1) Find the Taylor series about 0 for the following functions: (a) ce (b) sin(x), (c) V1 + x (d) cos(x)
Problem 1 MATLAB A Taylor series is a series expansion of a function f()about a given point a. For one-dimensional real-valued functions, the general formula for a Taylor series is given as ia) (a) (z- a) (z- a)2 + £(a (r- a) + + -a + f(x)(a) (1) A special case of the Taylor series (known as the Maclaurin series) exists when a- 0. The Maclaurin series expansions for four commonly used functions in science and engineering are: sin(x) (-1)"...
In(z) 3, Consider the function f(x)= (a) Find the Taylor series for r(z) at -e. b) What is the interval of convergence for this Taylor series? (c) Write out the constant term of your Taylor series from part (a). (Your answer should be a series!). (d) What can you say about the series you found in part (c), by interpreting it as the limit of your series as x → 0. (Does it converge? If so, what is the limit?)...
(2) Show that sin(x) is the sum of its Taylor series. (3) Find the first three nonzero terms of the Taylor series about 0 for the following functions (a) cos(x2) (b) e (c) tan(x)
0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about x = У' — (sin x)y У(0) %3D —9, У (0) 3 —3 =COS X x2+ у%3 —9 — 3х+ x4O(x5) 0 of the differential equation (1 point) Find the indicated coefficients of the power series solution about x = У' — (sin x)y У(0) %3D —9, У (0) 3 —3 =COS X x2+ у%3 —9 — 3х+ x4O(x5)
6. Let f(z) = z² sin z. (a) (5%) Find the Taylor series expansion of f(z) about zo = 0. Where does the series converge? (b) (5%) Find f(?)0) and f(*)(0).
(1 point) Find the indicated coefficients of the power series solution about x = 0 of the differential equation -(sinx)y y(0) = -5, y'(0) = 3 = cos x, x2 y 53x (1 point) Find the indicated coefficients of the power series solution about x = 0 of the differential equation -(sinx)y y(0) = -5, y'(0) = 3 = cos x, x2 y 53x