The function f(x) = 3x arctan(8x) is represented as a power series 00 f(x) = Σ cnx". n=0 Find the first few coefficients in the power series. Co = C1 = C₂ = C3 = C4 = Find the radius of convergence R of the series. R = Hint: Notice that d dx - -arctan(8x) = 8 1+64x²' , SO 1 ³/₁ 8 1 + 64x² Can you find a power series representation for a power series representation of 3x arctan(8x)? dx = arctan(8x) + C. 8 -? Integrating that (and finding the value of C) will give you a power series representation for arctan(8x). How do you then adjust to get 1 + 64x²

Q: eix+e-ix 7. Develop the Maclaurin series for f(x) e*. Remember i? = -1. Does this series look…

A:

Q: Start with the geometric series (a) Find the sum of the series 00 (i) Σ nx", |x| < 1 n = 1 (ii) SW n…

A:

Q: (x+1)y''-(2-x)y'+y=0  y(0)=2, y'(0)=-1 What are the first six non zero terms of the power series?

A: (.) Given differential equation is, (.)  Power series solution of a second order linear differential…

Q: 4) (a) Find a degree 3 power series for the function sin(x) centered at I fla) = f (a) + f(a) (x-a)+…

A: By using degree-radian conversation

Q: #3. Prove that 2 = tan [ = log (T_-_ iz)

A: To Prove:z=tan1ilog1+iz1-iz12.

Q: By using Power series, show that Taurinus's "log spherical" formula…

A: The law of cosines:                      a2=b2+c2-2bccosA where a, b and c are the sides of a…

Q: rĩ sec² 0 (e) tan 0 do. Vtan 0

A: That's easy. Have a great day!!!

Q: Use the Maclaurin Series for w(x) e*and q(x) = cosx to find first four terms for nonzero f(x) =…

A:

Q: Find the terms through degree 4 of the Maclaurin series for f(x). Use multiplication and…

A:

Q: What is the correct power series form of f(x) =/1-3x³ at a-0? * (1·3.5..· (2n- 3))· 3^x³n Σ n=0 2" -…

A:

Q: Approximate cos(0.2) to five decimal-place accuracy using the MacLaurin series for cos(x). cos(0.2)~

A: MacLaurin series of cosx is  cosx = 1- x2/2! + x4/4! - x6/6! + ......... We have to find the value…

Q: Solve the IVP by a power series showing details of your work. Find the value of the sum at x1 to 6…

A: Given: IVP is x2+2y''+3xy'-y=0, y0=1, y'0=1 and x1=0.5. To solve the IVP by a power series…

Q: 4) (a) Find a deqree 3 power series for the function sin(x) centered at T fla) = f (2) + f(a) (x-a)…

A:

Q: Use a power series to solve 3y" - y = 0, Find the radius of convergence. y(0) = 7, y'(0) = -8.

A:

Q: 5. Consider the function f(x) = r tan-(") (a) Find a power series representation for the function.…

A: series and sequences