00 Use the power series representation f(x) = arctan(x) = Σ n=0 representation for g(x) = on the interval (-1, 1). (Hint: arctan(x) = x²) - 1+x² dx Select the correct answer below: 00 O 8(x) = (-1)"+¹2n O g(x) = n=0 00 Og(x) = (-1)"x²n-1 n=0 00 (-1)"x²n ○ 8(x) = (-1)"x²+1 n=0 00 (-1)" 2n+1-1

Q: Which of the following information is correct for the sequence 3 7 dx 1 dx 1 dx dx {an}n=l X (a) The…

A: Given: The given sequence is ann=1∞=13∫13dxx,15∫15dxx,17∫17dxx,19∫19dxx.....

Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: Can the iteration xn+1 = cos (xn) be used to find the solu- tion of the equation cos (x) – x = 0 in…

A: Solution is given below

Q: find a power series representation for f(x) ln(14 -x)

A:

Q: Evaluate cos(x) – 1 + lim 2 12a4 Hint: Using power series.

A:

Q: 2#), 3. What are the first three terms of the series n=1 ? A. 2 4 6 x3 В. 2 4 6 + x4 x² x6 c. 2 4 6…

A:

Q: O Let f (x) be a function which is represented by the power series f(x) =E(-1)"-1)". n3 What is the…

A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

Q: How to write sin(x)cos(3x) in power series

A: We need to write sin(x)cos(3x) in the power series. Taylor series of function fx at a is defined as:…

Q: help me with part e and f please

A:

Q: Consider the following sequences n G In (1+n) (ii) e^/ (n²+1), (iii) √√n²+ √n²+2n -n. Which of the…

A: Let {an} be a sequence of real numbers If an≤an+1 ∀ n∈N then the sequence an is called monotonically…

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: Find Ln(0.98) by Maclaurian series F(x)=Ln(X+1)

A:

Q: Given . (13cosx1 elxl f(x) = . 13cosx . a) Sketch the graph of f(x) in the interval (-,) and…

A: We are solving only the a part of the given question for the solution of b part please do resubmit…

Q: sinx x0 e²x-1 5. Use power series to evaluate lim

A: Power series expansion

Q: Pls solve this question correctly instantly in 5 min i will give

A:

Q: Q1-) Determine whether the following functions are convergent or divergent: 1 1- En=1 ((3n-1)*/…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: F(t) = VN + Nt2 %3D

A: Given that F(t)=15+15t2 The fourier series will be f(x)=a02+∑n=1∞ancosnπx/L+bnsinnπx/LWhere…

Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

A:

Q: -0.25 Find an approximation for (1 – e**-!) In(1 – cos(,r² - 1))d.r with Simpson's rule -1.25 using…

A: Given ∫-1.25-0.251-ex4-1ln1-cosx2-1dxand n=4

Q: (-1)" (13z)" is 00 The first derivative of the power series f(x) = n! O -13 f(x) O f(x) O - f(r) O…

A: We need to evaluate the first derivative of the following power series : fx = ∑n=0∞-1nn!13xn

Q: DO 11/2 x cos x² clx

A:

Q: etermine the Taylor series of the function f (2) = (3+ x) around x = 1. 00 Š(-1)"4"(z - 1)" b)…

A:

Q: What is the 1st term in the power series expansion of the function y = cos x? A) x B 1 (c) о D) x^2

A:

Q: Σ (-1)". It is known that for all x E R, COS x = (2n)! n=0 (a) Find a Power Series Representation…

A:

Q: x-14 Find the exact value of * dx. (x+4)(x-2) Select the correct answer below: 3 In(8/7) In(4) + 7…

A: we have to find the value of  ∫34 x-14x+4x-2dx

Q: Determine a power series representation for g(x)=x° cos(x). CoS

A: Solve the following