The power series representation of f(x) = ln(x²-1) is given byOA. (-1)"hn=1 n+1Σ -x+1, -1

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Exercise 4.2 I. Find a power series for the given functions. 2 1. f(x) =, centered at 0. 2-x2 2. f(x) = centered at 0. %3| 1+x 3. f(x) = centered at 4. X-3 4. f(x) = centered at 2. %3D X-1 5. f(x) = centered at 2.
Find a power series for the function Select one: Σ n = 0\ 3m a. Ο Φ. Ο b. Σ(−1)" n = 0 3" 1 Σ n = 0 3" Od. ((-1)* η = 0 4" C. o X + tantilage H = 0 +4" +. tanti) +3" γ r *r* 1 Στατικο Σ +3+1 4" Sx – 15 4x + 11x - 3 centered at 0.
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Which of the followings are divergent series? 1. E 5+2" n31 2nt2 II. 1 00 1 4n1 II. E(sin1)" IV. cos(nn)7"/2 n-1 O a. I, II O b.I, IV O d. II, IV O e. II, II
As above, let Suppose Compute ||B||2 to the nearest hundredth. Answer: 8 9 -3 A = 40 9 -6 5 1 -1 10 B = A (49) A
The Maclaurin series Select one: x3x+2 Σ(-7)*- a. x²e-7x² O b. -7cos(x³)+2 O c. -7e³x+2 O d. x'sin(-7x³) represents which expression below?
(d) Let an 6n²+ n-1 ntn and bn = √n n+1' (i) Determine whether {an} is convergent or divergent. Explain briefly. (ii) Determine whether Σ(-1)n-¹b, is convergent or divergent. Explain briefly. n=1
3. * x-1/3 dx = 00, so the series diverges.
Steps: 1.What is the f" (x) of the function? 2. After getting the f"(x), what is the f"(a) of the function as a=1? + co ?(a) 3. After getting the f"(a), input it into the (numerator) of Taylor series expansion formula: E (x – a)", for n! - (x - a)", a=1. 4. After getting the Taylorseries expansion, find the intervalof convergence (using Ratio Test). f(x)= log,(2x – 1) 2 f'(x)= In (6) (2x-1) 4 P"(x)= - In (6) (2x-1)2 16 p"(x}= In (6) (2x-1)3 96 p''(x)= - In (6) (2x-1)4 f"(x)=???? To get the f"(x), find the trend among the derivatives.

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The power series representation of f(x) = ln(x²-1) is given by OA. (-1)" Σ -x+1, -1