Mathematics

Mathematics, 28.07.2019 00:30, catcatscats122

Use part (a) to find a power series for f(x) = x ln(1 + x).

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Mathematics, 26.07.2019 04:30, anaiyamills

Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). what is the radius of convergence? (note: you don’t need to use the ratio test here because we know the radius of convergence of the series p∞ n=0 x n .) (b) use part (a) to find a power series for f(x) = x ln(1 − x). (c) by putting x = 1 2 in your result from part (a), express ln 2 as the sum of an infinite series

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Mathematics, 05.08.2019 21:20, bzhsh8282

A) use differentiation to find a power series representation for f(x) = 1 (9 + x)2 . f(x) = ∞ n = 0 what is the radius of convergence, r? r = (b) use part (a) to find a power series for f(x) = 1 (9 + x)3 . f(x) = ∞ n = 0 what is the radius of convergence, r? r = (c) use part (b) to find a power series for f(x) = x2 (9 + x)3 . f(x) = ∞ n = 2 what is the radius of convergence, r? r =

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Mathematics, 31.08.2019 00:10, SunsetPrincess

Overview part 2: the following general facts are true: 1. c.sin(x) = 0 for any constant (function) c and any integer n. 2. c. cos(n) = 0 for any constant (function) c and any integer n > 1. 3. c c2 = 27c1c2 for any constants ci and c2. 4. cos(nx) â¢ cos(n.2) = at for any integer n > 1. 5. sin(n.2) sin(n.) = for any integer n > 1. 6. cos(n.) sin(m.) = 0 for any integers n and m. 7. cos(n.) cos(ma) = 0 for any two different integers n and m. 8. sin(n.x) sin(m2) = 0 for any two different integers n and m. a function is periodic if it eventually repeats. the sine and cosine functions, for example, are periodic with period 27. a fourier series is an alternative to a power series for periodic functions. in this assignment we will focus on functions that are also periodic with period 27. a power series represents a function using different powers of 2. a fourier series represents a periodic function using different sines and cosines: |(2) = (a cos(n.) + bry sin(n.2)) t=0 we could find the coefficients of a function's power series by using derivatives. but how do we find the coefficients of a function's fourier series? assignment part 2: question 4: let m be some integer > 1. if 2) = (an cos(n.2) + br sin(n.2)) t=0 then what's () cos(mr)? use the general facts from above and write the simplest expression you can.

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