Find the Fourier series representation of the periodic function below f(x) = ax² - b if --

Q: Confirm that summation d/36 ϕ(d) = 36 and summation d/36 (-1)^(36/d) ϕ(d) = 0

A: We have to confirm that ∑d/36φ(d)=36 and ∑d/36(-1)36/dφ(d)=0.

Q: Q/ for 8 ER, use the power series for the exponential function e² to show that (-1) ¹ (2n)!…

A: Please see the below picture for detailed solution.

Q: The first derivative of the power series (-1)" n = E- (18x)" is n! f(x) n=0 -18 f(x) O f(x) O - f(x)…

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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: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

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

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

Q: +00 (-1)"(3n + 4) 23n+3(n + 1) Differentiate the function f (x) = x ln(1 + x) to determine the sum…

A: The product rule of the differentiation is as follows: ddxu(x).v(x)=du(x)dx.v(x)+dv(x)dx.u(x)

Q: z-i) in the following (6) 1 <시리 <2 (C) r

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Q: 00 Write the Taylor series for f(x) = e at x =-3 as en (x + 3)". n=0 first five coefficients.

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Q: 6. (a) Calculate the Fourier Series of f(x) = |x], −1 < x < T. (b) Draw the 2-periodic function…

A: According to the Bartleby guidelines, I will answer first three subparts of a multiple subpart…

Q: f (x) = cos(2\x) Find the MacLaurin Series for = Cos(2.

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Q: Find a geometric power series for the function Select one: है n=0 6" + 1 a. O b. OC. Z Ž x" n=0 6²+1…

A: The given function is . The geometric power series of the above function is required.

Q: Find the third Taylor series for f(x) = 2^-x about 0. Use this series to evaluate the function at…

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Q: Find a power series representation for x2cos(2x) and then by differentiation, show tat the equation…

A: Power series exaption of the function

Q: Find the coefficient of the term involving a of the MacLaurin series of the function „5 f(x) = 112 –…

A: we have to find the coefficient of x^5

Q: etermine the coefficients of the x3 term of the Taylor series about the point 0 of the function f(x)…

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Q: Consider the power series f(x)=log(n)x" . The R.O.C. of f(x) is (a) 0 (b) 1 (c) 3 (d) 0

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Q: Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then…

A: given function f defined for -π≤x≤π by fx=1if -π2≤x≤π20otherwise and then extended to be 2π periodic…

Q: Use Taylor series to find Limit (x-> 0) Sin (x)/ x

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Q: expand the function f(x) = sin(x) / (coshx +2) in a taylor series around the origin going up to x^3.…

A: Taylor series of function f(x) around x=a is defined as:

Q: Find a series that converges to sin (z") dr.

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Q: Find the Maclaurin series of tan^−1 (x). Your answer should be in terms of summation notation

A: In the question it is asked to calculate Maclaurin series of tan-1(x) and also it is asked to…

Q: Find two power series solutions of (x2+2)y"+5xy'-y=0 about the ordinary point x=0. Include the first…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the Laurent series for function f(z) == in the regions (a) 0</2/<3. (61 3</2/<00 (C) 0</7-3/<1…

A: We have given a complex variable function f(z)=1z(z-3i) for the given conditions for z. To find the…

Q: What is the next term in the Taylor series generated by cos x after 24 (Simplify your answer. Use…

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Q: Represent this function by a power series. Then find the interval of convergence. f(x)= x/(9+x^2)

A: