Evaluate the indefinite integral as an infinite series. ex- 1 dx 2x + C n = 1

Q: _x²y" + xy' + (4x² − ²) y = 0

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Q: 3/ Determine the Fourier series of the function shown. y=2 2- 2 -27 2т х 0 27

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Q: Calculate the third term of the power series of sin x if x = 1.5. Answer.

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Q: Σ 1 as a rational function. Express the series x2n n=1

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Q: Bsinh lan da bs dx C√x 0 using the first four terms of the series if a = 2, b = 10, c = 6, k = 0.63,…

A: We know  sinhx=x+x33!+x55!+x77!+... ∫0kbsinhaxncxdx=∫0kbaxn+axn33!+axn55!+axn77!cxdx…

Q: -7<Xく -% -%くxく 0 0<ズく% %くズく fea)= a + 2X N -2ズ fex) = -1<ズくO 0くXく1 b) |3|

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Q: Find the sum of the series (-1)" n² + 1' n=1

A: We will use fourier series to evaluate the sum of this series

Q: Express the series as a rational function. n=1

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Q: 1 Express the series as a rational function. 1 (x - 5)* 27 (x - 4)

A: Given: The series ∑n=1∞1x-52n-1+1x-42n-1, To find: The rational function expression for the given…

Q: Pu Find the Fourier Series to represent the function

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Q: Evaluate the indefinite integral as an infinite series. | arctan(x2) dx Σ + C n = 0

A: Answer

Q: For the function 1 7x + 4 find a power series representation about ¤ = 0. What is the coefficient of…

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Q: (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C…

A: Given:-