Assume that sin(z) equals its Maclaurin series for all x. Use the Maclaurin series for sin(72) to evaluate the integral 0.67 I sin(7z) dz Your answer will be an infinite series. Use the first two terms to estimate its value.

Q: Write the given function as a power series: (cos(x)-1)/x. Your power series should start with n=1…

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Q: Without solving the exact answer, calculate sin(2) by evaluating up to six terms of Maclaurin series…

A: For the solution follow the next step.

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

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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: Euler's Identity says that for any real number x, e" = cos x+isinx where i=√-1. Given that i² = -1,…

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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: Use a power series and i2 = -1 to prove the identity: sin(x) = eix -e-ix / 2i

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Q: 2. Find the sum of the series sin?a + sin2(a + B) + sin2( a + 2B) + + sin?(a + n - 1)B ......

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Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (8x²) to…

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Q: Use the standard power series for sin(z) and cos(z) functions to determine the power series for…

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Q: Σ (-1)"(n + 1)n² (2n)! -2n+1 — — п n=0

A: Find a power series representation for x2cos(2x).

Q: sin x 5. Use series to evaluate dx .

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Q: Substitute x 2 for x in the Maclaurin series for sin x.

A: To Substitute x2 for x in the Maclaurin series for sin x

Q: Express ∫ sin x2 dx as a power series.

A: The given integral is ∫sinx2dx

Q: State whether y =tan x can be expressed as a Fourier series. If so how?. If not why?

A: State whether y =tan x can be expressed as a Fourier series. If so how?. If not why?

Q: Use a series representation of sin 3x to find values of r and s for which (sin 3x lim + s) = 0. x2

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Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (8x²) to…

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