4. Show that the series f(x) = E cos(nx) ni+ 2021 converges uniformly on R. Use this to show that f is integrable on [0, 27] and fo" f(x)dx = 0.

Q: Find f'(x) and f f(x) dx. 14. Find the nth Maclaurin polynomial for f(x) = 2 by definition. 15. Find…

A: 15. The given function is  fx = xex2+2. We know that the Maclaurin series of the function ex can be…

Q: 3. Prove that the series 1 x2n n! 1 + x²n n=0 converges uniformly on R to a continuously…

A: We'll follow these steps:Show that the series converges uniformly on R.Prove that the limit function…

Q: 3 Find the Taylor series of f(x,y) around 1, (2-4x)2

A: In this question, we find the Taylor series expansion of the function  f(x)=3(2-4x)2 around x=1. And…

Q: Show that Show that Show that fexx dx converges for any p = R. In xdx and f′ (x(ln x)(1 + x²)−¹)dx…

A:

Q: Find the macluarin/Taylor series centered at C F(x) = sinsin(3x), C = 0

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Q: Find a Maclaurin series for the function f(x) = | t sin(t*) dt.

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Q: if x +0 e- - Let f(x) = 8 }. Compute f'(0). As it turns out, all the n-th derivatives of f if x = 0…

A: The solution are next step

Q: ii) Obtain the Fourier series of the function g defined by g(x) = | f(t)dt, justifying your method…

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