Prove that 2e 5 2 sin (Tx/4)+1/2 dx ≤ 2e-1 1+2√2 (i) Show that zloga 7/4 dx - (log) (log x)-3/4 (ii) Hence determine whether the series n= 1 n(logn) 7/4 is convergent or divergent.

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A: Here , f(x) = x3-3x2-1 We find required value.

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A: Here I am attaching image so that you understand each and every step.

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A: Series problem....

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A:

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A: For (a), We need to find the Fourier sine series for the function, f(x) = x3 - π2x on the interval…

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A: Given: fx=x, 0<x<πx+π, -π<x<0 To find: Fourier series

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A: The problem is asking us to determine whether the infinite series ∑n=1∞sin(n) is convergent,…

Q: a power series. Use the 2n +1 Integrate the function as 00 E(- 1)". Maclaurin series sin x= (2n +1)!…

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