11. For each x,, Show that x, (-1)"x, converge or diverge. n=1 n=1 (*Using comparison test and alternating series test) 1 (1)xn cos-• cosn

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A: Please see the below picture for detailed solution.

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Q: Expand f(x)=sin(x) on the  interval (0,pi) [Fouries Series] a) in consine series b) in sine series

A: PART A: Concept Used: The half range cosine series of the function fx is given by  fx=a0+∑ancosnπxl…

Q: 2 ,-n² and convergence of an where an what do you conclude about the series? ne

A: Given: ∑an where an=ne-n2

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Q: Find a power series for f(x) =

A: Given,          f(x)=6x(x2+1)2,   x&lt;1

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Q: 24. Let f be a function such that f'(x) Maclaurin series for f? = sin 9 (A) x - + 10 216 9 X (B) 2x…

A: Step 1:Step 2:

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Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- 6 +…

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Q: 20. Using = 00 1-x n=0 a) Find a power series for c) Find a power series for 1 1+x¹ - 4x³ (1+x¹) ²…

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Q: For the series ∞0 n=1 (-1)" 6n0.5 +8 calculate the sum of the first 3 terms, S3.

A: For the given alternate series, to find the partial sum and error bound for it.

Q: Show that as a half range series of cosine terms for 0 < x < 1, /cos 2x cos 4x cos 6x + 12 2² 3²…

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