(2) Find a power series for the function centered at 0. 3 1 (x + 1)² 1 (x + 1)³ (a) f(x) = (b) f(x) = 2r 5 2 1-x² (c) f(x) = (d) f(x) =

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A: Find the derivative of function

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A:

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A: The solution is given as

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A:

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A: Power series of fx about x = a isfx = ∑n=0∞fnan!x-an              —⊛

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A:

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A: Answer to the question as follows:

Q: (IV) Find the half-range cosine series of f(x)= x(7-x) in (0,7). Hence find the sum of 1 1 the…

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A:

Q: (a) Show that, for any positive integer n. R-2 n-l n² + 3n 2n =an(n-1) - ¹) (-) + n()** for some a,…

A:

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

A:

Q: (2) Find a power series for the function centered at 0. 3 1 (x + 1)² 1 (x + 1)³ (a) f(x) = (b) f(x)…

A: Taylor series about x=0,

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Q: A Taylor series is something we often use and looks like dy y(xo+h) = y(xo) +h(x) + h² d²y 2! dx²…

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Q: A. Use power series to solve (1 – x)y' - 2y = 0

A: In the question we have to solve the differential equation using power series.

Q: (III) Find the Half-range Sine series of f(x) = sin(x) on (0,2).

A:

Q: (a) Find the binomial series for (1+¹/² up to and including terms in x².

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A: Given:

Q: half range sine series

A: