Express the function as the sum of a power series by first using partial fractions. (Give your power series representation centered at x = 16 x² - 2x - 63 f(x) = n=0 f(x) = Find the interval of convergence. (Enter your answer using interval notation.) 0

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A: BY this  theorem we can convert flux integral to line integral.

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A: see my solution

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A: dydx=x+1y4+1 (y4+1)dy=(x+1)dx Integrate both sides ∫(y4+1)dy=∫(x+1)dx∫y4 dy + ∫dy  = ∫x dx + ∫dxy55…

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A: The solution of the given differential equation is  y=e(x22-2x+C)or y=Ce(x22-2x)

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A: For the solution of the problem follow the next steps.

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A: To determine:  Local Max and Local Min

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A: The explanation is as follows