6. Let f be the function defined by f(x) = 3 / (2x^2 - 7x + 5). (c) Using the identity that 3 / (2x^2 - 7x + 5) = 2 / (2x - 5) - 1 / (x - 1), evaluate ?[5,?] f(x) dx or show that the integral diverges. (d) Determine whether the series ?[n=5,?] 3 / (2n^2 - 7n + 5) converges or diverges. State the conditions of the test used for determining convergence or divergence.
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\] This integral can be split into two separate integrals: \[\int_{5}^{\infty} \frac{2}{2x-5} dx - \int_{5}^{\infty} \frac{1}{x-1} dx.\] These integrals can be evaluated using the formula for the integral of 1/x, which is Show more…
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