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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(c) First, we can rewrite the integral as follows: \[\int_{5}^{n} f(x) dx = \int_{5}^{n} \left(\frac{3}{2x^2-7x+5} - \frac{2}{2x-5} - \frac{1}{x-1}\right) dx\] This integral can be split into three separate integrals: \[\int_{5}^{n} \frac{3}{2x^2-7x+5} dx - Show more…
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