Practice Final Exam #41. Find the integralZ(x2− 4)dxx(x2+ 4).2. Evaluate the integralZdx√8 + 2x − x2.3. Evaluate the integralZln x ln(ln x)xdx.4. Evaluate the integral or show that it is divergentZ∞0dx(x + 1)2(x + 2).5. Determine whether the sequence is convergent or divergent; if it is convergent, find thelimitan=ln2nn.6. Determine whether the series is divergent or convergent∞Xn=1n2− nn4+ n.7. Determine whether the series is conditionally convergent, absolutely convergent, or diver-gent∞Xn=1(−1)nn + 1n2+ 11/3.8. Find the radius and the interval of convergency of the power series∞Xn=1(n!)2(2n)!xn.9. Solve the differential equation1 + 2xy2+ 2x2yy0= 0.10. Solve the differential equationy00− 2y0− 3y = cos 4x.11. Solve the differential equationy00− xy0− 2y = 0using power series.12. Find all solutions to the equationx4= 1.Find x−1in the form a + ib for all
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