Practice Final Exam 4 1 Find the integral Z 2 Evaluate the integral Z x2 4 dx x x2 4 dx 8 2x x2 3 Evaluate the integral Z ln x ln ln x dx x 4 Evaluate the integral or show that it is divergent Z dx x 1 2 x 2 0 5 Determine whether the sequence is convergent or divergent if it is convergent find the limit ln2 n an n 6 Determine whether the series is divergent or convergent X n2 n n 1 n4 n 7 Determine whether the series is conditionally convergent absolutely convergent or divergent 1 3 X n 1 n 1 2 1 n n 1 8 Find the radius and the interval of convergency of the power series X n 2 n x 2n n 1 9 Solve the differential equation 1 2xy 2 2x2 yy 0 0 10 Solve the differential equation y 00 2y 0 3y cos 4x 11 Solve the differential equation y 00 xy 0 2y 0 using power series 12 Find all solutions to the equation x4 1 Find x 1 in the form a ib for all solutions
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