MATH 152 Midterm: MATH 152 TAMU 2010c Exam 2b Solutions
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Fall 2010 math 152: e the denominator contains a repeating lin- ear factor and an irreducible quadratic factor, so the form of the partial fraction decompo- Cx + d x2 + 2x + 3: a as n , e n 0, so an . 5: b since sin2 x 1, a improper integral only if p > 1, so comparison with . 1 xp sin2 x x2 dx converges by: e |an| = , so the terms of the sequence alternate between approaching. 3 (odd-numbered terms), which means the: d the test for divergence fails since n. Compare with which is convergent by the p-test. n3 5 0. Us- n3 5 ing the limit comparison test, we see that. = 1, so the given series is convergent: d (a), (c), and (d) are p-series with p = respectively, so only (d) is convergent.
