MATH 152 Midterm: MATH 152 TAMU 2010a Exam 3b Solutions
Document Summary
Math 152 spring 2010 exam iii: b: which of the following series converge abso- Recall that an is absolutely convergent (1) which diverges by the test. 1 n n which is a convergent p series. Hence this is the only series that converges absolutely. (b): if (a): for divergence. cos(n ) Pn=2 ( 1)n ( 1)n (c): ries. (d) vergent p-series: a: the series ( 1)nn2 n2 + 1 diverges by the test for. Divergence since lim n ( 1)nn2 n2 + 1 6= 0. Pn=0: a: recall the maclaurin series for ex: x2. + 1 x ex = 3! xn (n + 2): b: to nd the unit vector in the direction of b a where a = h0, 2, 1i and b = h1, 1, 3i, we will rst. A = h1, 1, 3i h0, 2, 1i = h1, 1, 2i. To make this a unit vector, we will divide by the magnitude: h1, 1, 2i.
