MATH 1552 : Practice Exam 2
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Put your name on the all pages that you turn in. If you need extra writing space, write on the reverse side of the problem you are working on and label it accordingly. Credit for answers without supporting work will be limited. 0 e 3x dx converges or diverges, and if it does converge, nd the value of the integral. 0 e(x2) dx by using simpson"s rule with six subintervals. Use the fact that the error in simpson"s rule is bounded by. 180n4 where k is a bound for |f (4)(x)|, n is the number of subintervals, and the integral is over the in- terval [a, b]. You may also use the fact that the fourth derivative of e(x2) is 4e(x2)(cid:0)4x4 + 12x2 + 3(cid:1) and that this function is monotonically increasing on the interval [0, 1]. Let p let {sn} be the corresponding sequence of partial sums of the series. k=1 ak be an in nite series.
