MAT-2510 Midterm: MATH 2510 App State Spring2010 Test2 answer key
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Be sure to show your work: (28 points) converging questions. To come up with a proof rst we"ll need to do some scratch work . 3n2 n2 + 2n + 3(cid:29) converges. (a) prove that (cid:28) see that this sequence"s limit is 3. =(cid:12)(cid:12)(cid:12)(cid:12) n2 + 2n + 3 n2 + 2n + 3. 6n 9 n2 + 2n + 3(cid:12)(cid:12)(cid:12)(cid:12) of the fraction until we have something simple enough to set equal to and solve for n. The following because increasing the numerator increases the fraction. Likewise, the < holds because decreasing the denominator increases the fraction. Now we have a simple estimate for our fraction: write our proof. So 15/n = = 15/ = n. now we"re ready to. Suppose n n , we have that n (cid:24) 15 (cid:12)(cid:12)(cid:12)(cid:12) =(cid:12)(cid:12)(cid:12)(cid:12) n2 + 2n + 3 n2 + 2n + 3 n2 + 2n + 3.
