MAT-2510 Midterm: MATH 2510 App State Spring2010 Test2
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/28 points) converging questions n2 + 2n + 3(cid:29) converges. (a) prove that (cid:28) 3n2 (b) show that (cid:28) sin(n) n4 + 1(cid:29) converges. Hint: ignore sin(n), then prove sin(n) is bounded and use a theorem. (c) prove that (cid:28) n2 + 1 n (cid:29) diverges. (d) let an a and bn b. Show that an + bn a + b. /20 points) some set stu . (a) let a, b, c, d be sets. Suppose that a b c d, a b = , and c a. Prove that b d. (b) let f : x y and let t y . Prove that if f is onto, then f (f 1(t )) = t . Half of your proof does not need the onto hypothesis. /28 points) for each of the following functions, decide if f is 1-1, onto, both, or neither. Assume that f g : x z is a bijection.
