MATH 2224 Midterm: MATH 2224 VT 2224c Test f s05

• School: Virginia Tech
• Department: Mathematics
• Course: MATH 2224
• Professor: All

Document Summary

Common final exam, spring 2005: consider the in nite series correct? n=1 ( 3)n/5n 1. 3(cid:2) 3 (x2 + y2 + z2) dxdydz. N + 2 n2 + n + 1 n=1. 0 (cid:2) 2x x2 (cid:2) 2 (cid:2) 4. 0 f (x, y) dxdy f (x, y) dxdy x2. 0 (cid:2) y/2 (2) (4) f (x, y) dxdy f (x, y) dxdy: the rst three nonzero terms of the taylor series for f (x) = 3 x expanded about the point x = 1 are: (1) (3) The mass density of the lamina is (x, y) = x2 + y2. The mass of the lamina is (1) (3) 0 r2 drd (cid:2) /4 (cid:2) 2 (cid:2) 2. 0: given a = correct? n=2 ( 1)n ln n and b = n=1 ( 1)n. 1 + 3 nn (1) series a and b both converge. (2) series a converges and series b diverges.