MATH 104 Midterm: MATH 104 UPenn Exam m104 sExam 2

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31 Jan 2019
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Math 104 sample final exam 2: a scientist collects data that relate two variables, x and y. Instead of plotting y as a function of x, she plots log2 y as a function of x, and gets a line whose slope is 3 and whose intercept on the vertical axis is 4. Parallel cross-sections perpendicular to the base are squares. The volume of the solid is: (a) 1/3 (b) /2 (c) 4 /3 (d) 4/3 (e) 16/3 (f) 8 /3. 4(i/n)2 = (a) 4 (b) e (c) (d) 4/3 (e) 8/3 (f) : (cid:2) ln x x3 dx = 1 (a) 1/4 (b) 1/3 (c) 1 (d) ln 2 (e) ln 3 (f) divergent: (cid:2) 4. 3 (a) ln(4/3) (d) ln(12/5) dx = (b) 2 + arctan(3) (e) /3 arctan(1/4) (c) ln(9) (f) /4 ln(3: consider the two in nite series: (i) (cid:1)n=1 ( 1)n(n + 1)3n.

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