02-03 Fall Final Exam

# 02-03 Fall Final Exam - MATH 104 - FINAL EXAM Friday,...

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Unformatted text preview: MATH 104 - FINAL EXAM Friday, January 17, 2003, 8:30AM—11230AM McCosh 50 Note: Average was approximately 60 percent. Considered hard but fair. 1. ( 8 points) Compute the following integrals: “0 / (Tia—an“ (h) / a31n(a:+1)d:c 2. (12 points) (a) Let R be the region bounded by the :c-axis and the graph of y = 1/(513‘1 + 1) as :1; runs from O to 00. Find the volume of the solid of revolution obtained by revolving R about the y-axis. (b) Calculate the area of the surface obtained by revolving the graph of y = 6” between the points (0, 1)‘ and (1,6) around the x-axis. ' 3. { 16 points) Determine whether the following integrals converge or diverge. Give your reasons. 00 da: (a) ﬁ + m3 0» f5 dw (c) [01 L0 + m) dad x3 °° dac d f ( ) 1 m Ina: _ 4. { 16 points) Determine whether the following series converge or diverge. Give your reasons. 00 "2 a ( ) “5 + 1 oo ( 1)nn2 00) ED mg + 1 oo 2. n (c) n ,3 “:0 n. co 1 33—2 "' .1 ' = ' 5 {2pomts)Let ﬁx) r§)n_1.2( 3 ) (a) For what values of as does the series converge? Give your reasons. (b) Find f(50) 6. {12 points) 3 - 1 — 2 cos a; (a) Use Taylor series to compute lim (i—T—L. w—rU x(s1n a: — 1:) dt 1 + t4 centered at a: = 0. For what values of :1: does 1; (b) Find the Taylor series of = f o it converge? 7. {12 points) For the questions below express your answers in the form a + ib where a and b are real numbers. Simplify your expressions for a and b. . . 7+z' 43 (a) Simplify (3+ 41,) . (b) Solve Z4 = —8iz. 8. {12 points) Find all real solutions to the following differential equations. (a) :11" + 221’ + 10y = 0 (b) 2y” + y’ — 3y = 0 ...
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## This note was uploaded on 09/26/2010 for the course MAT 104 taught by Professor Edwardnelson during the Fall '08 term at Princeton.

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02-03 Fall Final Exam - MATH 104 - FINAL EXAM Friday,...

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