Math 1B - Spring 1994 - Ribet - Midterm 1, 2, and Final

# Math 1B - Spring 1994 - Ribet - Midterm 1, 2, and Final -...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 09/28/2000 THU 09:01 FAX 6434330 MOFFITT LIBRARY 001 Math 1B Spring, 1994 Professor K. Ribet First Midterm Examerbruary 22, 1994 ' 2 d 13. (6 points). Calculate / 1b (37 points Write a deﬁnite integral which represents the length of the curve y = tan m, nggw/él. 2 {7 points). Find the area of the surface obtained by rotating the curve 3,] = 81:30.17, 0 S a." g 271' about the line y : 0. Decide whether each of the following sequences converge or diverge. In the case of a convergent sequence, ﬁnd the limit. Explain your reasoning! 3a {4 points). an = ——' . nsin(l/n) if n is odd 3b 13 . 6n = n s) ifn is even; 36 (4 points). cn=w+—-..+__ 1 4a {7’ points). Evaluate] msin_1wdm. 0 4b (7 points). Suppose that = 3. Use Simpson’s rule with n = 4 to estimate f(8): 3 2 2 4 5 (’7 points Write as a sum of partial fractions: 3:4 —i— 2.712 ' h ' ' m 2"” 2 d f 11 ' 1 6a (6 paints). Evaluate t e 1mproper 1ntegra1 1 \$2 + 1 — w + 1 :c. (I t e rntegra is divergent, answer “divergent” and explain your reasoning.) ln 3 . d 6b (5 points). Find/1:12 gm i 1. Second midterm exam—April 7, 1994 00 1a points If the series 2(1 —— converges, calculate its value. If it is divergent, n=1 explain Why. 09/28/2000 THU 09:01 FAX 6434330 MOFFITT LIBRARY 002 sin a: , _ , (1:1: as an inﬁnite series. 1 1b (5 points). Use Taylor series to express / 0 CC 251 (5 points}. Find the radius of convergence and the interval of convergence of the DC . . . (w — 2)” 1nﬁnlte serles E —3—~—. n 71:1 00 2b (4 points). For What positive values of .1: does the series + converge? n n=1 3 . . . 1 . . 3 {7 pomts). Show that Ismx — a: + < 10—7 if 0 < a: < [Coriander the Maclaurm polynomial of degree 4 for sin 4a (6 points). Find y(t), given that 7531' + y = — sint and that Mar/2) = 0. x—y 4b (5 points). Solve the homogeneous differential equation 3/ = s Decide Whether each of the following series converges or diverges. Explain your reasoning! . m n . 1 5a (4130212253). 25—1) 718111;; 00 n! 51) (4 points). 2 —; n71; n=4 ' 0° (InnJM! t . ‘ 5c (4 pom 3) “2:31 TIN/E , l l l l 1 5d ' _ { g A. , , _ (Moms) 2 2.3 2-2-3Jr2-2-3-3g + + 1 212-2-3-3 2-2.2.3-3-3 1 What is the radius of il- 6 (7 points). Find the Maclaurin series Jfor 3 8 — w convergence of this series? Final exam “May 2],, 1994 (—1)”. nlfn ' 00 1b {6 points]. The alternating series 2 n=1 a. Converges conditionally; _ b. Converges absolutely; w C. Diverges; % +1 1 __ 1c (’7 points). Evaluate the improper integral / 1 f' 1 + 3: dx. (If the integral is divep _1 33 gent, answer “divergent” and explain your reasoning.) 2 09/28/2000 THU 09:01 FAX 6434330 MUFFITT LIBRARY ‘003 2a (5 points). For which values of a: does the series Z + (312)”4'1) converge? Find n20 the sum of the series for those values. (LN 21) (7 points]. Consider the differential equation —.— : (N + 1)(N — 2)(N — 3)(N a 4). oft Suppose that NOE) is a solution to the equation with N({]) z 1.5. Then tlim NU): —>oo . Is necessarily —1 h; Is necessarily 2 ; Is necessarily a number other than —1 or 2 Can be any real number ; 5°99?” Does not exist 3a {6' points). Find /(cos:r + sin 3:)2 tanxdw. 3b {5 points}. Given = 0, use Simpson’s rule with n : 4 to estimate f(8): 2 l 4 (9 points Calculate the integral / (is. Check your work carefully! 5a (6 points). Find lim {72” +4”. 71—400 5].) (5 points). Find the equation of the curve which paSses through (1,1) and Whose slope at each point (:6, y) on the curve is y2/5L'3. 6a (’7 points). Find f(m)([)) Where = (1 + ac) cos :c. m 613 {6 points Determine Whether the sum 2 n n=1 7 (8 points). A tank contains 25 kg of salt dissolved in 500 L of water. Brine that contains 0.03 kg of salt per liter of Water enters the tank at the rate of 25 L/hour. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the mixture after 41' hours? 8a {6' points). Find given: f”(zr;) — 2f’(ac) +2f(\$) = 0, : l, f’(0) = 1. Sb (7 points). Solve the diﬁ'crential equation y” + y 2 w + cos 3:. 9 {8 points). Find a series solution for y” = 2.233;" +23; with the initial conditions y(0) = 17 I y (0) = 0- ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern