# 3b - MA 241 Test 3 Fall 2007 Form B Your name on your test...

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Unformatted text preview: MA 241 Test 3 Fall 2007 Form B Your name on your test is your pledge that you will not give nor receive informationfhelp on this test. No calculators, No cell phones, No PDAS Show all work. Circle your ﬁnal answer. No credit for guessing. Please begin each problem on a clean page in the blue book. Please do not leave if you have to pass over a peer on your row. 1. (15 pts) Solve the 2'” order differential equation with the given initial values y” 4- 5y’ + 6y - 0 y(0) - 0, y’(0) a 4 2. (15 pts) The complementary solution for y" «2y' + y - sin(x) is yc - Cle“ + sze" Use the method of undetermined coefﬁcients to ﬁnd the particular solution, y P. 3. Determine if the sequence converges or diverges. Show all steps. (10 points each) a. an .. “(3) n 2 b. a»I 1: r n +1 4. Determine if the series converges or diverges. Name the test, show the criteria for the test and make a concluding statement. If the series converges, ﬁnd the sum. (10 points each) a. 2+i+§m+ 2H °° 1 °° 1 1 b. =- -—- Elﬁn-+1) 2L: n+1) i2n+3 1—5n 11-! Continue on next page Form B continued: 5. (10 points)A bacterial culture with growth constant 0.10 initially contains 800 cells and grows at a rate proportional to its size. Let P(t) be the number of cells in t hours. Find the number of cells when it is growing at 500 cells per hour. 6. (10 points) Let x(t) be the position of the mass (with respect to equilibrium) at any time t. A spring with mass 1 kg has damping constant 2 and spring constant 3. Determine if this spring is over damping, critical damping, or under damping. W I, ”,4 57’w7w r2+-j‘r+g,—0 g (“EMMA-0 A - -3 r (I a 2“}- (axe y :7 9(0) 0 '9 ﬂ; (9’ TLCLQCE‘C‘ ', {075 513369637 j) Wow 9 1/: “976,,ch f 3’ ' ’ a rm“- f V: “#6294: ”Z we'd-h so» a»: - n 1- 48 ——Ll€ — ‘_' "ﬁn/£11—L/ J] n. _ 7 3p ; ﬂavw+ L“, #0:»; A! ‘ 4- ﬂ gig/:14 coax 72L, x v A ” 249m "E”O‘by 9;,” 1(03/105; Isa/”WW —»4 ’n X * ﬂ" 0 .1 r 0.5 98/; 1y a}; o W 3 I2“). @173 567/ {25: XL! : )(J'Jm 4*} x4300 ' ' - M f/ﬂ)‘¢7n “7:39'130'3/5 71w ’ {new ﬁn; ”>0 0 x mm W. m 4M) ’l .2 ~ / - ”M 115‘)!” A, j)» J?” :/m [715/ 7 K ”200 [CH/,7? ”.90., l7 )ZWH/jd Vacant, WW I Z. 2. Mmz: ’41 5’ r73: 73“ ...
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