Test 3 Fall 2005 Answer

Test 3 Fall 2005 Answer - Math 122 Test 3 i i November 22,...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 122 Test 3 i i November 22, 2005 A Total Directions: CJI . Numerical experiments do not count as justification. . No books, notes or or drawing comical pictures of your Chemistry 111- structor. You may use a calculator to do routine arithmetic computa— tions. You may not use your calculator to store notes or formulas. You may not share a calculator with anyone. . You should show your work, and explain how you arrived at your an— swers. A correct answer with no work shown (except on problems which are completely trivial) will receive no credit. If you are not sure whether you have written enough, please ask. . You may not make more than one attempt at a problem. If you make several attempts, you must indicate which one you want counted, or you will be penalized. For example, computing the first few terms of a series is not enough to show the terms decrease. Computing the first few partial sums of a series is not enough to show the series converges or diverges. Plugging in numbers is not enough to justify the computation of a limit. You may, of course use numerical experiments to help guide your work, but they do not count as justification for answers. . On this test, explanations count. If l can’t follow what you are doing7 you will not get much credit. . You may leave as soon as you are finished3 but once you leave the exam" you may not make any changes to your exam. . The exam has 7 questions and a total of 100 points. Happy Thanksgiving 1. (10 points) Find the limit of the following sequence: V712 +n— V712 —- n}ocfi2 r.” \ 2. (10 points) For Determine Whether the series con'vergeS or diverges. find its sum. «w \fl; M23} ’2’” ":5 MM w {)0 Z n:0 1 + 3“- 5n v» -, xi w ,5 '3 NR \ta: ) If it converges, 3. (20 points) For each of the following series7 determine if it converges or diverges. Fk'u' each test you use, you must name the test, perform the test, and state the conclusion you reached from that test. 00 n TL ‘1 (( > (n + 1) t m WWW (“a = Q Y"; W \k W w NJ,“ is Wm 35- “M kkkkk V m )f h J N “is; {in Kfix“fi C: ‘1 it; “:1; E OO 1 (C) 2 3712 + 4n + 5 77:} km GET” “Ifilgtmgz e to, Kim \J 4. (20 points) Determine if the following series converge almolutely, C(ny verge conditionally, or diverge. For each test you use, you must name the test, perform the test, and state the conclusion you reached from that test. 00 ‘ .i t r I ,t. \ M x (a) Z<~1>fl arc/tan rz/ Lag W; _ {flag (I) y “:1 1 + n? K ,. ,m“ l” (“3M , min“? MW 4 “ia 7;» «cm: KQ ‘ AL AAAA ,. a m A m “T?” W LEW ’15??? to w 1 fl - thug: ,3) mg 35;? fl { ““““ _ 1., « ~ " VYMN \‘ V ' ' 3x3 «m MAN‘er KM Tthm . K MW 7 ""““ WWW l: at (M six-«9 ET h «13,535 “a a? W 00 1n n n 1 n. . M“ (c) 2H)” (fl) L t J , m A; ,9 n n—H £2 {:2 m a” @525,» “a” ' W W I M fl @ fi 7N y»: i Erna!“ M g CV1, RR [fix > i .mvw 'W L 2 an ‘I‘M¢/V“ % “an” 39%“: WNW Xx ‘ N M)! N ‘9 Wngwa W 5, 3m :5; C; 5.: J (15 points) Consider the power series: 00 (1; .i— 2)” “2%” 7L \/ 1'1 72, (a) Where is the power series centered? gown (13) Find the radius of convergence. 1 , . WWW g M “vii “i (:53 x ‘ iii“ _ i Mt: \ K rwja‘\ 41K \ “ii. {3:3 (Ex; ’2'"Z”‘”T”""§x ;. ,, \N is \ 3 \ties'tw * (m an) (c) Find the interval of convergence. [Hintz Check the endpoints.] :32 m ‘9 L) X \XCJ C W ‘ k If,» ........ \ V y \ (Fm ‘ Mi "I" ’35 M) wumww fnflmw. K wfi invmt he“ RVEan 3; five“ E a i N gum ._ N M” (cm ‘i 3 , ‘‘‘‘ m x -M ........... W. ,3“ V” W | 5 4%.MVTW mmwwimw \ \ "j: Mn?” 5 i r 6. (15 points) Given the Maclaurin series for f (:13) is \ ngmB Match each of the following functions with the correct Maclaurin series: \1 a) 1 + 1:2 + 3’; + £339 + “2;? 2 ‘ ,3 CM b)1+2:1:+Z—17§——r§'7’y+ , 2.2 » ,.3 jg?) C)1+2m+g.§_+l7m + .2 m H 2 3 .1... f(:1:)(sin d) 1 + '21: +- 1—55— fl of 7. (10 points) Indicate whether the following statements are true or false by circling the appropriate letter. A statement which is sometimes true and sometimes false should be marked false. 00 “W‘in a) If 2 anar" converges at = “3, it converges at a: :: F 7L:1 NW 00 “4 If a 1’ 1 " conver es for :1: = ' and “A — . n2 :2: = «~1 then it must converge for CE 2 —1.5. If the sequence {am} converges then the C) an V T _ F sequence ~77 converges to 0. / DC- 00 If the series an converges and the series 2 b” con— n=1 'rL::l f d) 00 T I F verges (an and b,” nonnegatrve), then the serles 2mm“) n21 converges. 00 00 e) If 2 an diverges, then 2 km diverges. T F 11:1 nzl ...
View Full Document

This note was uploaded on 02/17/2010 for the course MATH 122 taught by Professor Butler during the Spring '07 term at Case Western.

Page1 / 7

Test 3 Fall 2005 Answer - Math 122 Test 3 i i November 22,...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online