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6 Pages

### 242test1key010

Course: MATH 242, Spring 2011
School: Delaware
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Word Count: 258

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ath M 242 Section 010: Test #1 NAME: _ L/C Please circle your l ab/discussion: 020 021 022 This test has 6 questions on 6 pages. The p oints per page are 5, 5, 5, 5, C, 6. Show your &quot;work. A correct answer w ith l ittle or no reasoning may reeeive a low score. (However, there is no need to be wordy.) The 7th page has some formulas you can refer to if needed. r n^ i -, i i [5 p oints]...

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ath M 242 Section 010: Test #1 NAME: _ L/C Please circle your l ab/discussion: 020 021 022 This test has 6 questions on 6 pages. The p oints per page are 5, 5, 5, 5, C, 6. Show your "work. A correct answer w ith l ittle or no reasoning may reeeive a low score. (However, there is no need to be wordy.) The 7th page has some formulas you can refer to if needed. r n^ i -, i i [5 p oints] Question 1. Evaluate l im 1~ COy X O . s\ ^ ~2l III/ / _ rmO ^ [5 points] Question 2. Let R be the region b ounded by y = 1/x, y = 1/x'2, and x 2. Find the area of t he region 7?,. ? J_ 'X => -X = at <x=o.) ate. 1 -X J- x--t -x \J 2. + is TOP is BOTTOM [5 Question points] 3. Let R be the region bounded by the curves y - x2 5x + 6 and y 0. Find the volume obtained when R is rotated around the y-axis. 0 -tDP c*- S'x - J ... r" + 5-x 2r\x BOTTOM f'2TT [5 p oints] Question 4. Evaluate / c~xcosx dx. Jo Of -X u = e. O d\i - cos V = Si /\T :r = /e-*jMx] 27T f^, L -X pas-h aa^. fake Si* #\$ udu - v = cos x r 0 X- X Cos, 1 2rr "coso ZTf -2TT [e ^ CosZrr) -e. 2. _ \e o 2ir [6 points] Question 5. E valuate / ln(3x') dx. lT)\A ?&TJ5. I *'/ - = 2. 3-2, Us e. - ~ - 2, U - Jh\ - 2_ [6 points] Question 6. Evaluate / see'5 a; dx. U' . s>t a x X -/x J-f- sec -x - x -f x C
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Delaware - MATH - 242
M ath 242 Section O il: Test #1NAME: _frPlease circle your lab/discussion:030031032This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, G, 6.Show your work. A correct answer with little or no reasoning may receivea low score.
Delaware - MATH - 242
Math 242 Section 012: Tost #1NAME:KEYPlease c ircle y our l ab/discussion: 040 ( 8:00) 041 (12:30) 042 ( 1:30)This t est, has 6 questions on 6 pages.The, p oints per page are 5, 5. 5, .r&gt;, G , fi.Show your work. A correct answer with little or no r
Delaware - MATH - 242
Math 2 42 S uction 0 14: TostN AME:KEYPlease c ircle your l ab/discussion: 060 ( 12:00) 061 (11:00) 062 ( 2:30)This test has 6 questions on 6 pages.The points per page are 5. 5, 5, 5, 6. 6.Show your work. A correct, a nswer with l ittle or no r easo
Delaware - MATH - 242
M ath 242 Section 050: Testi/c:NAME: _(^f^This test has G q uestions on 6 pages.The p oints p er pa^e are 5, 5, 5, 5, ( i, 0.Show y our w ork, A c orrect answer w ith l ittle o r no r easoning m ay r eceivea. low score. (However, there is no need to
Delaware - MATH - 242
Math 242 Section 010: Test #2N AME:Please circle your lab/discussion:020021022This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer w ith little or no reasoning may receivea low score. (How
Delaware - MATH - 242
Math 242 Section 014: Test #2NAME:Please circle your lab/discussion:060061062This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer w ith little or no reasoning may receivea low score. (Howe
Delaware - MATH - 242
Math 242 Section 012: Test #2NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low sc
Delaware - MATH - 242
M ath 242 Section 014: Test #2NAME:&lt;^ ^ VPlease circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receive
Delaware - MATH - 242
Math 242 Section 050: Test #2NAME:There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low score. (However, there is no need to be wordy.)The 7th page has some f
Delaware - MATH - 242
Math 242 Section 012: Test #3N AME:KEYPloa.sc c ircle your l ab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 0, 5, 6.The 7tli page has some formulas you can refer to if needed.[5 points] Qu
Delaware - MATH - 242
Math 242 Section 014: Test #3N AME:'Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, C, 5, 6.The 7th page has some f ormulas you eari refer to if n eeded.[5 p oints] Que
Delaware - MATH - 242
M ath 242 Section 050: Test #3NAME:_There are 6 questions on 6 pages. P ointy per page: 5, 5, 5, 0, 5, 6.The 7th page has some f ormulas you can refer to if needed.[5 points] Question 1. D etermine whether the i nfinite seriesis absolutely convergen
Delaware - MATH - 242
TO S OMfcdx.8. Evaluate-x-K/0010-0.6f)0rh.9. Evaluate / ye~-6y dy.JoU'-O.b-0.6Jo10. Evaluate6'~0 -r /2 cos o1 + sinXV~Jo,rffl.U11. Evaluateu=It +=?323UJ:,12. Evaluate /_1/1.\.il:i2shr 0 cos-0 &lt;/0.7ofNTT/2-00U
Delaware - MATH - 242
IDCHf\Pm 7In problems 23 to 28, evaluate the integral or show t hat it is d ivergent.,00,PML23.i'&quot;%'3L\J324.,dxMM25. /f l/audx13r&gt;\?rovooH&gt;-4--V\MvoXr.X\MotocX^-t&lt;xcto4-P\IO4-14:tou]OS
Delaware - MATH - 242
1. Sketch t he curve. Indicate the direction in which the curve is traversed ast increases. If possible, eliminate the parameter to find a Cartesian equationof the curve.la.x = 3i - 5,y = 2t + la+5&quot; - s-tM&quot;3fH1l-1-lb.3.&gt;x = t2 - 2,3(/ =
Delaware - MATH - 242
iitIii questions 1 to 28, d etermine w hether t he series converges or diverges.iooV^ / o-n3-&quot; +1.3/2p-sn?;rsOO-12. V tan-j^vi n1&lt;:.os KIntA-M^1fw^ ^-^ . ^ ~^)3 c osy?,3.77/V2 _ 2q3'^5 AKI ^-2^choose c, ^V)J|c.*I^/ ^/HfCCO
Delaware - MATH - 242
Iii questions 29 to 36, d etermine whether the scries converges absolutely, converges conditionally, ordiverges.n29.3n0&gt;30.J'IJnofisi/In=l5011In questions 37 to 42, find the interval of convergence of the power scries.3. - 2 )/^a-Z
Delaware - MATH - 242
(?ay71/-7CXTOoT7T007X=Y)p~l7._vi /3/3/3-/Wt /i i^.^/ ^3n3&quot;- Ji lt*i^*&quot;-oi&quot;^tA -^oOi&lt;~)~y^,tTi 3 + 5'&quot;)'.-IK00f-i' n5An+1n3/2 - 2rartA/|AI&quot;/6^J=.^_/-x16. V ^n)*17.n siTi1n^W00O Tl/aL,
Delaware - MATH - 242
In questions 1 to 28, determine whether the series converges or diverges.11.3n + 3/2nn=1tan2.n=11n3.3 cos n3/2 2n=1 n14.n=15.n=1132n1+n1ln(n + 1)6.1n=2 n(ln n)27.1n=2 n ln n8.12n=2 n(ln n)9.12n=2 (ln n)310.1n=
Delaware - MATH - 242
The last page of your test will contain exactly these formulas in exactly thisformat.sin2 x =11 cos 2x2cos2 x =11 + cos 2x21dx = ?1 + x2sec x dx = ln | sec x + tan x| + C1+x2 x3x+++ = ?1!2!3!xx 3 x5 x7++ = ?3!5!7!1x 2 x4 x6
Delaware - MATH - 242
Review for beginning of Math 242This document covers some topics that you should have learned in Math 241or whatever your equivalent course was.If x = 3, evaluate x2 , x2 , 2x2 , and 2x2 .If x = 3, evaluate x2 , x2 , 2x2 , and 2x2 .Expand and simplif
Delaware - MATH - 242
Strategy for testing seriesWe skipped Section 11.7, which is very short and contains some strategyfor testing series. Heres my version of that strategy.STEP 0. Does the nth term an approach 0? If it doesnt, then the seriesdiverges. (I think of this as
Delaware - MATH - 242
INFINITE SERIES (Chapter 11)General facts:A sequence is nothing but an innite list. A series is a sum of innitely many numbers.An innite series may either converge (i.e. reach a nite total) or diverge (i.e. not reach a nite total).1A famous example o
Delaware - MATH - 242
This page has some formulas that will NOT be given on your test.You will probably want to memorize these formulas, and also understandwhen and how they are used.This is an INCOMPLETE list of SOME things you will need to know. R2 r2 dxVolume by washer
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin cos tan 0/6/4/3/2dsin x =dx
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin cos tan 0/6/4/3/2sin2 x =11
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 25 and 27This is a longer list of problems t han u sual. It can also serve as pract.iec forTest 2.r1'2 cosla. Evaluate /,rr/21x dx.7O\$ 2 / X COS ^o^6(A ' S'^ ^/-COSIb. Evaluate /o,cos x dx
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin2 x =11 cos 2x2cos2 x =11 + cos 2
Delaware - MATH - 242
Math 242 Section 014: Test #1NAME:Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may rece
Delaware - MATH - 242
Math 242 Section 012: Test #1NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may recei
Delaware - MATH - 242
Math 242 Section 050: Test #1NAME:This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low score. (However, there is no need to be wordy.)The 7th page
Delaware - MATH - 242
Math 242 Section 014: Test #2NAME:Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low s
Delaware - MATH - 242
Math 242 Section 012: Test #2NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low sc
Delaware - MATH - 242
Math 242 Section 050: Test #2NAME:There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low score. (However, there is no need to be wordy.)The 7th page has some f
Delaware - MATH - 242
Math 242 Section 014: Test #3NAME:Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 6, 5, 6.The 7th page has some formulas you can refer to if needed.[5 points] Question 1
Delaware - MATH - 242
Math 242 Section 012: Test #3NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 6, 5, 6.The 7th page has some formulas you can refer to if needed.[5 points] Question 1.
Delaware - MATH - 242
Math 242 Section 050: Test #3NAME:There are 6 questions on 6 pages. Points per page: 5, 5, 5, 6, 5, 6.The 7th page has some formulas you can refer to if needed.[5 points] Question 1. Determine whether the innite seriesn(1)n n4 + 5n=0is absolutely
Delaware - MATH - 242
Math 242 Final Exam, Spring 2011Sections 012, 014, 050NAME:There are 12 questions on 12 pages.The points per page are 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6.The 13th page has some formulas you can refer to if needed.[5 points] Question 1. Evaluate the l
Delaware - MATH - 242
Math 242 Review Chapter 10 HighlightsFor slope or concavity of parametric curves, use the following:dy=dxd2 yd dy==2dxdx dxdThe latter equation comes from(u) =dxdudtdxdtdydtdxdtd dy()dt dxdxdt.For converting between rectangul
Delaware - MATH - 210
Math 210-011 Final Exam, Spring 2011NAME:_There are 12 questions on 12 pages.The points per page are 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6.[2 points] Question la. Construct a t ruth table for P V (P + Q).PQTTFFTFTFTFTTTTTT[2 points] Qu
Delaware - MATH - 210
Math 210 Homework 1Due Friday February 18th1. Classify each of the following statements as true or false. 3(i) 3 is rational or (4)2 = 16(ii) 4 = 2 + 2 7 &lt; 50(iii) 4 = 2 + 2 7 &lt; 50(iv) 4 = 2 + 2 7 &gt; 50(v) 4 = 2 + 2 7 &gt; 502. Rewrite each statement
Delaware - MATH - 210
Math 210 Homework 2Due Wednesday February 23rd1. (This example is due to Lewis Carroll.) Consider the statements: Animals that do not kick are always unexcitable. Donkeys have no horns. A bualo can always toss you over a gate. No animals that kick a
Delaware - MATH - 210
Math 210 Homework 3Due Monday February 28th1. Connectives for statements are similar in some ways to operationson sets. This question will illustrate that.(i) Construct a truth table for (P Q).(ii) Construct a truth table for (P ) Q.Your answers to
Delaware - MATH - 210
(TO0CA&gt;nDo?V 3' ^n^-1 H ~n-i H T; -nHTS Tl -1 HJ^7jT7Tin H -nHnTMjJoj&gt;71 T -M?&quot;o!-oOiCi- D.- g=VA/Jcns-rr^c^c^&gt;cCOOD-sonCtoCo3CneDObc10DrscCoCONCX)COoc*ctoImSCCoCO]octo
Delaware - MATH - 210
Math 210 Homework 4Due WEDNESDAY March 9th1. Let f be the function from N to N dened byf (x) =3x + 1if x is oddx/2if x is even(a) Is f one-to-one? Why or why not?(b) Is f onto? Why or why not?2. Let f be the function from Z to Z dened by f (x) =
Delaware - MATH - 210
Math 210 Homework 5Due Monday March 14th1. Let R be the relation on Z dened by(x, y ) Rif and only ify x 10.(i) Is R reexive?(ii) Is R symmetric?(iii) Is R transitive?(iv) Is R an equivalence relation?(v) Is R a partial order?2. Find q and r as
Delaware - MATH - 210
Math 210 Homework 6Due Monday March 21st1. Let a and b be integers. Prove that 3a + b is divisible by 7 if and only ifa + 5b is divisible by 7.2. True or false? In each case, if true, give a general proof. If false, give anexplicit counterexample. (A
Delaware - MATH - 210
Math 210 Homework 6SOLUTIONS (possibly a little terse in some cases)1. Let a and b be integers. Prove that 3a + b is divisible by 7 if and only ifa + 5b is divisible by 7.SOLUTION. Suppose 7 | (3a + b). Note that 7 | 14b. Therefore, 7 |(3a + b) + 14b
Delaware - MATH - 210
Math 210 Homework 7Due Monday April 11th1. Using the suggestions below, construct a proof of the statement: If aand b are positive integers, then gcd(a, b) is the smallest positive integer thatcan be written as xa + yb where x and y are integers.(i)
Delaware - MATH - 210
Math 210 Homework 8Due Monday April 18th1. Solve the system of congruences:7x + 2y 3(mod 15)9x + 4y 6(mod 15)2. Solve the system of congruences:x1(mod 4)x8(mod 9)x 10(mod 25)3. Prove that 5n 1 is divisible by 4 for all natural numbers n.4.
Delaware - MATH - 210
Math 210 Homework 8Solutions1. Solve the system of congruences:7x + 2y 3(mod 15)9x + 4y 6(mod 15)Solution. Multiply the rst congruence by 2 to get14x + 4y 6(mod 15)and then subtract the second congruence to get5x 0(mod 15)This implies 5x = 15
Delaware - MATH - 210
Math 210 Homework 9Due Monday April 25th1. How many numbers in X = cfw_1, 2, 3, . . . , 100 are divisible by at least oneof the numbers 2, 3, 5, 7? (Be careful: since 100 is not divisible by 3 or 7, wecant say that exactly a third or a seventh are div
Delaware - MATH - 210
Math 210 Homework 10Due Monday May 2nd1. For the purposes of this problem, pretend everybody has exactly threenames: rst, middle, and last. (In real life, some people have no middlename, and some people have more than one middle name, but ignore that.
Delaware - MATH - 210
Math 210 Homework 11Due Monday May 9th1. This question involves the 8 leaders of the G8 countries:Berlusconi, Cameron, Harper, Kan, Medvedev, Merkel, Obama, Sarkozy.(i) In how many ways can the 8 of them stand in a line?(ii) In how many ways can the
Delaware - MATH - 210
Math 210 Homework 11Solutions1. This question involves the 8 leaders of the G8 countries:Berlusconi, Cameron, Harper, Kan, Medvedev, Merkel, Obama, Sarkozy.(i) In how many ways can the 8 of them stand in a line?Answer: 8! = 8 7 6 5 4 3 2 1.(ii) In h
Delaware - MATH - 210
Comments on Homeworks 1 and 2Homework 1, Question 4.I wasnt as explicit as I could have been. Technically, you could just writex (if x is real, then ex is positive)x (if x is an integer, then x cant be both even and odd)x (if x is a prime number, the
Delaware - MATH - 210
Math 210, Section 011, Spring 2011Discrete Mathematics IInstructor: Idris Mercer, Ewing 529, idmercer@math.udel.eduIn emails, please include the words Math 210.Oce hours: Tuesdays 12:001:30, or by appointmentWebpage: http:/www.math.udel.edu/idmercer/
Delaware - MATH - 210
Math 2 10 Section O i l : TestN AME:.KEYThis test has 6 pages. The p oints per page a rc 4 , 4, 5. 5, 5, 5.[4 p oints] Question 1.Let P be the s tatement &quot;-42 =- 1 C.&quot;.~ H~ ~ (/Let, Q be t he s tatement &quot;7 &lt; v'JH).1'Let # be the a tatunient &quot;j
Delaware - MATH - 210
Math 210 Section O il: Test #2NAME:!_This test has 6 pages. The points per page are 4, 5, 5, 4, 5, 5.[2 points] Question la.Compute gcd(161,196).= L-ltl + 35= 4-35 + 2i35T = 1 -21 *2i -i'H ^- 2-1 +o[2 points] Question Ib.Write gcd(161, 196) a
Delaware - MATH - 210
M ath 210 Section O il: Test #3NAME: _ - _This test has 6 pages. The points per page are 4, 4, 5, 5, 5, 5.[2 points] Question la.Find all .solutions of the congruence 2.x = 18 ( mod 5 0), w here 0 &lt; x &lt; 50.= 15 a fIv~ Q* fi/i^o^ 25 )/[2 points] Q
Delaware - MATH - 210
M ath 210 Section O il: Tost #4NAME:This tost, haw 6 pages. T he points por p ago arc 5, 4, 5, 5, 4, 5.[5 p oints] Question 1.How m any i ntegers in cfw_1. 2, 3, . . . . 1000 arc not divisible by 2, 3, 5. or 7?coo10 00I'3I COOjIrtfl4333. + ^