ARNOLD PIZER MATH Summer 2001 Homework Set 0 due 1/1/05 at 2:00 AM

534 Pages·2012·5.24 MB·English

ARNOLD PIZER MATHSummer 2001
Homework Set0due1/1/05at2:00AM
This (cid:2)rst set(set0)isdesignedto acquaintyouwith usingWeBWorK. Yourscoreonthis setwill not becounted towardyour
(cid:2)nalgrade
Youmayneedto give4or5signi(cid:2)cant digitsfor some((cid:3)oatingpoint)numericalanswersin ordertohavethemacceptedbythe
computer.
First enter the function sin x. When enteringthe function,
1.(1pt)set0/prob1.pg you shouldenter sin(x), but WeBWorK will also accept sin x
This problem demonstrateshow you enter numerical answers or even sinx. If you remember your trig identities, sin(x) = -
intoWeBWorK. cos(x+pi/2)and WeBWorK will accept this or anyother func-
Evaluatetheexpression3( 7)(10 1 2(7)): tionequaltosin(x),e.g.sin(x)+sin(x)**2+cos(x)**2-1
(cid:0) (cid:0) (cid:0)
In the case aboveyouneed to enter a number, since we’re
testing whetheryoucanmultiplyout thesenumbers. (Youcan Wesaidyoushouldentersin(x)eventhoughWeBWorKwill
useacalculatorifyouwant.) alsoacceptsinxorevensinxbecauseyouarelesslikelytomake
Formostproblems,youwill beabletogetWeBWorK to do amistake. Tryenteringsin(2x)withouttheparenthesesandyou
someoftheworkforyou.Forexample may be surprisedat what youget. Use the Preview button to
Calculate(-7)*(10): see what youget. WeBWorK will evaluatefunctions (such as
Theasteriskiswhatmostcomputersusetodenotemultipli- sin)beforedoinganythingelse,sosin2xmeans(cid:2)rstapplysin
cationandyoucanusethiswithWeBWorK.ButWeBWorKwill whichgivessin(2)andthenmutiplebyx.Tryit.
alsoallowyoutouseaspacetodenotemultiplication. Youcan
either 7 10or-70oreven 710. Allwillwork.Trythem. Nowenterthefunction2cost. Notethisisafunctionoftand
(cid:0) (cid:3) (cid:0)
Now try calculating the sine of 45 degrees ( that’s sine notx.Tryentering2cosxandseewhathappens.
of pi over 4 in radians and numerically sin(pi/4) equals
0.707106781186547or,moreprecisely,1=p2). Youcanenter
thisassin(pi/4),assin(3.1415926/4),as1/sqrt(2),as2**(-.5), 3.(1pt)set0/prob1b.pg
etc. This isbecauseWeBWorK knowsaboutfunctionslikesin Thisproblemwillhelpyoulearntherulesofprecedence,i.e. the
and sqrt (square root). (Note: exponents can be indicated by orderinwhichmathematicaloperationsareperformed.Youcan
eithera(cid:148)caret(cid:148)or**). Tryit. useparentheses(andalsosquarebrackets[]and/orcurlybraces
sin(p=4)= )ifyouwanttochangethenormalwayoperationswork.
fg
Here’s the listofthefunctions which WeBWorK under- So (cid:2)rst let us review the normal way operations are per-
formed.
stands. WeBWorK ALWAYS uses radian mode for trig func-
Therules aresimple. Exponentiationisalwaysdonebefore
tions.
Youcanalsousejuxtapositiontodenotemultiplication. E.g. multiplicationanddivision andmultiplicationanddivision are
enter2sin(3p=2). Youcanenterthisas2*sin(3*pi/2)ormore alwaysdonebefore additionandsubtraction. (Mathematically
simplyas2sin(3pi/2).Tryit: wesayexponentiationtakesprecedenceovermultiplicationand
division,etc.). Forexamplewhatis1+2*3?
Sometimesyouneedtouse()’stomakeyourmeaningclear.
andwhatis2 32?
E.g. 1/2+3is3.5,but1/(2+3)is.2Why?Tryenteringbothand
(cid:1)
usethe(cid:147)Preview(cid:148)buttonbelowtoseethedifference.Inaddition
Nowsometimeyouwanttoforcethingstobedoneinadifferent
to()’s,youcanalsouse[]’sand ’s.
fg way. This is whatparenthesesareusedfor. Theruleis: what-
You can alwaystry to enter answers and let WeBWorK do everisenclosedinparenthesesisdonebeforeanythingelse(and
thecalculating. WeBWorKwill tellyouiftheproblemrequires thingsintheinnermostparenthesesaredone(cid:2)rst).
a strict numericalanswer. The way we use WeBWorK in this Forexamplehowdoyouenter
class there is no penalty for getting an answer wrong. What
1+sin(3)
counts is that you get the answer right eventually (before the ?
2+tan(4)
due date). For complicatedanswers, youshouldusethe (cid:147)Pre-
view(cid:148) button to checkfor syntaxerrors andalso to checkthat
Hint: thisis agoodplaceto use[ ]’sandalsoto usethe(cid:147)Pre-
theansweryouenterisreallywhatyouthinkitis.
view(cid:148)button.
2.(1pt)set0/prob1a.pg Herearesomemoreexamples:
Thisproblemdemonstrateshowyouenterfunctionanswersinto (1+3)9=36, (2*3)**2=6**2= 36, 3**(2*2)=3**4= 81,
WeBWorK. (2+3)**2=5**2=25,3**(2+2)=3**4=81
1
(Here we have used ** to denoteexponentiation and you can 5. Thedistancefromxto-5ismorethan1
also use this instead of a (cid:147)caret(cid:148) if you want). Try entering
A. 5<x
some of these and use the (cid:148)Preview(cid:148) button to see the result. (cid:0)
B. x+5 1
The (cid:148)correct(cid:148)result for this answer blank is 36, but by using j j(cid:20)
C. x< 5
the(cid:147)Preview(cid:148)button,youcanenterwhateveryouwantanduse (cid:0)
D. x+5 >1
WeBWorKasahandcalculator. j j
E. x 5
(cid:21)(cid:0)
ForthisproblemWeBWorKonlytellsyouthatallyouranswers
Thereisoneotherthingtobecarefulof. Multiplicationand
arecorrectorthatatleastoneis wrong. This makestheprob-
division have the same precedenceand there are no universal
lemharderandisusuallyusedonlyforT/Fandmatchingques-
rulesasto whichshouldbedone(cid:2)rst. Forexample,whatdoes
tions. The idea isto encourageyouto think ratherthanto just
2/3*4mean?(Notethat/isthe(cid:148)divisionsymbol(cid:148),whichisusu-
tryguessing.
allywrittenasalinewithtwodots,butunfortunately,this(cid:148)line
If you are having trouble reading the mathematics on the
with two dots(cid:148) symbol is not on computer keyboards. Don’t
screen, this means that youare using (cid:148)text(cid:148)mode. If youare
thinkof/asthehorizontallineinafraction. Askyourselfwhat
usingNetscapeorMSIEthenyoucangetaneasiertoreadver-
1/2/2shouldmean.) WeBWorKandmostothercomputersread
sionoftheequationsbyreturningtotheproblemlistpage(use
things from left to right, i.e. 2/3*4 means (2/3)*4 or 8/3, IT
thebuttonatthetopofthispage)andchoosing(cid:148)formatted-text(cid:148)
DOES NOTMEAN2/12. Some computersmaydooperations
or(cid:148)typeset(cid:148)insteadof(cid:148)text(cid:148). Sometimesthereisa 15-20sec-
from righttoleft. Ifyouwant2/(3*4)=2/12,youhaveto use
onddelayinviewingaproblemin(cid:148)typeset(cid:148)modethe(cid:2)rsttime.
parentheses.Thesamethinghappenswithadditionandsubtrac-
tion. 1-3+2=0but1-(3+2)=-4. This isonecasewhereusing
6.(1pt)set0/prob4/prob4.pg
parenthesesevenif theyarenot neededmightbe a goodidea,
This problem demonstrates a WeBWorK problem involving
e.g. write (2/3)*4eventhoughyoucouldwrite 2/3*4. This is
graphics.
alsoacasewherepreviewingyouranswercansaveyoualota
Thesimplestfunctionsarethelinear(oraf(cid:2)ne)functions(cid:151)
griefsinceyouwillbeabletoseewhatyouentered.
thefunctionswhosegraphsareastraightline. Theyareimpor-
Enter2/3*4andusethePreviewbuttontoseewhatyouget.
tantbecausemanyfunctions(theso-calleddifferentiablefunc-
tions)(cid:147)locally(cid:148)looklikestraightlines. ((cid:147)locally(cid:148)meansthatif
4.(1pt)set0/prob2.pg wezoomin andlookatthefunctionatverypowerfulmagni(cid:2)-
ThisproblemdemonstratesaWeBWorKTrue/Falsequestion.
cationitwilllooklikeastraightline.)
Enter a T or an F in each answer space below to indicate
Enter the letter of the graph of the function which corre-
whetherthecorrespondingstatementistrueorfalse.
spondstoeachstatement.
Youmustgetalloftheanswerscorrecttoreceivecredit.
1. Thegraphofthelineisincreasing
1. 5< 7
(cid:0) (cid:0) 2. Thegraphofthelineisdecreasing
2. 6 1 6
(cid:0) (cid:20) 3. Thegraphofthelineisconstant
3. p 3:1416
(cid:21) 4. Thegraphofthelineisnotthegraphofafunction
4. 8 8
(cid:0) (cid:20)(cid:0)
Noticethatifoneofyouranswersiswrongthen,inthisprob-
lem,WeBWorK will tell youwhichpartsarewrongandwhich
parts areright. This isthebehaviorfor mostproblems,but for
true/falseor multiple choicequestionsWeBWorK will usually
onlytellyouwhetherornotalltheanswersarecorrect.Itwon’t A B C D
tellyouwhichonesarewrong. Theideaistoencourageyouto
thinkratherthantojusttryguessing. Thisisanotherproblemwhereyouaren’ttoldifsomeofyour
Ineverycaseallof theanswersmust be correctbeforeyou answersareright.(Withmatchingquestionsandtruefalseques-
getcreditfortheproblem. tions, thisisthestandardbehavior(cid:150)otherwiseit istoo easyto
guessyourwaytotheanswerwithoutlearninganything.)
5.(1pt)set0/prob3.pg Ifyouarehavingahardtimeseeingthepictureclearly,click
ThisproblemdemonstratesaWeBWorKMatchingquestion.
onthepicture.Itwillexpandtoalargerpictureonitsownpage
Matchthestatementsde(cid:2)nedbelowwiththeletterslabeling
sothatyoucaninspectitmoreclosely.
theirequivalentexpressions.
Someproblemsdisplayalinktoawebpagewhereyoucan
Youmustgetalloftheanswerscorrecttoreceivecredit.
getadditionalinformationorahint:Hint
1. xisgreaterthan-5
2. xisgreaterthanorequalto-5 7.(1pt)set0/prob5.pg
3. xislessthan-5 This problemdemonstratesa WeBWorK questionthatrequires
4. Thedistancefromxto-5islessthanorequalto1 youtoenteranumberorafraction.
2
Evaluatetheexpression j107(cid:0)272j. Giveyouranswerindeci- as correct or incorrect, so you can go back and do problems
25
malnotationcorrecttothreedje(cid:0)cimj alplacesorgiveyouranswer youskippedorcouldn’tgetrightthe(cid:2)rsttime. Onceyouhave
asafraction. donea problem correctly it is ALWAYS listed as correcteven
ifyougobackanddoit incorrectlylater. This meansyoucan
Now that you have (cid:2)nished you can use the (cid:148)Prob. List(cid:148) useWeBWorKtoreviewcoursematerialwithoutanydangerof
buttonatthetop ofthepageto returntotheproblemlist page. changingyourgrade.
You’ll see that theproblems youhave donehavebeenlabeled
PreparedbytheWeBWorKgroup,Dept.ofMathematics,UniversityofRochester, cUR
(cid:13)
3
ARNOLD PIZER rochester problib fromCVSJune25,2004
RochesterWeBWorK ProblemLibrary WeBWorKassignmentMAAtutorialdue1/1/05at2:00AM
Completethesentence:
world! Youcanviewthesource forthisproblem.
5.(1pt)setMAAtutorial/matchinglistexample.pg
Youcanviewthesource forthisproblem.
2.(1pt)setMAAtutorial/standardexample.pg Matchinglistexample
To see a different version of the problem changethe problem
StandardExample seedandpressthe’SubmitAnswer’buttonbelow.
Completethesentence: ProblemSeed:Changetheproblemseedtochangetheprob-
world; lem:1440
Enterthesumofthesetwonumbers:
3+5= Placetheletterofthederivativenextto eachfunctionlisted
Enterthederivativeof below:
f(x)=x5 1. x20
2. 2x2
f (x)=
0 3. tan(x)
4. sin(x)
Youcanviewthesource forthisproblem.
A. 4x1
3.(1pt)setMAAtutorial/simplemultiplechoiceexample.pg B. sec2(x)
C. 20x19
Multiplechoiceexample
D. cos(x)
To see a different version of the problem change the problem
Let’s print the questionsagain, but insist that the (cid:2)rst two
seedandpressthe’SubmitAnswer’buttonbelow.
questions(aboutsinandcos)alwaysbeincluded.Hereisasec-
ProblemSeed:Changetheproblemseedtochangetheprob-
ondwaytoformatthisquestion,usingtables:
lem:2762
Whatisthederivativeoftan(x)? 1. tan(x) A. cos(x)
A. (cid:0)cot(x) 23.. scions((xx)) CB.. s(cid:0)ecsi2n((xx))
B. sec2(x)
C. tan(x)
Andbelow is yet anotherway to enter a table of questions
D. cosh(x)
andanswers:
E. sin(x)
Enterthelettercorrespondingtothecorrectanswer:
A. cos(x)
B. sin(x)
Youcanviewthesource forthisproblem. 1. tan(x) C. s(cid:0)ec2(x)
2. sin(x)
D. Thederivativeis
4.(1pt)setMAAtutorial/multiplechoiceexample.pg 3. cos(x) notprovided
Multiplechoiceexample
Youcanviewthesource forthisproblem.
To see a different version of the problem change the problem
seedandpressthe’SubmitAnswer’buttonbelow. 6.(1pt)setMAAtutorial/truefalseexample.pg
ProblemSeed:Changetheproblemseedtochangetheprob-
lem:3734 TrueFalseExample
To see a different version of the problem changethe problem
Whatisthederivativeoftan(x)? seedandpressthe’SubmitAnswer’buttonbelow.
A.sin(x) ProblemSeed:Changetheproblemseedtochangetheprob-
(cid:15) B.cosh(x) lem:4322
(cid:15)
C. cot(x)
(cid:15) D.(cid:0)sech(x) Enter T or F dependingonwhetherthe statement istrue or
(cid:15) E.tan(x) false.(YoumustenterTorF(cid:150)TrueandFalsewillnotwork.)
(cid:15)
F.cos3(x) 1. Allclosedsetsarecompact
(cid:15)
G.sec2(x) 2. Allcompactsetsareclosed
(cid:15)
1
3. All differentiable strictly increasing functions have Identify the graphs A (blue), B( red) and C (green) as the
non-negativederivativesateverypoint graphsof a function and its derivatives (click on the graph to
4. Allfunctionswithpositivederivativesareincreasing. seeanenlargedimage):
isthegraphofthefunction
Youcanviewthesource forthisproblem. isthegraphofthefunction’s(cid:2)rstderivative
isthegraphofthefunction’ssecondderivative
7.(1pt)setMAAtutorial/popuplistexample.pg
Youcanviewthesource forthisproblem.
TrueFalsePop-up Example
To see a different version of the problem change the problem 9.(1pt)setMAAtutorial/onthe(cid:3)ygraphicsexample2.pg
seedandpressthe’SubmitAnswer’buttonbelow.
ProblemSeed:Changetheproblemseedtochangetheprob- On-the-(cid:3)yGraphicsExample2
lem:1620 To see a different version of the problem changethe problem
seedandpressthe’SubmitAnswer’buttonbelow.
Indicatewhethereachstatementistrueorfalse. ProblemSeed:Changetheproblemseedtochangetheprob-
lem:451
? 1. All differentiable strictly increasing functions have
WARNING:UseSHIFTreloadwhenrefreshingtomakesure
non-negativederivativesateverypoint
thattheimageisrefreshed!!!!!
? 2. Allcompactsetsareclosed
? 3. Allclosedsetsarecompact
? 4. Allcontinuousfunctionsaredifferentiable.
Youcanviewthesource forthisproblem.
8.(1pt)setMAAtutorial/onthe(cid:3)ygraphicsexample1.pg
On-the-(cid:3)yGraphicsExample1
To see a different version of the problem change the problem
seedandpressthe’SubmitAnswer’buttonbelow.
ProblemSeed:Changetheproblemseedtochangetheprob-
lem:1458
WARNING:UseSHIFTreloadwhenrefreshingtomakesure
thattheimageisrefreshed!!!!!
Identify the graphs A (blue), B( red) and C (green) as the
graphsof a function and its derivatives (click on the graph to
seeanenlargedimage):
isthegraphofthefunction
isthegraphofthefunction’s(cid:2)rstderivative
isthegraphofthefunction’ssecondderivative
Youcanviewthesource forthisproblem.
10.(1pt)setMAAtutorial/staticgraphicsexample/staticgraphicsexample.pg
StaticgraphicsExample
2
Toseeadifferentversionoftheproblemchangetheproblemseedandpressthe’SubmitAnswer’buttonbelow.
ProblemSeed:Changetheproblemseedtochangetheproblem:2428
ThisisagraphofthefunctionF(x):(Clickonimageforalargerview)
Entertheletterofthegraphbelowwhichcorrespondstothetransformationofthefunction.
1. F(x=3)
2. F(x+3)
3. F( x)
(cid:0) (cid:0)
4. F(x 3)
(cid:0)
A B C D
Youcanviewthesource forthisproblem.
11.(1pt)setMAAtutorial/hermitegraphexample.pg
Hermitepolynomialgraphexample
Toseeadifferentversionoftheproblemchangetheproblemseedandpressthe’SubmitAnswer’buttonbelow.
ProblemSeed:Changetheproblemseedtochangetheproblem:1823
Wearedevelopingotherwaystospecifygraphswhicharetobecreated’onthe(cid:3)y’. Allofthesenewmethodsconsistofadding
macropackagestoWeBWorK.SincetheydonotrequirethecoreofWeBWorKtobechanged,theseenhancementscanbeaddedby
anyoneusingWeBWorK.
Thesetwopiecewiselineargraphswerecreatedbyspecifyingthepointsatthenodes.
Clickonthegraphtoviewalargerimage.
3
Iftheblackfunctioniswrittenas f(x),thentheorangefunctionwouldbewrittenas f( ).
Thisgraphwascreatedusingahermitesplinebyspecifyingpointsat
x -4 -3 -2 -1 0 1 2 3 4
y 0 1 2 0 2 0.5 1 1 2
yp 0.1 1 0 -2 0 1 2 -3 1
Listtheinternallocalminimumpointsinincreasingorder:
Youcanviewthesource forthisproblem.
12.(1pt)setMAAtutorial/htmllinksexample/htmllinksexample.pg
Andthetablebelowhasthreemoregraphswhicharestored
HTMLlinksexample inthedirectorycontainingthecurrentproblem.
This exampleshowshowtolinkto resourcesoutsidetheprob-
lemitself.
Linkingtootherwebpagesovertheinternetiseasy. Forex-
ample, youcan get more information aboutthe buffonneedle
problem and how it is used by ants to (cid:2)nd new nest sites by
linkingtoIvarsPeterson’scolumnontheMAAsite. Youcanviewthesource forthisproblem.
All of the (cid:2)les in the html directory of your WeBWorK
13.(1pt)setMAAtutorial/javascriptexample1.pg
coursesite canbe readbyanyonewith awebbrowserandthe
URL (the addressofthe(cid:2)le). This isagoodplaceto put(cid:2)les
JavaScriptExample1
thatarereferencedbymorethanoneprobleminyourWeBWorK
To see a different version of the problem changethe problem
course.
seedandpressthe’SubmitAnswer’buttonbelow.
Here is thelink to thetothecalculatorpage storedin the
ProblemSeed:Changetheproblemseedtochangetheprob-
toplevelofthehtmldirectoryofthetutorialCourse.
lem:3266
Finallythereare(cid:2)les, suchaspicture(cid:2)les,whicharestored
withtheproblemitselfinthesamedirectory.
4
13.(1pt)setMAAtutorial/javascriptexample1.pg
Find the derivative of the function f(x). The windows below 14.(1pt)setMAAtutorial/javascriptexample2.pg
willtellyouthevalueoffforanyinputx.(Icallthisan(cid:148)oracle Find the derivative of the function f(x). The windows below
function(cid:148),sinceifyouask,itwilltell.) willtellyouthevalueoffforanyinputx.(Icallthisan(cid:148)oracle
f0( 2)= function(cid:148),sinceifyouask,itwilltell.)
(cid:0)
You may want to use a calculator to (cid:2)nd the result. You f ( 1)=
0
(cid:0)
can also enter numerical expressions and have WeBWorK do You may want to use a calculator to (cid:2)nd the result. You
thecalculationsforyou. can also enter numerical expressions and have WeBWorK do
ThejavaScriptcalculatorwasdisplayedhere thecalculationsforyou.
ThejavaScriptcalculatorwasdisplayedhere
Youcanviewthesource forthisproblem.
Youcanviewthesource forthisproblem.
14.(1pt)setMAAtutorial/javascriptexample2.pg
15.(1pt)setMAAtutorial/vector(cid:2)eldexample.pg
JavaScriptExample2 To see a different version of the problem changethe problem
To see a different version of the problem change the problem seedandpressthe’SubmitAnswer’buttonbelow.
seedandpressthe’SubmitAnswer’buttonbelow. ProblemSeed:Changetheproblemseedtochangetheprob-
ProblemSeed:Changetheproblemseedtochangetheprob- lem:3710
lem:2414
Matchthefollowingequationswiththeirdirection(cid:2)eld. Clickingoneachpicturewillgiveyouanenlargedview. Whileyoucan
probablysolvethisproblembyguessing,itisusefultotrytopredictcharacteristicsofthedirection(cid:2)eldandthenmatchthemtothe
picture.
Herearesomehandycharacteristicstostartwith(cid:150)youwilldevelopmoreasyoupractice.
A. Setyequaltozeroandlookathowthederivativebehavesalongthexaxis.
B. Dothesamefortheyaxisbysettingxequalto0
C. Considerthecurveintheplanede(cid:2)nedbysettingy’=0(cid:150)thisshouldcorrespondtothepointsinthepicturewheretheslope
iszero.
D. Settingy’ equalto aconstantother thanzerogivesthecurveofpointswheretheslopeis thatconstant. Thesearecalled
isoclines,andcanbeusedtoconstructthedirection(cid:2)eldpicturebyhand.
1. y =2y+x2e2x
0
2. y =2sin(x)+1+y
0
3. y = 2+x y
0
(cid:0) (cid:0)
4. y =y+2
0
A B
5
C D
WeBWorK can use existing javaScript and Java code to
Youcanviewthesource forthisproblem. augmentitscapabilities.
16.(1pt)setMAAtutorial/conditionalquestionexample.pg
Thejavaappletwasdisplayedhere
Thegraphaboverepresentsthefunction
Conditionalquestionsexample
If f(x)=23x+11,(cid:2)nd f ( 6). f(x)=x2+ax+b
0
(cid:0)
whereaandbareparameters.
17.(1pt)setMAAtutorial/javaappletexample.pg Foreachvalueofa(cid:2)ndthevalueofbwhichmakesthegraph
justtouchthex-axis.
Javaappletexample ifa=1.5then
To see a different version of the problem change the problem ifa=-2.5then
seedandpressthe’SubmitAnswer’buttonbelow. ifa=1then
ProblemSeed:Changetheproblemseedtochangetheprob- Doesthisrelationshipbetweenaandbspecifybasafunction
lem:2927 ofa? (YesorNo)
WARNING:UseSHIFTreloadwhenrefreshingtomakesure Doesthisrelationshipbetweenaandbspecifyaasafunction
thattheimageisrefreshed!!!!! ofb? (YesorNo)
Writeaformulaforcalculatingthisvalueofbfroma.
ThisproblemillustrateshowyoucanembedJavaappletcode b=
inaWeBWorKexampletocreateaninteractivehomeworkprob-
lemthatcouldneverbeprovidedbyatextbook. Youcanviewthesource forthisproblem.
PreparedbytheWeBWorKgroup,Dept.ofMathematics,UniversityofRochester, cUR
(cid:13)
6
ARNOLD PIZER rochester problib fromCVSJune25,2004
RochesterWeBWorK ProblemLibrary WeBWorKassignmentSampleAnswersdue1/2/05at2:00AM
1.(1pt)setSampleAnswers/sample numans.pg Nextenterthestring(cid:147)AcDdB(cid:148).Allspacesareignoredso
This problem demonstratesvarious WeBWorK proceduresfor (cid:147)AcDdB(cid:148)and(cid:147)AcDdB(cid:148)arevalidanswers.
dealingwithnumericalanswers. Inparticular,byenteringsyn- Thisusesordered cs str cmp
tacticallyincorrectanswers,youcanseetheerrormessagesgen-
eratedbyWeBWorK. Note thatexponentiationcanbe denoted Enterthestring(cid:147)AcDdB(cid:148)again.Thistimespacesandcase
by**or(cid:136).SeeAnswerEvaluators fordocumentationonthese areignoredso(cid:147)acddb(cid:148)and(cid:147)ACDDB(cid:148)arevalidanswers.
procedures. Thisusesordered str cmp
Enterthenumber52.1.Youareonlyallowedtoenteranum-
ber(e.g.52.1,5.21E1,521E-1,etc.) Enterthestring(cid:147)AcDdB(cid:148)oncemore. Nowtheorderand
Thisusesstrict num cmp spacesareignoredso(cid:147)ABcDd(cid:148)and(cid:147) BdDcA(cid:148)arevalidan-
swers.
Enterthenumber52.1again.Thistimeyoucanenteranum- Thisusesunorderedcs str cmp
berorfraction(e.g. 52.1,521/105.21/.1etc.)
Thisusesfrac num cmp Finallyenterthestring(cid:147)AcDdB(cid:148)onelasttime. Thistime
theorder,spaces,andcaseareignoredso(cid:147)abcdd(cid:148)and(cid:147)BDd
Enterthenumber52.1athirdtime. This timeyoucanenter CA(cid:148)arevalidanswers.
anyarithmeticexpressionequaling52.1(e.g. 52.1,100/2+3-.9, Thisusesunorderedstr cmp
(5*10**2+21)/10,etc.)
Thisusesarith num cmp Youcanviewthesource forthisproblem.
Finallyenterthenumber52.1afourthtime.Nowyoucanen-
3.(1pt)setSampleAnswers/sample funans.pg
teranyexpressioninvolvingelementaryfunctionswhichequals
This problem demonstratesvarious WeBWorK proceduresfor
52.1(e.g.52.1,50.1+ln(e**2),tan(pi/4)+ln(exp(2))+cosh(0)-
dealingwith answersinvolvingfunctions. Inparticular,byen-
1.9+arcsin(0)+5*sqrt(10**2),etc.). SeeAvailableFunctions
tering syntactically incorrect answers, you can see the error
for details on enteringexpressionsinvolving elementary func-
messagesgeneratedbyWeBWorK.Notethatexponentiationcan
tions.
bedenotedby**or(cid:136).SeeAnswerEvaluators fordocumenta-
Thisusesstd num cmp
tionontheseprocedures. SeeAvailableFunctions fordetails
onenteringexpressionsinvolvingelementaryfunctions.
Youcanviewthesource forthisproblem.
Enter the derivative of sin(x) (e.g. cos(x), sin(x+pi/2),
2.(1pt)setSampleAnswers/sample strans.pg cos(x)**2+cos(x)+sin(x)**2-1,etc.)
This problem demonstratesvarious WeBWorK proceduresfor Thisusesfunction cmp
dealingwith stringanswers. SeeAnswerEvaluators fordoc-
umentationontheseprocedures. Next enter the derivative of sin(t) on the interval
Enter the string (cid:147)Hi there.(cid:148) without the quotes but don’t ( p=2;p=2). Note that now the variable is t and that
(cid:0)
forgettheperiod.Spacesbeforethe(cid:147)H(cid:148)andafterthe(cid:147).(cid:148)areig- sqrt(cos(t)**2)isavalidanswer.
nored,butotherwiseyoumustenterthestringexactlyasgiven Thisusesfunction cmpwithparametersspecifyingthevariable
with2spacesbetweenthewords.Actually,viewingthisinhtml, andinterval
youwillnotseethetwospaces,buttheyarereallythere.
Thisusesstrict str cmp Finallyentertheantiderivativeofx +sin(x)(e.g. .5*(x**2)
- cos(x), (1/2)*(x**2) - cos(x) + 3, sin(x)**2 + cos(x)**2 +
Nowenterthestring(cid:147)Hi there.(cid:148) again. Thistimeallmulti- sec(pi/4)-cos(x)+(x/sqrt(2))**2+ln(e**x)-x,etc.)
plespacesaretreatedasa singlespace. E.g. youcanenteras Thisusesfunction cmp up to constant
manyspcesasyouwantbetweenthe(cid:147)Hi(cid:148)andthe(cid:147)there.(cid:148) and
youranswerwillstillbeacceptedascorrect. Youcanviewthesource forthisproblem.
Thisusesstd cs str cmp
4.(1pt)setSampleAnswers/sample unitsans.pg
Finally enterthestring (cid:147)Hi there.(cid:148) athird time. This time This problemdemonstrateshowWeBWorK handlesnumerical
case is ignored and all multiple spacesare treated as a single answersinvolvingunits. WeBWorKcanhandleallunitsthatare
space. E.g. (cid:147)hithere.(cid:148)and(cid:147)hI THerE. (cid:148)arevalidanswers. used in elementary physics courses. See answerswithunits
Thisusesstd str cmp formoredetails.
1