Time to conquer Calculus!

[Pages:10]Math Superpowers for Every Student Award-winning Photomath app makes math easy to

understand and master



Time to conquer Calculus!

Refresh your memory or practice new concepts in caTlcIuMlusEwiTthOtheCseOadNvQanUceEd R CA E TO CONQUERTTCIMIAMELECTUTOLOUCCSO!OpNrNoQbQUleUmEsER. RCCAALLCCUULLUUSS! !

Use Photomath to check your answers or to helpRyeforeushwyoourrkmetmhrooryuogr hprasctteicpe nsewwchoencnepts in calcul memory or dpryeaoctteuicr'emrnepeinwrsoetbculoetncmhckesRe..petRIfbsrneeiefnsrshescostyahomlocuyuorrelummrscemwmaoiestosmhretyotsraho,yerpsyopeproraaprudcortvaiapwccnteriiccilneealpedwtrnnoepeebwcroloesebncmodloceenslmu.pcttesots.piotiansnpicnaUpflcocsalueylrlcumPumslhuawosuttiotw.lhmtiFittaphhutlhetleshleteossmaeocdhavaleudatcnvhtkacienoycdconeoudrsnaacnersewpperratossbtoltertmohtose.help you wo hteIhnbtesosotmchoeerccmkasoyestosthu,earypeoapnunrdsowwpfioerlrrliasnytoeoereusdrtooUtlryduoeohsetfUeuyeetaidool'erspPeprneerutepmhn'eyPlfrocsryooietemhtnruuo.mosmeicmttnwuktoaeah.locmttt.ekrtiIhkaph.nFbtletItuehesonhsblomltrtmcesoshsaoouoetetmcrlghchueocmhkeeartcncisocsyoomketasdtonnsethsouy,scpeestaoerfysstahppuo,eoarewtaprnueynrsprdehoasaowpntwueyntpfordnioseoorlwwrrlipfasuioenyrltrrloieoreasrenuytrsdoeoretoereoutlrsdufroteoheotftlreeaiuoeorlrhptpfeneeeaipnolrpnylfpcneyoopencruyl.yfmcdmyeoooeewruuua..mtmlot'etwru.rraiekpmlotFtl.rsitueikptnhFlulmlertuecohsklatumolrh.tlogsheuaIuohttnlbgchiusoohesttnnscoeistooscmptennoseapescprrwteescasmpharwattseeostoenhstasthte,toneaypeopnurdowpfiorlrlianyteoeeusdrotlruoetfeaiorpnepnlfcyoer.mmualt

Question 1. The graph of the follo

n 1. is

2 at:

cToQisnhuceeoagsvntrceiaaodpvneoh1wd.oonTfwwhQystneauhQysw=urceugdea=hurcxfsraehodft-tpxs-oilhto-hfl5tr-ooiahn2o5owrtaan2:fail1itsltln:.li1hvsgcve.TaoacelfTnhoouqcenehlulaosceagvwaotroegviifafnroedpganxohdpewsohqouwnufcownahfttwahtitohreahdnaretfd:ofysfolofulro=olAclrwaho. xlwxial-ntl-cceeCpp2525tt.

((100,,

- -

3 7) 3 7)

D. 3

E. 2

Solving withQPQQS?uhouuSloevceestianosstngttimoiitwoohanienntthhe6q33P.u::haotAAFitooinmniadnthPthhoetomdaetrhivtoagtriavpeh ifto. rReevaiecwhthoefvetrhtiecal f?oSSoollllSvvoiicwnnianggintnwwerpgiictterhhopePPtbqhh(luteoohattmeootmmaitsoaaoyttnmhhcsphteotcek) aynoducroamnpsawreewr hweritehthPehvoatluoems faatllhin

? ScarneleaatciohnetqouathtieoncuirnvePshotomath to graph it, then determine if

QSoulveisntgiownit3h:(tAPQA?QAHoAQDR.mh..iSoouu2uno--omcaeetatstettt323a:ossnihhsh=nitteenmSteiirrxita(uooee=oa35c2bnnaaht,nxhcrrs0seeteoo)44=2qislaaDt::vu:nnux12aoeyy,ttmeitybboah-rrnyiieeennaait=nkkxdessreP>cwiirennhipi25votttttahhho(teem0id,dvccxa-uuetirr)hn3vvee7tto)hgeraepdhitiitn, gthteonodleotnermPihnoe -if

CB?BCBCTQS......oyyIuStl552323vhMcei==2enasgrntEettiwaaoeanintanTrh3xecxhP3O-ah:neoxyqAtCouwmaOiatttihohNnbQrienaUPkhsEoinRtotmhCeaAtchuLrtvoCegUrapLhUitS, t!hen determine if

RefDre?.shSyycoa=tunhre3meraeeccmoahosrreeyxqaounrayptriboarcnetiacinke snPpeiwrnhoobcttloheonemmcesca.putrhsvientocaglcrualpuhs witit,htthheense daedtvearnmceidne if

Question U4s:e Photomath to check your answers or to help you work through steps when ydoeuQbxt'eQAryre=um.sueit-tn1usehec32tskteih.toeiIgnonbernssoa7tmp4.oer:hcFmassoiestnstho,deafypeopnutyrdhowpf=eiorlrlianaytxeoereu2sdero+66atlruoetfeaio1orp,nefpnlfctyyoerh.mm=eualtt.ri-pFeluexglmlios,aotnlhuxtciboo=nnosceuap0rntesadattonedd

B. 2

Quest3ion 1. The graph of the following equation

y =C. -5 5 is concave downward for all values of x x-2

such that:

5

A. x < 0 B. x < 2

3

C. x < 5

D. x > 0

E. x > 2

Question 5: A

Question 5: A QuestionQ5:ueAstion 5: A

Question 6: Question 6: QuestionQ6:uestion 6:

A. 2 cos(2x) A. 2 cos(2x) A. 2 cos(2x)

B. tan(x)2 B. tan(x)22 B. tan(x)2

3 sin(x)2

C. C.

3 csions((xx))242 cos(x)44

C.

3 sin(x)2 cos(x)4

D. -3 sin(x)

Question 5: A Question 6:

D. -3 sin(x)D. -3 sin(x) A. 2 cos(2x)

Solving with PhoStoolvminagthwith Photomath ??? SsopSSScuocfcaalpsalbenlpsaurtvaenfuehabsnitrfntbtrentsethoegsintthottfentihthcfuteiwtthtueaethhetu?eiethqetleessteqcehueseeSeuceuSasqyccaPassytolaaalupstiahlca=elnoaurivac=autoforenbiurtroenlttnteewwaslioihorwigantiotnmiifneitoitntfitnnwotththorauhPtehhhreiPthtqfritteehshoefdndehhuhdeoddxtorxccdasxohrey.tc.aoPPtt.tooeatlrhiTohhcm=crhrToemourTeoonoesoaecltsoeawactrtistoefinfiotrhteitccnBCDmifinhepocnt.omoptn..h.o.rladcdnPhaldnntt-Sa3ftdacehachoSddcdwdeaddsto3dpxonrdwdexcaxirdhasi.xt(nos,ryltti(oxa,.iyrrht(cxntmytrTc)kxhceSat)a(ke2h2e)aoe4axp4cpweksy2t2pttey)toebfihic"ob"pto"ny..tco.la.dnbth.a.ahr"h.S.decor"d"ewdeaddto.xacroo.ionca,ytMrnaMcldntctltkhaachtu.heaktuhpleyektMhealeobeat"ebsctooab.sutoo.aarukhob.rtrr"lretteeadcoetoanao.oucmtnsaldnmtalMllduoallctrtamuehokleearaltbesaloulofrnrtedtaonamldl

OR

o?r

?

RReewOwnrReriwtiteeftothrh?emesRusoolelaulwOutwrtRioiiitontenhbtbhPyyehhhosaotanolnudmdtriaroetepnhp?lablacySciScnihonagalgnvnyiydnt=hg=reewwpweiliqtaitthhuchiandPddtddxxgdixhoayonantn=odidnmtwthaPhietthehnhnostdscdoxcamananantdht. heSnwsitccahn

to

the

calcula

? RenwewritfoermthuelanswoeiwltuhftoPirohmnoutbloamywahitthahnPdhorestuopmblsaatctithiuntge y = wwiitthh ddddxx.anTdo tfihnednddddxsx,catanp "..." on the

QQunueeeswsttifiooonrnmQ77u:u:lae1s1w16t1iitohnP7h:ot1o1math

left of the calculator for the secondary keyboard. Make parentheses are in the correct place

6

6

Solving with Photomath

OR

SNolovtien:gTwhitehaSProehlavoitinsogmbwoaiutthnhdPedhobtyomthaethgraphs of y = x2 + 1, y = -x,

Nxo=te:0 Tanhde

axNr=eoat1eis:

bTohuenadreeda biys

bthoeu?ngdRreaedpwhbrsiytoetfhtyhee=gsroaxlpu22ht+isono1f,byy

=h=anx-d2x+r,ep1l,acyin=g

y-x=,

with

dd ddxx

and

th

x = 0 and x x==1 0 and x = 1

new formula with Photomath

? Graph each function by typing each one into Photomath's calcu-

? ?

GFrraloalpmathtoorter.ha.RecRh?egevrfGviuaeipnrewalwhcaptttihwtohohrenee.eabsbRbceoyheoeuuvtnftyiunhdepndwaeicedtntdtgiyahoareen=reQaeabcbahoxuyu2eotn+ynsdpete1iidnionigstanoregeaPr7aceh:aotote1no6r1methianatthno'syPch=aolct-uom-x ath's

calcu-

? Fromfrotmhexg?=raFp0rhotmowxeths=eeeg1r.tahpTahtheywree=fosrexee22tt+ohac1tailyscug=lraetxae2tte+hret1haairsenagyrwe=aetne-reextdhan y = -x

ftrtooomccaalxclcuu=lalat0teettfotrhohoexmecian=ilnxctteu1e=gl.garratT0ael lhtteohreexfion=SNrteoeo1lgttv.eroia:nTclgThaelwhcreuietflhaaortrPeeahtohoisteocbmaaolrcaeuutanhldawteed

ntheeedarea we need by the graphs of

y

=

x22 +

1,

y

? Scan the integral to get the soluxti=on0 and x = 1

? Scan the in?teSgcraanl ttohegeintttehgeraslotluotgioent the solution

? Graph each function by typing each one into Photomath

lator. Review the bounded area

7? From the graph we see that y = x22 + 1 is greater than 77 from x7 = 0 to x = 1. Therefore to calculate the area

to calculate the integral

? Scan the integral to get the solution

77

6

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xQSNQSooo=ulutvleevi0:nisngaTtngiwhdoQS?eQ?iwotQ?nxRhulaRuivRr=tue7eiP7eehewnnewenOsa:h:1egswnOretPsorwRiteiwrtiiRwtst1hwtiioe6otioefi1obfoometntofnthorhtontrhamuoerhmP7teQ?mn7emuhs7uh:sdol:uQ?Rsoualo:elaoalultd1eaueRltwu16otwunOw611htsimw1e6biteeoir1RtitwnOoiywtiinhsaotitnehrRtntoehwtbifPhbtihPonytboePhyerhfhyomhonhtehog7rhtahoutamsroen:taoo7alnmoadunmslpd:muo1ldahwra6atlrt1easuitr1ehiopwt6hettp1ohnlhipialoftalbcnhaPyciycnihbPni=gnhoyghtgayhoxynytma=2do=n=+amrdwtewahw1pirtite,ltihhapthyhcldaiddxn=dcdxdgxiana-nyagndnxd=yd,tth=wtheheinwetnhnistscshdcadcxanadndaxnnQSN?adoonQSN?RultvtdoeeoheiRul:wnnttveseehegenirTt:wnnweistiwseghnrToetcwifeitaiwsothntoechnrhafeiamotnrteP7nhrehausmarhe:oP7leaoulsiah:ust1olw6oatli1buimst1iow6toot1nbhaimuiottonbnPhhaudythnbPehhodyhtaeohndbmtadyonbamrdtyt ??NGForrtoalftemaropot:homcTtra?Nx?he.?xSNhlax?xSNecoo=GFReocu=oGtlo=g=hrtGvellerto0aevrra:aliv0era:famaltni00pria:ualane?pptTegeaahtTpnnogawhthtTnotthahrdcwonohhherdw.ehtewGRrdt.eaieeiiexxa.ethiRsoxcaeeatRhcxairegnhRhr=n=caehabvr=sree?xSNhvPtr=beeaebfpiavPooeef1iueaov1eoh=p?xSNyG1eiufgalhhentu.1iuiuvwowhornesioetwor=tcGnisnta0inlwhTc:altyenstvtowblcadtettdaropibpgtiamh0ahttoiTho:baelntetmhhoiionaoeeencdhupnowogaeahenurtTrdysadhennhgeutneob.eienbawtbhahtdbfbnrdxeob=hrydeRbhoefcaob.eyeideuaouoaetrhyru=dxteateyRhPencducaexhtnuyvndhhtfyadr=nhbea2p1tiudycPtnbepeevdotyohbionp+feaitywhddni1iusetynidnceieycootdgnneitewt1agabhtstmatigchn=grdhloeoaoehirtceieebanatmenruseeireuaabhogectotaaaaxngclbahhoagenrbugacy2hrpdratoryhnretabPheoebp+uhaetodpadaontyhyohpnnsehyttue1nsophddeehbstpnoetseryiyieoiiodninodbsnpfniomttefnaytggithofgdaynhrtoayareroetgyePteeaen=ahaPh=aaPrheagc=eh'etwyahroshxceaoxgacteor2hxc=thorpo2toaa2n+nmtho+molophee+-csmnahea1nua1itxdeoan,sn1-teh,fth,tyio'hyynos'yiyfs'nt=scP==oy=ct=achoaP-la=--cloxc-lhuxPtc2uxxox-u,xh-,+tm2-,?x?oo+am1t=x??GFt,oah1rr=ytGFo0m',alfshmarrpry=a'oo0atcaalfshnommaranpt=taordct-lhhehcnd.omaaxteu'xxr-dlsRhecc.-,g=haxuex=xceRrc-v,aafg=h=0e1iuprlevcnafwht01iuupcoentwhtwltixacohoetwtteni=xohosebebenr=1.eosyb.ebut1eotynhTy.udtapthnhTeytiednaphryetgie ? Scan th??e?SiFncFrtarftoeftrnoomrftgoo?mroormtcomcahatmcaltehlFacxclhtxeclauirxoecun=ollug=atlc?gg=amlretaeur0atge0?Fattep0lretparttahttFothhhthotftlothrmoreoehewextoeoxwfteomxirmecostn=igteoaon=ihghtsn=mcllrteetsxeceeua1taehetg1ueetl.g1epxg=rec.giiltr.oaatnur.ThrhathTg=anltal0theTlhaerpaelhwaatehthst0tegetprooeheeryehtlwrretyeufxroeahfose=etofwi=leroeixn=rfeoseroetiexnen=ext1esr2tgto2eet.toer+1thoe+gachT.ctaarltc1aoaahl1hTtatcllecaliuhcsriuytsleuaalgfrayl=glotarecterrefte=ueoeaextarttlh2taettehxoeeh+rte2treecaot+a1atrharthcelariech1aaasenaulenaciwlggswayuwryeatrlegeaee=eranr=tenaetteeneaaeh-tee-erttedeexdehwxdrtrae?herttaaehh?SnarnaceSeanwanytcnoeeawy=tdtcnoneha=e-teclnechoaxed-uielneclxdatuientlgeatfrerttoagehlrmteathloientgotieengtgteertatghlrteahlseo

?? SSccaanntthheeinin?tte?eSggcrSraaaclnlatnttohotgegh7eieetntttinethhgteeregassorloaltulloutttigooioengtnetthtehseosluotluiotnion

? Scan the integral to get the solution

7 77

77

7

8

 ................
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