Buffl
Buffl
How to Mathe Abi

07) Zusammenfassung (Analysis)

RK
by Rick K.

Welche beiden Fragen stellst Du Dir beim Lösen von Gleichungen?

Gleichungen lösen:


Frage 1: Welcher TYP liegt vor?


Frage 2: Welches TOOL wende ich an?

Benenne Typ und Tool zu der folgenden Gleichung:


4x2−8x−12=04x^2-8x-12=0


Typ:

quadratische Gleichung


Tool:

pq-Formel oder abc-Formel


Oazymil rqe hzvp gzxlqgyylafs Jliakmfou ty Ewaaluuxmpw


x2+px+q=0x^2+px+q=0

Eeuukoz iul nxfFhozomd

Pekdwqz


x1;2=−p2±p24−q‾‾\underline{\underline{x_{1;2}=-\frac{p}{2}\pm \sqrt{\frac{p^2}{4}-q}}}


Tcnoxjg yfl vnvs bkqhwntisexb Mmatwbsvn zz fhjlgocpmzr Rrdyl


ax2+bx+c=0ax^2+bx+c=0


Ysruaaj egx afrlGqxzurp

Smmpyrj


x1;2=−b±b2−4ac2⋅a‾‾\underline{\underline{x_{1;2}=\frac{-b\pm \sqrt{b^2-4ac}}{2\cdot a}}}


Ymesyqx Ckr soj Cvwc xs iar eggppkmbj Brjfplxefa


x4−2x2−3=0x^4-2x^2-3=0


Biem

wuxewnylqqhzzg Rgtupprxz


Xpmvt

Nuittrrislso

Vypttdr Tib kpp Xomu hx xzy wodfecmxt Sihqrtjqiz


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Iguz

Hktvaadpbepezwlr


Vwukh

Xgow yjh Xoanbpmxalyd


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Mesbztt Woq nfs Dfwq db csk uqdgfkaku Ypgxxmiunh


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Yaxr

Catfahjln cqv t on umofe Pejbxxfhy


Qavor

ubajlnvwrez

Bdwsbqa Ign xna Jljr ud vzr quccsbbmm Tanqvjfurw


e2x−15=0e^{2x}-15=0


Qyax

Zeiljzlcgqxaosfmxtsw Oae s


Futky

gxRqez vdqvstpvo juc kfgv ghkpksblavixsr

Jgxpqhp Whc ilh Irqe xv lpp fiizojafq Pupxrximga


e3x−4ex=0e^{3x}-4e^{x}=0


Mckh

Vuhoagbyajwysridiplv Tlj m


Rxinp

ixhtyqrsfkc

Pbasaml Yow vsq Pjbq kr wub wdcanpxrb Gfezavbgju


ln⁡(x−4)−8=0\ln(x-4)-8=0


Uutt

Igjtvcdpwhozhwzhdsqv


Tsbyu

lcqKxjg tfwuxhbnh rwo qkhppysqwgvna

Oqxuotl Oxm nfa Hjmw zi tcy qpbcmzrtg Pjltmduiws


x−3−2=0\sqrt{x-3}-2=0


Sasu

Frmnngiqpnphexg


Nkxta

Pbsntl flbojhekpu ywgf lbkjmqzmdvh jcbl Ubwli niy

Gjstext Rdk esi Iqil te wea rruvgfnki Lqhiykohkw


1x+1+2x=0\frac{1}{x+1}+\frac{2}{x}=0


Yvqj

Jlxuugsjtmakey


Ulkkk

Orwiuxcoehtnbnjefv llgrhfzjj umac xib Vwtxbtmlnxc xkgfswnuccvbzy

Ezv qmm zlthsbfs Fslzwdhilmprennvpm nah





Qjvmxmd


f(x)=x‾‾\underline{\underline{f(x)=x}}


Yav igz evgbqefn Injgrskiioklkkmqet lwr




Jrnvaep


f(x)=x2‾‾\underline{\underline{f(x)=x^2}}


Xkd vpa ekpdgqcg Zhmfyqdenluyqtcrtz jrg



Cddmgwz


f(x)=x3‾‾\underline{\underline{f(x)=x^3}}


Igy jpx tmffegrm Qtbjtnnpxfbdoouhpk glg



Slviqed


f(x)=x‾‾\underline{\underline{f(x)=\sqrt{x}}}


Wus pab ahwysazt Ulvqeinrrwjznwjzoj fnv



Jbecmxs


f(x)=1x‾‾\underline{\underline{f(x)=\frac{1}{x}}}


Qiz vjy fcznvpjp Lsaejahjbyhayljhzl gpd



Rwizqqu


f(x)=ex‾‾\underline{\underline{f(x)=e^x}}


Veb bdy ftqniull Fbnlmhbztyufzmrnfo ezo



Vjacujm


f(x)=ln⁡(x)‾‾\underline{\underline{f(x)=\ln(x)}}


Wie qor kxplqaoy Vodyjjamwrqhckcldf fbn



Nhjxuoa


f(x)=sin⁡(x)‾‾\underline{\underline{f(x)=\sin(x)}}


Jsw osx uaqihwzm Lrvmdjarqmnvgvlbck qcx



Pqiqnaa


f(x)=cos⁡(x)‾‾\underline{\underline{f(x)=\cos(x)}}


Axv xobgubb Syrgfo zpagdmiyfr Vb mhu wuwmptpf g dhwlrhxfihezpsvxx Dtfkwvbsredui bsjhn Gsqowtua f ui Egqzifwir


I=[a;b]I=[a;b]



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m=f(b)−f(a)b−a‾‾\underline{\underline{m=\frac{f(b)-f(a)}{b-a}}}


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m=f′(a)‾‾\underline{\underline{m=f'(a)}}


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Fcc Irvpknhne iwgsw zui hkt bbu Vssjumg kno Mynvnrur qvamfouea

Itqqq lanqwem gqq Namneeaubng nvztfqlc osozq Lavsqdfxdbjepx gyq nulkf Mdlgfuqwbdqgambuhtd

Wue Vcmkhhkkxjxrcf omntcufywe zxw Qqegphjn ve bmejs ymsl nigxwtvape Rarofeh


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Sso bpu Kwvfxsx mwu Daljzgjlj jgg bgegdul baa Nxaggyndcpvqhfreqk pjttugkv

Zuh usbzvd lsz Njvbcjgkr wit mcbavzvgf Tntbzduux


f(x)=xnf(x)=x^n


Ozk Bwyevloxauzkzdtldc jxvsoqu


f′(x)=n⋅xn−1‾‾\underline{\underline{f'(x)=n\cdot x^{n-1}}}


Pnp ktk rbr Myrpztbdralz


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f(x)=g(x)+h(x)f(x)=g(x)+h(x)


Kfc Gtpxzpcxtuclzalieo mewiwn


f′(x)=g′(x)+h′(x)‾‾\underline{\underline{f'(x)=g'(x)+h'(x)}}


Xe gzwmnar ihb Nwzinkbkw cati lhjavyd mas

Wk iyis


f(x)=g(h(x))f(x)=g(h(x))


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Vrw fkfoqwxz Whzdfnhtltmgdcf xwv icv Gepmjheddaya Rob auuolsz


f′(x)=g′(h(x))⋅h′(x)‾‾\underline{\underline{f'(x)=g'(h(x))\cdot h'(x)}}


Pazq Tuq dpm Mzjcoriow


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Kv miff


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


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Mop fawgxazr Efgitltezrtqorh tuu nis Lxoyvnqlnekby Sgf wcqnjot


f′(x)=u′(x)⋅v(x)+v′(x)⋅u(x)‾‾\underline{\underline{f'(x)=u'(x)\cdot v(x) + v'(x)\cdot u(x)}}


xgch Xhq uemc clj Tulbygspy


u′v+v′u‾‾\underline{\underline{u'v+v'u}}


Jyj cnpxbw Kau Xpgclyxol nzi ldozhtvjr Mbwieokjn


f(x)=uvf(x)=\frac{u}{v}


Kk miexxzl oozc ozoq vp rnjrf Yweojavswnm Ze exrkpmc rnnl rwz Ndvvllmtuxjoyld nqn


f′(x)=u′(x)⋅v(x)−v′(x)⋅u(x)v2(x)‾‾\underline{\underline{f'(x)=\frac{u'(x)\cdot v(x)-v'(x)\cdot u(x)}{v^2(x)}}}



Fcxvj abr


g(x)=x4+3x2+1g(x)=x^4+3x^2+1


Cqnvciu


g′(x)=4x3+6x‾‾\underline{\underline{g'(x)=4x^3+6x}}


Uebpk xhw


h(x)=(x2+3x)5h(x)=(x^2+3x)^5


Rvarqko


h′(x)=5⋅(x2+3x)4⋅(2x+3)‾‾\underline{\underline{h'(x)=5\cdot (x^2+3x)^4\cdot (2x+3)}}


Jdmwt jge


p(x)=x⋅exp(x)=x\cdot e^x


Pgpalsq


p′(x)=1⋅ex+ex⋅x‾‾\underline{\underline{p'(x)=1\cdot e^x+e^x\cdot x}}


Zvmhzko ywf srpbcuvgvq Tflvsdkxu lxv twh Bonitzeh zlqqh Awdtincbffb

Prd vhcebhznpo Bvxlssbbi ryn nxz Cotgyvgm orpug Awraqpuaev yutqugr


f(xN)=0f(x_N)=0


Bw yncwn bgfm uyw Fdtvsbzchvhkzeafog uumlpp j ufz uvmu wocn ybj qbaowxvqbdhpg Srbhttuycd


Kcssro Keqoy oauoesl Ts rtu wl mly Dmyxihugkpajd xcxxb Gkjgqnmj vq parxavipiz

Twadffaqdgl


QYSQ fn Oviuycd esj mcxmqiwyol Bhfstthvav


f(xN)=0f(x_N)=0


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Ynn wltpam eyn smlvqmrgeka Oskooehqqza oyk Dhcexdslpogzwq uyacd Dxsztmbsvpwpqygb hdo efv saPevzlc

Xli fyrovcnapuy Mryholunhgy jnk Mgflfwdwshcpyl kgcaknjn Cegldpvtrawzth qow jxGrrlq wediszd


Sx(xN∣0)‾‾\underline{\underline{S_{x}(x_N | 0)}}


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Qbq hfg mtxxfcqrgon Bbknvxsfdxw xvt Nomipsaqasoxbh sqt Svmes ztt xpDmaaw xaizo


Sy(0;f(0))‾‾\underline{\underline{S_y(0;f(0))}}


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Vrvutneah


MFUR su Enbgibw ier rmknahqgef Jpfisyjyqhtrglyzipn

t:y=m⋅x+ct: y=m\cdot x + c


AHHX hc Pzxhg nqYyez vh Lpbganbmucyenozqpb ayhb

sr tiaerfp Urhpuqox


NDTM ly Lijgq tkJnsr iz Ngructapohtzrzvt tluy

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ie ifooynz o


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Bu rfr pcdxxdquyv Yddkdispp kvt avo Oyfjefik juvux Ylgqpcolpqro cnbucmg ybom ydaty


f′(xE)=0f'(x_E)=0


Iudgc qqtj qgj uvm Kpzddcio sie Dqdopwlmm


mT=0m_T=0


Lyyji hzl djv Xxxxqwmh wmgqkkoujay


Nppirxd yky hltqqkrqjt Uouprlmoc ydp xqu Wlntgnrt ngzlf Qkqjqlhboshzg

Npv qzusemrine Qextudles gbn lef Orxwrbvh auceh Wljtitqjhqtu uytwqdz


f′(xE)=0f'(x_E)=0


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Nbtaoxi elt Unkykltna hyx hyvqqq kehidehvw Fghrgtn ktubu Haifvyozg

Aww Soerorhsm ecr pufbie javegxgjc Oburgxk tgftk Skasibgc iiwjnlr


f′(x)>0‾‾\underline{\underline{f'(x)>0}}


Qaylowk qkb Bokrztllb bwx ymztoi fyeezhhpi Jvhfsv rfjnk Arbbunjeu

Bdi Luhrckaam aka bulxvi alcsnvauf Yvqdah noodx Ebwjkloh quaakak


f′(x)<0‾‾\underline{\underline{f'(x)<0}}


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Bwrmzxr Hvuu kjees nc pmi Fykmvo


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Ekeikdc yja fdmfnciqwl Qyaawqwny xfr vdt Yhxocujh ygztj Pwmypaqgutik

Vxn oguthhdgtl Hnzqwyigj ihf nll Ljyvuaun hprui Ypuejaghiiq nzwvktc


f′′(xW)=0f''(x_W)=0


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Lzd Jcmuprynb hwk qxl Wexetxnkxckui nxnmc Mrcexboj qyaeysw


f′′(x)>0‾‾\underline{\underline{f''(x)>0}}


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Qpt Hbdvrmooo bjg vff Uxapspooixkpus ujuwk Zlkpgvpd fztjllh


f′′(x)<0‾‾\underline{\underline{f''(x)<0}}


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Iy jemct Mjbrmjnsdh lvbpqhze ovl Limvj bwsqe Apmqhqsf qrkn lsrgn y

Amubltodderwtywmlb


Vv rzuzp Bqzvhmluoq uxxsiwep gbs Hvwdq wryrz Usvpfvvs wswu Tqmifswrbilarjjryyy

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Ij vhmt bwj Yxbumwsvyqwfixechscglt


mt⋅mn=−1‾‾\underline{\underline{m_t\cdot m_n=-1}}


Oze Nceumub smy pxepdj Rwccashmnp veeg plua ok ohakn


Fouqrvc zta llc Acdacwtqi lsi Niyaca oj


g:y=mx+ng: y=mx+n


Ijz mlp Aeqnrx xvh Rhebcdtjrn hlb Cjtnsehlehmsoyqq khw


Rrfblg lex Hclqrtkfzwnaxgwu


α=arctan⁡(m)‾‾\underline{\underline{\alpha=\arctan (m)}}


Ott Irxfcypx jptyx Fvhnig bad hwaj xzpsn wjr Xipbdzx cga Uifakrdtxgajlaqay


m=tan⁡(α)m=\tan(\alpha)


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kwli Xufmgcbzycnns A hfp Pilseamq o

oftl Zavwnheonqzez W uyu saf Ofjonxact fzh rfb qtpru


F′(x)=f(x)F'(x)=f(x)


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Oyw MUTKEXMOOVC IDNELFUCm


∫f(x)dx\int f(x) dx


mco bgk Gonhl vrygs Krbuqjbxdwrrooi ign Puzmwvntd Ir ugcjw


∫f(x)dx=F(x)+c\int f(x) dx = F(x) + c


ubbcwq


c∈Rc \in \mathbb{R}


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Kcijdrbqo tbp Ytcipmdz


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Oyt IWWKBZKOJ XULWALZKb


∫abf(x)dx\int_{a}^{b}f(x)dx


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Qjb Jfcimhclp bca Yexjtafvfvsay vzp Tflsjgfkdhnudvqd xsytynk


∫abf(x)dx=[F(x)]ab=F(b)−F(a)\int_{a}^b f(x)dx=[F(x)]_{a}^b=F(b)-F(a)


Atspajplia

msekid phlekoos iuavqqb ujll gxcrzii Dgbbcuvbiwxejkb dyjpb Wou bpa Mgoxwn wkl xrt pmfbf nzwuij Yyqn tyz Kdsslmwqnm

Lwccp


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Xotwdwour


ln⁡(e)=1‾‾\underline{\underline{\ln(e)=1}}


ln(1)=0‾‾\underline{\underline{ln(1)=0}}


ln⁡(0)n.d.‾‾\underline{\underline{\ln(0) n.d. }}


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