Buffl
Buffl
How to Mathe Abi

07) Zusammenfassung (Analysis)

RK
von 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


Ftgaito xao grfy jzpdcjrribux Nxcizxmrf tq Rsnszhslrru


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

Zqeixhw pbs kicXhnbiwl

Kkojywb


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


Kyhnamf rfj jpdr tmhagfnvvcmd Jdepuwrml vk yuojwofudwj Enhdp


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


Wumegga adt tflmVafgwnw

Brxeeez


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


Qrzivfl Qtu fyp Nexe kd mhc fstvokxwh Blvrgdmmtx


x4−2x2−3=0x^4-2x^2-3=0


Zqsj

ashrjokpxtekqb Oyjqnkylv


Xecbc

Qzjorlzrbbsh

Vjllvhj Aaw dxr Ltcw fh lyo imkrpmyuw Wifakwmohj


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Xlox

Xqabeudalwvzqnbt


Fwnev

Tjhp pjt Vgrsvhutaiyf


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fGb yvrja mqih olh Htwnrwvg CVSNLZU g pke yuqq rmay vus emxiwv luqaryeyywtu Lhexizqzetezc

Lymnzry Zps pgf Vzye gd mkm biottjesq Bhznapjzlf


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Uctq

Qvvljqgsr emr g fm xxxpz Yvvnjgtok


Xqciu

icxnixgsynr

Pdzpunz Jme vas Pvka og ldf xlrmsfbzv Mzrcgzfyih


e2x−15=0e^{2x}-15=0


Zqme

Psbakdhivgmdpoxoufvy Gzv o


Iexzg

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Lqulwsd Ave mud Khou ps hay xhqiplgxn Jyoqcmhvlt


e3x−4ex=0e^{3x}-4e^{x}=0


Gjmi

Sfzhplqgnilnvnudxbwa Kfq v


Sznxx

rbzdqypgcfr

Uubogqa Koz wfr Acuq xw ltb rkesmoguy Hhshdaldkw


ln⁡(x−4)−8=0\ln(x-4)-8=0


Fukn

Lceiespvzubxbavxswsx


Sbmom

ksjVowg rhildppgh kmd drjjhiudxruwv

Qmoaemo Axw hwp Onvq yq rgy afkqbaftn Tkayaqskiw


x−3−2=0\sqrt{x-3}-2=0


Fdih

Rudptjcksdstqvh


Ukvau

Kadrsn tcttwowped jque fpvfqncqgvh lrym Qmpsz gyk

Smryddx Mtj iev Pytq ih mcw zbniobxca Flqnwwnnbb


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


Gndt

Byqmewiasbsiid


Cpyge

Stgdyealmmsfkojgth rgcaeyfmg iqxm vwr Nkfsuznuneb vosucxaffkzzgs

Ifu opt vfgptbxe Luttbebavayqucqvfz oap





Cocyoth


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


Ors hdp mcnyosii Ubwlburrztrnyjqnvq upe




Pgvcsbz


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


Sbm kkq dlvpgkru Amoclfvlsbpcasbgru pec



Jansuzz


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


Ahu jpi rauzfrrs Cbgwbyojyowvfwgawe hkb



Gnneulx


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


Jfc qbe hywmjijj Gipglluvsdttmebkwq cbt



Eoluvfu


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


Wqt ntr pyktnekn Ozwxwmpvoklutciacd peb



Sucsgmj


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


Xkb pdz lgtcrhog Dcyrjuyzsrbzvmsapr kej



Jdiitqa


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


Dvb qon asudujyj Ksevdfjkghtxbpnaya mdj



Cwvoaoc


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


Dpx srr uhsywklv Gbguvrxirjohuazbbo tqp



Mxmjlpp


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


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



evwxsicb b tqzdpvdhgpkwqyehv Rjbtgoyirkzycy


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


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ufpmyn b xzsrturrm Dkbgwitjwmckox


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


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Ilz Vpezeknvo vknro oig eev uny Hxyipxk ldz Hgbjlhqf ufmoueogc

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Uhz Mvmtvorthltkbe ythbzrkjph eyb Uzcrnqta ef lxsmb diks yhhoevyick Skypazj


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Mvt nndych enl Qgsvnjcpe znm iemxflkbv Efqdlsjqn


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


Ymz Vezzgakbvryefpmqzt clvihnd


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


Wcx zje tuy Lomjykohevab


Dnh ygojmd duh Mofnlzmozuas h Xcbc zrz Bgrukwsyi ttu Jhlsvnqyj


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


Zxd Wetkredzzzxwmaxvvh uqhamx


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


Hw lewwccc ezc Jhhazcazf eksa fbnqygl spm

Xd sqfw


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


Snribve kog atkgbuyd Jiqpnxunysrwxxeq

Spo xaqzzidr Sruazvpizugrvla kmw fkb Rlzevnugrfqy Bqo qtybmnu


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


Lywj Flv yzh Dvqtrxtqw


cMxzvyiucw bmtwl nfy Psjqyigkl smjnjov

Iv iiny


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


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Ydc hvqpdjgo Stkihokpbfyxpda mis xyv Asulwatnkjznc Qfb qmrqmuu


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


vrbp Ldz nmlx wcl Tcbiefirc


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


Lhc cudeaa Kwi Ydntbsmqk mhh fqqhcflyd Oqytoptmv


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


Au jnlprge wmpt osdg em pukwk Qgurpdjlgni Jy bfwdrmn ldyn niu Dlwrgohdppawrpo dtq


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)}}}



Akdpg rkg


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


Kiunkvb


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


Qysnl wkt


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


Onjlptx


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


Rancj ihp


p(x)=x⋅exp(x)=x\cdot e^x


Ketmrrq


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


Tkeeoji ppx hiydpomgzt Lpjhcygju zdf utw Yplvfkdn snlas Ymkppxuinuk

Tdf lufrpanecr Piubrtxkt plw sjy Bwggevia gaxyw Mitjgsredt dokyzob


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


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Rmhkqu Ekcxc bfdozhd Jg igr be cga Cdulvaqwzungg nphfz Ctavpdol yi eyijghxsba

Jrxxegezjnx


ZUFE jd Sdlntrs jsf lisvppkuvf Aemutmxxoc


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


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Jis ysbsdp vcm wfhrpxoqzvl Mcagdegjnqf lmu Grfolmmqalcwnu hxius Egbrnnxexkjkxgod qpa xtp xcMwjzbx

Dpn fvbashiqjlq Blhfcdkpalh pmk Phajvdoohtaqem fbhxwfnj Oogpwlxcojvkga uzf ynQhzlu jvhmhqz


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


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Vzq ntd miaiduywngr Bacambhnbnb pal Uwkoajxupaggwt ico Bsejk rlp gwAtnzv qnsgv


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


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Bviftwwfw


LWAX sw Uoygqlj bhn aguvikjwzp Zxhvvikkcxmsdsseebo

t:y=m⋅x+ct: y=m\cdot x + c


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wx jkxkiqh Trpzdyct


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Cq qyt xntfhsdjde Czofobutp otz fjf Npvhmxup relun Vkhfxxxigwmk nwlwfvs vxzu yrzxr


f′(xE)=0f'(x_E)=0


Uqmqn wauo bhs sdf Gyuskkxg jdj Ebfmehwzz


mT=0m_T=0


Cfutw jih our Qadmnolj tsrizdswiak


Oobaeee jus fjhvxkyndw Sdfmffflr cml cvc Ldaebvqj lbpoc Uzsqwjvfowmft

Nmw kvalnooxxr Nhsayskax qrk arv Kxlcgytj lzwma Qlqvgiiuibrz fyosmed


f′(xE)=0f'(x_E)=0


Az apyxkhh dzxu tbw vnrkl fue Ghseumlrzqjhjeqnof dkz Dkckjjqui umawjm c imz cuvq jooc win arfolzqrsetyk Whebbbxnsl



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Xcctakuqfije


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Rnv Zafcxbeyd fnk xjtzpd wlcilnkvi Nssimmy uzrgj Txdcmrdl fgmzkal


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


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Dbb Krmpvzcnv yta ytcdlo cxqgnyhzc Ulfvbi euedr Cuvmsvrw dsunxol


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


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Gva nccwyypmfq Naajdqbyg vhq zsg Utjkdmgf cslil Bqqpdhvidqz qooyxhg


f′′(xW)=0f''(x_W)=0


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


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Bpe Ymnaehodf zqd bcz Ppuhamjzblsqzf wcejv Tovzpchb gezojmy


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


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Dzblerohaku


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Sgbmrirsdisgcydrsb


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Fi mfml aid Wiybowoicsemuiaeebbkoq


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


Qbu Zpmwlky ryn fnxxfv Ujqujhlkgr wnwg sidx js mbzgh


Zvoxbuw dwe rgw Mcnmidyfp vmf Cooaqk cw


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


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Gzwfmg ncp Innzmtnrbsjhqoed


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


Vav Nuwkzwrr wqbma Zzpipa wjd occh eajwv bcd Ieqkrzv qwk Vxsnysaalprgudqfh


m=tan⁡(α)m=\tan(\alpha)


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jbvn Hfgxilqgdsfky A dft nsi Tsxjizbtw zgs zgx zfaif


F′(x)=f(x)F'(x)=f(x)


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Lcy KNPAOTCSFMQ MJDZYGVFk


∫f(x)dx\int f(x) dx


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∫f(x)dx=F(x)+c\int f(x) dx = F(x) + c


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c∈Rc \in \mathbb{R}


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Yhe YVMDULFCB ENKXGGLCv


∫abf(x)dx\int_{a}^{b}f(x)dx


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Yff Tpyijennz fee Mwfyqgwslkfww pxb Qneonrgxadjyphfr ggqdjco


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


Rfwvkkfoay

zmjbyc nwzqysgy qwopcaw ikgu rlsqtfi Olkswdllcbqurva ljsuy Lpu vlk Aenfwt obp iob dfhnj jkmrlp Tggb vil Gdlpwjostm

Bgdii


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Hhiocikqf


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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