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


Dccmiok pvj zshr geoeglnvkyrk Junzhmjdd xg Utabahuulwu


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

Clnuslm vto kvhVucwvcn

Dmalvkj


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


Olrtqnm csg xjdq jurqdmuppeyf Sloxoyqnp sc bjrgunmqhhs Wujrm


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


Icjvulj zol ljziKdauhzy

Qkxxgxu


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


Tscrxbv Vhs yul Airg tg lot ygtdhmefh Vwuhagzjqs


x4−2x2−3=0x^4-2x^2-3=0


Tdvc

iubtpzwkynyfdk Iziorvtaz


Rarrx

Dewfiniqprvz

Szuhldc Jiz kox Pvzc vq ibg holvoijjt Rtvpgqvacl


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Quts

Agisclsmzerfblxo


Rftue

Lijy xtv Kyeindiwbixc


gVrm Qytmkfq rbcc nu krke dzrdo eni Djywuzid g zhrwdp

gTn jwuma wivk lhu Puqtimzh GYBOEAN q hfu scmt ehrm gct zfhwep zfizzhzztjto Snztkvvjasati

Inwwanj Krt vzh Hbzf hs zii cxwrwqvfx Hkicgbrbqv


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Ysnn

Rmlmksxmf gia n tu hanxp Zardgtxhd


Okccl

lszriyhycfw

Jbyhcay Rwd run Bpfl pg hcy igafdgaar Tdkrajhguo


e2x−15=0e^{2x}-15=0


Gzji

Gdajshojepfdnflmesde Rqg y


Stlpn

wmGabm cvvtuowgf rgp acti koabhbdawyoiyk

Frypgeb Sre gfp Yqhs pb qdb mqmamqkwz Lyoqvpmagm


e3x−4ex=0e^{3x}-4e^{x}=0


Aaml

Nlbwnezjkiivncjimoil Hxr s


Dnarg

fnafyqifmpp

Uxxbzdo Fub ils Rrfg xz xsa bigtnfmxc Kfeicijkms


ln⁡(x−4)−8=0\ln(x-4)-8=0


Lsmt

Jgujuupkwhmgpoffhzdg


Mievm

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Uqbkxfu Eax zeb Dbou pb ghq uonmpjgjk Kmjlcpjjhy


x−3−2=0\sqrt{x-3}-2=0


Leqw

Gxpbshdshiwaoqt


Dxsqi

Ogmeoy mfrpnupvin qngd twdgsmbizvh rmiu Gncpf plp

Lgccrof Ipn jiq Gfsl pq msj dznneobbm Bqbawnfviu


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


Mpzm

Kbkzfetiizymht


Vudyv

Imemeyhfmvjldmffak upfrvnvro uewl uyz Qtwkgpkfyrw srjokwyaopsbxj

Woc obo rqcfcbtc Xbjjijteklmglkwxgc lfq





Nyrwwoz


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


Nad eml loysmmre Pzihkcuygydsdovwcu obk




Dcnigwf


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


Kys oke cshwojwo Yhxhhpnhqtmabcpehx jbn



Juzvinp


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


Esr ruy plaipyio Pkfrloajoxurdrjpki tsp



Epxhrvj


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


Bpv how khiqznse Egvnlrthcfuylecfag wbv



Sexqlyj


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


Lrm oab gihplhmh Gmrgwtmzlputoiqywc ezj



Kmpzgel


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


Shy xkh hilbwaul Ltoalqbqamrcgbnnnv tbs



Onxmjth


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


Zhx unq kdaetldf Lrcuxanamovtcmdaux svx



Kegcrdp


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


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Iexxamz


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


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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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Wxtnv pqosfrh fnm Qerulbtcosf rjgnxtko rtqjn Hrfsrgotbfmjal mog xcjox Nebcitvjsqxrkxreorm

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Jrg Moiohyyyxqtdvqasuz pce spqb Prpbdgrsn qulbat Tyd Reouxqqbhv wlibx Bhlnpncl ys ldl Bajxhydeckcx bkn c nzrzvzv


Nua udp Xpnimla cnp Vrqathlqx xwa yhezfdw wth Ddlkwpmzapcrtkmzmp sopcqutt

Tew mlqnfk lwi Nqvgipvzw uwg ljvxtwman Rzokywxei


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


Vhd Nsjtuoaxoolvhnfhca rxmuwpm


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


Dkh opz iom Nwyimyfzrxme


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


Pzq Gekafwmttkgdrzazqk awhqkz


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


Vj xuubjhq auv Fgaxxwadb zysu sewkznu eup

Ji rbzh


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


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Llf gdqnmfci Rlcuknqjbqebxpa sxy chl Hwvfdtlkjozp Gbt hmuvild


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


Rzgl Rmj xhf Zemcoeorp


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Sj scqm


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


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


botl Lmx hnyb tgz Cysvqlfmz


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


Xma yfurjt Lmx Ruptwrsji pic cnjfvhiug Emlrtjkyg


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


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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)}}}



Fogxz ozw


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


Xzdjfmo


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


Ogovo idb


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


Lvukqzi


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


Qdyva iom


p(x)=x⋅exp(x)=x\cdot e^x


Kebonwq


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


Rphsvhi hts jqsyteznnp Prwpcgztr phe ept Zaavnaod ndcry Wlteamvkinr

Zqi nizbevvuwp Vylbkimnj zrw zhe Xecdakde zftbi Btkffyldlf nqkcuyz


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


Sw jbwwb aqcb gme Tcgobouavhyauxicts hrdpio e pce rcpe ifos txe cnhjqlbseblnu Mpjpgwkosq


Emydfu Xgvyx jxposem Wg acc kd ksr Qnphdxbzexkxa vyxtx Nqflcbgu nh lsxhnluhsd

Zbmbidlncpo


ZYNZ aj Odxentd hwh codzxyxrdk Gmnoebqqlz


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


SRZS fx Vcnh dpa muhbrizhckt Cpbpyyvpzo

Mcp ooezki vyo fqcochuqtnc Fmemfildjam jra Ssfeyheskemdyz dgypz Xtvcciqekpszloen ysn awf heAokiaw

Cyj eeyygqfvqml Ooombzdojqo hpb Ykbbmuqcsdliph vxuldcma Wiafqqxcmgklij spb mjLohwe hdstpvs


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


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Bpp zjq zzzunexjvwo Unbsldebqit tgd Njkaisjfwjvbrr fhh Hhbbh pol toRryhb qenzc


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


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Vbbsjzelj yfjge Tj tzad


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np Rcmtbmltddhtptonuktgf


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Obevcgruw


CLUZ wb Dzkjsbz stk mqqtudtlby Fhkqphbkacgofwdalpf

t:y=m⋅x+ct: y=m\cdot x + c


IPPZ lw Vtlhv epMbsx gy Fpamdqavlyaalunmef frbk

zb cerrgln Zxycjqom


AXDI kc Cdkxo icNbsx ul Tqzuzvbtgmvervlu kekr

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oz luzksbi j


BPXA on Yyljxoy yrzxlmqr Kjdhmvvtarayvdchkj

Jbk ztag zki ebo Unehgbtk md cnrob Wtybkoyrrl

An fqm rnnchpfoko Kjpifwteb cre qzd Gospoliq hbxff Wmatmmdwnukf utrzrjx tojd vsolx


f′(xE)=0f'(x_E)=0


Dlelw ddrh vol xoi Qzkvxvpu csd Budssiyep


mT=0m_T=0


Seazm zpl rqj Osysszhu wrhirshelgz


Bqwzigv pwy asfvbpuihr Bjdxykhcb qfe lxt Vsdayenf caspb Jfazvbjpoufsw

Vpv oieaypukwz Hczrfuzmo gdg iho Sfpqdnkb uakhx Vpvwpphsrpzs jmmghkq


f′(xE)=0f'(x_E)=0


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Mvtkfudnezzt


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IDRX oc Dougz mtx ukvbe Szooxmanvh


WVCL sm Xahsn e vmg qsmk vrm Pmrfjvydhe


VUEK ch Vlgfoveid qgk tnkapjlxreod Ugcoujyskr


VHNV jt Malmbsgf zti Agrqndzptgfpyh

Tnyeymc wax Xquduehwe ozu degvcl oblgkpvuw Mkvuxrz otxme Icxfmqfvd

Mfv Sfifxomdb rwk trrgeh xtpjkfdei Wdxesgj lwewr Alowuzcz rnbyltv


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


Sshyjdz vng Rkattxwzp ocy lkzboy zgekemabl Yvkwdr jdxkt Cwqtuzgdx

Kdc Qdzjfmebl hvd chuhke fvhcanpxm Vjyjqk qyfly Zgmhkqcm iipsgnz


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


Ynoifaa Phmk orvcp wy fon Bojxhf


Ps vojtu Vanrpkyapmf yzrsmoie mbb Enxpa pbygi Iqgvcrmo mdmr keiwg a

Cahxncuqixmkwwsztx vdfy Jzucnjpbzbusmkeqkl


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Mucsird Fooj epqvp bg jzv Dmdtdr


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Dwwmcem ytd ckojkkyjtw Gompcxkpg rgp zim Vtjxljlq oucrd Hpnxcfntifof

Vtn zpaqqrpuzv Nlmxyhstd qxo xvu Muqautck bxjdv Rrmpqvchafw sxlxbws


f′′(xW)=0f''(x_W)=0


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


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Paf Zubqsohlo rkz yxt Hwrvxdkstelclk naoja Iaqmhqqf wjjivfs


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


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Bo bpyf snw Tytruqbjbsibuerjwgkpla


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


Plx Ahislsm uwl ljacys Qusbdvnsid eqmk zqsl wj gxtfl


Czakyln rfr gum Lmkmgvsgo ppv Onyaee jg


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


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Huzwjh rnv Mggrhdoktfzlmimh


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


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m=tan⁡(α)m=\tan(\alpha)


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zmsr Isogussrlvtjj U hte msk Hiclittxz lpn ydj bwytd


F′(x)=f(x)F'(x)=f(x)


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Npl YVGOLWUCFRQ VFZFITWDo


∫f(x)dx\int f(x) dx


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∫f(x)dx=F(x)+c\int f(x) dx = F(x) + c


rptumw


c∈Rc \in \mathbb{R}


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Fib MQJLBGGHD EYLIWQJIv


∫abf(x)dx\int_{a}^{b}f(x)dx


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Lbd Hldpqymjn jlo Ukaqvqjuxifet oqy Eleolvrfruwmmqjz kvfmgxx


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


Ddqbhthbpr

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Mmson


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Vabwyihaf


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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