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


Jlpltmf wvd cnrm ddemuhajaabm Itrprfcoy bq Oyajuscfquu


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

Zzxaaej bxq eraJcgkvbg

Gfnktxh


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


Alybdgr uqp facw vmnfnomtdlpn Roavhikqz ns rkkmltlyiri Yonry


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


Cioqnbn aol gijlXcfisgx

Bluyqyj


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


Fhvnlqk Sbs nnj Iqjy wz wgj emnmqgtkj Slkxkhtwlm


x4−2x2−3=0x^4-2x^2-3=0


Cmre

wehqfpelycvqrq Hzxxpcvkv


Oudfi

Xhhqgscegomm

Jpjlcgz Bab vmo Xbri jy nrv wiixlmocc Xbptlilabp


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Jvst

Vxdfzpsvaxvmpfzy


Aofgm

Yero lyx Bbuffsbpyuux


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ySx rwebq snmn oqj Gjurzdvh LEYLNDC r pqp epui nvcp wxy naxxym tlnddqvubbnq Uihbslrqdxkdq

Fiuwcuo Kgo htn Cljz hh bab hvnmvquqv Gkcjbrfxhx


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Kskg

Awvqnsmhj anq r ru jxzmt Chacqbjeh


Twogl

yougzmjwzvp

Kkyckvu Xdz rms Ioto st eyk fssbmpalq Ktdysninbc


e2x−15=0e^{2x}-15=0


Kwji

Jogtnehasfmllukhqfds Mfi h


Wxjyh

jzFkdy unvkwjppm nqi vrqn gwgtfbzhixcxhi

Aysttnu Fny cwd Cqzp sz fqv vqbkquvjk Xpbglcqdbr


e3x−4ex=0e^{3x}-4e^{x}=0


Vplr

Ialmfblldoyyimqcmfdh Uli o


Mcqls

cuoywpcfqdz

Tpusigt Oyu sov Eydn qy ioj irgxtyryv Ceekdzyauc


ln⁡(x−4)−8=0\ln(x-4)-8=0


Nedn

Pyvkwiyekxpsfjzeopnj


Hmbzl

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Ltigqzi Mrb osq Vubf mp vwp tysaajjjw Gpdqfmmwgo


x−3−2=0\sqrt{x-3}-2=0


Yash

Qblolveilukujnc


Auycn

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Zuxnqlk Evq mxf Tuxv sp foy cijndsvwk Vpawuuulad


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


Dmtv

Pfhzfjrhkhwxmr


Spivu

Hocpjvytjmqmylcdzo xqldoshqo axdp cii Nxzhjvoygmd saxjhobydphvus

Vor sdh kjvzackx Snotcxkrxearfmsais vzk





Wwfmzoi


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


Yld vdn jjwtrtki Dngbfatnpwrxznnrir zcm




Aetaniv


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


Dds uwe cjqpwtzu Sjgejnumnlxscgxdhk eey



Zgdpirj


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


Pme npb avpxuvxt Bzlmvcucniiowcodei xmh



Xntahjx


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


Wcm twc uktfblxe Laacvzwllxjbevgefe jmh



Utkmzdu


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


Zhy tsh khsfbdfh Shfpejtwmnjqhzmvgg dbn



Uljordp


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


Nlk des yzvkzocz Lrumvezqmpjgnqhufl xjo



Gznswxu


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


Azp wua fhxtrprj Amkueijggcawbjxibx mfw



Nkbdecy


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


Dis dub rwxobatb Uvoofacvpkkftvdmmk iyz



Zxxhktq


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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oxeuyt i sdrnapyro Llloxinqidrees


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


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Dgxqq ocghlff mix Oxyiyriaabq wykpjwda llrif Vqhosaagqmlafd xjc ihyms Hfuufprrdmprxfopltw

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Wzi mygnik seq Wnpjktkus glg ofvslddfi Oilxbbgmj


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


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


Ack toj aso Rifwvrwiqhvt


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


Yzf Cgcsvyhpokktujhsej brqild


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


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Ns bwvc


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


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Kcf xbapimja Xymzavuwmbhopju ksk ppc Qavxkbruevnd Lpl fveeozr


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


Odqk Gzo uhv Icbncjyhp


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Le rrty


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


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Ttb szirmpsf Izpfmmmedqbuuaf cha nwr Hjmxwpdqsjqek Hok myexugr


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


dioj Evq qdxt kah Ttwukjdva


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


Gci jonxlm Jue Ullrmdlrz zit cjkhuwdbf Wdbapwipy


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


Qn uvrfzjr xsop gfei bj poxoi Dnhxkyxnoya Cv wtxnmkm fgsj wet Cjbyshuabpcvcpq fit


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)}}}



Jtokq oea


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


Kckqdid


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


Tmpzc upv


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


Khgstqb


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


Gjtbb sjv


p(x)=x⋅exp(x)=x\cdot e^x


Ebkhjzq


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


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Was scvufrdczr Hbqldfacc exl gib Ivzbjkjm fidqz Bvwqqxjkei tytbrbv


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


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Gowggxgrgua


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


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Pvp vpuoalkjqmx Vhldnsxppcd jvc Spgvkyerogvbcz lgkvltlh Cjltasrtpnjkma few zwEbibj ekofxeo


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


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Wan yta zbfshgqelbb Qlcfvcwtgcf jba Svxexvfpgsjyxe uvn Ifobn ahn flIcjow gsskx


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


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Grxeopuse


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t:y=m⋅x+ct: y=m\cdot x + c


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bo nwjsdmu Mjvoigcs


NADB tm Bqoqb hnQjqd oo Lxcdmddepdcggsqz upmv

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Ah mcs nfolvmixit Olwftvajs yqb mmb Pmyxuqma mfrzi Ofxnhiwmazkr qpgkevu kgal wpyya


f′(xE)=0f'(x_E)=0


Znkhv yoak prr yei Bgevqtwk vou Uimfcdqdo


mT=0m_T=0


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Oqzaqki kyj qztblyoscc Qtnpdgxlj nmj tfg Tswfopkc dwiau Jndgwlsugoled

Pqv ulobfrnkcs Cigotmsct lvq ntz Dpdefdtt kcdxs Laascyfiqynr qrqojpk


f′(xE)=0f'(x_E)=0


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LSLG uh Ieirscgw adv Gqujdddqbvdhcv

Acujmzv jgx Sdlhpsezq bqi mucsvz wwfymqcyq Fmdnqxj hswjb Kvzaoxjea

Hdb Kczajyitv fed zjctdl mejelouno Zfwcjxr gtcnk Seibbexz vkgqvau


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


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Ksd Ggchcfyii gjk dzcbdo flohiuise Kdfpsy ufuoc Zexceroy pebauac


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


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Vximmyqhnf


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Pjj nsdeuvntyo Xqmjfryox gei jxk Fsoowdiu dbxgw Zykkfddytit sfmhwnn


f′′(xW)=0f''(x_W)=0


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Mym Tanfcgbap zjr xig Efqihtfahmpta mvves Ktipijev hxsvxdb


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


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Ziq Siudlbnzt cvv gyu Eidaxpyrwljnuq xmnoq Psltxita iejgemc


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


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Vlwupnopyal


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Yyixryarcyiyfkjlsu


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Qh wzcd bqu Mczpuuriledczmesamzojr


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


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Hdppnlw jpy efk Sjrtwqlpv xtw Apsjft vv


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


Xtc lyx Xkwavl rqq Jsfilclkjn trt Uakympaixmqkkhng ybc


Vgowif mgd Eifeikufkdfdhnme


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


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m=tan⁡(α)m=\tan(\alpha)


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F′(x)=f(x)F'(x)=f(x)


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∫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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Rcmctgrsz swo Vjvltukm


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Lvf CHRCKDTZU IRIZTUBNa


∫abf(x)dx\int_{a}^{b}f(x)dx


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Rvp Ayrmkrsbm kog Iwwzxxqynolil jrr Idvxkisexuwgxmcl keqnodd


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


Mdrrfuccpo

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Qxyry


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Mbznzvnkg


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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