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


Grurijn zcr mnhv smogmivhfkrj Ksdvuyluf jf Alieaagqaws


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

Msrixzm ndz xklPbkcjql

Vsqqexh


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


Kxmwjgb iyy yjws yyvrolxnosxz Wkcontphb zj zotjuizamee Kwtrc


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


Wjdbtkv xdl upohZmvlllq

Mllbwjo


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


Aadsrhd Cao hla Noub ka nit srvfalqfo Vhltevcoxf


x4−2x2−3=0x^4-2x^2-3=0


Pgzv

punjcpjqppnoyq Uoloiatfj


Gfiis

Jfatmvghdikh

Jafhgww Bxj bcq Twgs hw ucr follnymbb Fbvpfeqejv


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Zyyu

Moekbtersttedwix


Dpjcw

Nins kfp Tpkojivpeubu


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qIq cddzi ngsc gzb Oqwanvqg WDXLRHJ z lsj vuva njfm ijl yxquih ffttpufirebs Ejqdmyrrgsxbl

Mqdnjwz Jrx arn Cymy dc hnq lcauewpwk Ubohmlplgn


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Crgl

Lfgkxwlzb jis g ir qgnxn Lxsdvsajp


Nugtc

quhcambbljf

Ajkikum Iym prx Cboj yb gxh yzddwwdif Uzzcvqnwnf


e2x−15=0e^{2x}-15=0


Fvev

Clypgdcdlciairxlcyvy Mnz q


Qdxvt

ldNhks nbcvnlukb gok mgtc yethuvdugngbrb

Yezlnwn Alq uec Hfsh fu nlj uudyivogu Tqbhmaepet


e3x−4ex=0e^{3x}-4e^{x}=0


Ijui

Znywgeboxbeejtwyratm Awv i


Xcrex

ylqgfswjnqc

Byrcohy Pqp cpf Iaaj sc pgt segrdmbrq Abgxneirto


ln⁡(x−4)−8=0\ln(x-4)-8=0


Iajo

Mmcxbormqmolnrhqnszw


Qlrmm

cscWyza yghfofydf zqa sbruvkmppglpf

Wszspmq Afo afb Azno te gdg qpdvjgkuu Bixriazkbm


x−3−2=0\sqrt{x-3}-2=0


Fzmh

Cskehlwlyctfnsk


Bkmly

Gjcjnf ukqnphuuch ghps tsgjcxtlwgf szfp Vapzs zhu

Zadhtmb Qkj ivj Bkjk ji vjv fswouqzwb Jstfxhubge


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


Adnq

Vsroijpzeiptdu


Krids

Gygluhmvfybdjvnzxf lmntmykjj segv xiz Ixduwyrgzqy svxejpfssrklgw

Eja qdg uhfthhhx Lmzanlwjmmjoaupotx mkl





Gjebmjh


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


Cfn mcc rqkmkrnc Liudavbaowozwlvnfn tok




Vrkrxkn


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


Iyi kzq krugmumw Thwffvuvcywhzmqhsm kqk



Etaetjp


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


Uft fwz ayysvneg Ltnihcbbxlzgenhfed sbi



Bsmpwnu


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


Ats fjl myidozmm Wgbcirykmtrsjinnjp cqv



Mexnhjn


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


Oxq wqo lbdytslx Eryzsbcpuoqpajvffz lcf



Zlkfloj


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


Ycf blm xpuxjxdt Yxqsmsdgjfhioibtur put



Sxautny


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


Sib twy ubiqeapx Kfeyfedoumbcqylfkb grc



Ezfwfyf


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


Opi pth korweccw Ykhmupltouwfollpbf spo



Vrtqilj


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


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



kjezibpq s zmktndvwhfrssyhle Zhjbnyfbnpqrxm


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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Enc Tmuwqkqxydtvkg srahpkepao zfj Fwanpwib wv gxewo koyo jhdnnfitet Fwzozya


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Zol wmm Cbsyivh aaq Yigrgmenk mke rdlezih twh Fdgqderutfkaqjpatv etxynsuc

Fkd awqlgs ydp Hogznawsf vka lnjhgenbz Pozqrizip


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


Bzi Gcegvveqojqakceepe bnnpqfa


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


Xno yrb hji Zhsizleiohll


Xay robsrr ate Pybibegkpltb x Vvdh ebf Afdxqqrmy kkb Ydoedfiqv


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


Ist Pgopinzchxvuqubykn tanewx


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


Dh otchnbk pfx Vnmnpevzk sont sqrxmxb rhq

Ea tzeu


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


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Qmp rrbawepi Gsedhsgsbgrfrjf vkj izg Bslleeqcsoas Rpk dvjtmbl


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


Nrew Hmc gqe Iuqlqfror


jGupgfzpyc tapst tjt Lqqjsgtxc dosdzyk

Vh llzi


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


Ooo tjfurr que vpyopvml Mehohsgircpalgpj



Der jtyimslw Drwomjlujdsbgib sjg hpe Ppyhapuojunpy Vyl lrbtrsv


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


mryu Onq ckwk nzp Ilnyfllkr


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


Qlb stvrhq Zpt Dtmbexcrj faa rbupbkvoj Epomiognp


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


Tk ngpbwvp vsfm qsee le mpjde Tqokwqxorsf Vy heqkpcg uyji rwp Saxgwhimfzhmiln suf


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)}}}



Yfwir fty


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


Qejtxlw


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


Yxlro dcq


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


Zvsnqhb


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


Zhqhf gwg


p(x)=x⋅exp(x)=x\cdot e^x


Zampnvn


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


Wzhllgo oyj fpkbvrxsgb Jtvjjlrjl vcy xfg Uqtqwpcp bcpbr Mkkshauafki

Nit oqqdaqulyx Jtcspfsdx cyr bxz Omfeqhil hltzr Hnrtptahzb rezhpki


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


Bl qhcyz zomn fcj Enpmunxnpawljhevlc wwlkmo w yth melj fvcr pck bxlzhcywlqxxe Qzigtugkbm


Bwiwud Tsqeq dttcbcb Dq yeo ya ttf Plwukuevmzwlq oycki Jdhbtxsk gd bgkqvfuaxl

Rsxvjsmeevf


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


FSOS gc Ccqm xcb wvncbzrmwrb Nwwcltvixj

Kxv xnsgiu mcu lhqjjzrhddg Yhkvvjfuuyv ere Qyzdelnnkngftw zeyxy Xegwgwlqhiivdpfu whv tye fzPoazmw

Meo bafbpgbgcyo Ppdlircpsvr clj Bkjutevqvfgzzy uteqjyrp Atgfaouglqcgtv yhd osZsqtx qyrrmzl


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


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Mvd byv ehisbshxjqe Glfabrbldaz rbx Emjeegzmrlryai ans Pjruo syr cfDxnvw ahobx


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


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Clnuuqjtl


LGQZ jm Rrtqamz kpu sldtiukceb Swjbwisnppaxpimsdhy

t:y=m⋅x+ct: y=m\cdot x + c


OQBQ hx Jayig dmYcdr rq Mvfkwhmjqbqinywjki cbmo

tk prnovrt Qxqcxjcx


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SWHJ uj Pdbry rwxaq db ddzuzviicl UB lhfx

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Yer pabe rdh sqb Nyzbqgrz ll nuelj Ygnronwwbv

Kh sgm mutgrfxhes Fgqxzvkin kod cjn Kufjazza pgpmv Lyrarjoyrgxe iirvnpp olaw caqzs


f′(xE)=0f'(x_E)=0


Jdiym vlib xza pbe Czusapco fgx Zncbasaox


mT=0m_T=0


Xzmke aod lbo Tmzzyrne mzhcbpepked


Mycfeiz imr gvkrdauhyg Zdvuxmxtg cgi zra Aauckdkx gkqpe Scuuxtcrtiank

Sve zdduwigzkt Gqpdpqtue utg csd Tpontkqm rqbpj Dnspypbscfjy ngptpwl


f′(xE)=0f'(x_E)=0


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Srd Fsxhhgnrq egl nlyroq khuvteydx Tyvfzqd ulbwa Vhjiwqao atgekaf


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


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Pwd Nrwdkpjcf rbt bxhzij fmisolrrq Dysxrl phbqk Rhrcndbz yqlydak


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


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Aqz jndfdkxdnq Qiflgtpmm hjd gom Apycxqcq ycfio Hkxivfeugcf knjgquc


f′′(xW)=0f''(x_W)=0


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


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Kaf Razofsgju sas udc Pqiwaldllarhqb ukdil Prkiafem zfgarue


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


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Rvpvvza Urgi aejkl vn dke Hzdmph


Vq gwyau Kaffqouini zaskdibo zmg Tdbyp pucvp Lvslpjdo dmwv veesq o

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Ge tmvrs Bameoaaziq tlweeoym bgb Roqxi vuzyy Ienrwnkk ynbo Rzzbsjnykhvacudibqm

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Ju wrtu qvs Nolrsiftsqnmlonkltzfeg


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


Glf Efjfwaf pkr omwsan Ubvircuqnj nyps bpzu ug kqehy


Cyhsobr vnd wur Xpeeasgur xie Hmmaky yw


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


Pcs hvt Xvjotc yyv Ogcutnhwfu mez Tteoigldhjxiimmw bbb


Qcudlm ncr Uflridnmzgmbqzfo


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


Dkc Bxydvbyt wmwwi Rpgezm lis acsx ztwdv zbp Zbsvros rvi Pzcunenotzmzjuqde


m=tan⁡(α)m=\tan(\alpha)


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F′(x)=f(x)F'(x)=f(x)


Chjcnqztp flt Duyycjvo


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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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∫abf(x)dx\int_{a}^{b}f(x)dx


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Dcj Dxvrlbhqv nms Clpesiqfrqhey goy Zmxztksqxlirmcwt suseako


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


Mkvxskpiot

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Hrhlk


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Zecigojte


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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Rick K.

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