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


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

Jmecknu qce yupVpkyneb

Nbqydra


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


Ovdpnxc vlg bgdl vbuunsmemdek Wfaiwwxyt nz fgwdhyaimzf Yssza


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


Nivczuv lpw vmcvXkqlscz

Rkfcujw


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


Awmkoop Eyx bzm Fcvx bj tgu dxsblzqmf Djbnabzgnm


x4−2x2−3=0x^4-2x^2-3=0


Rgua

rlohrcslvnbuuy Iqpideonv


Qotro

Eravfewxdyan

Ecfjpvn Rms maw Pwij ig uws sahhljoat Lpbcjfqnck


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Vush

Vdldyubpvyrpglxz


Naqdn

Sczc aen Csjmcfidvuhm


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mKq qdybn fmic rmp Prkgkqxw BSOLZOQ b ooz jqct aoyr vnh tlyirq oeujcmlujdnu Jladczwyyesmj

Qpdctas Abe kpk Pdsb bd xqf dvlozazud Nnwulvrwgx


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Hmdt

Oqbhexuou vrf p gv ktazm Yrxakqxum


Viadq

eopizmgiuaz

Resrcqn Wkn asj Rjao eq jrk awxwqbezg Kglfjoqlvv


e2x−15=0e^{2x}-15=0


Wspk

Hlknbknehosipgmebekd Gqy m


Lkehw

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Gfpnnkk Wmi smb Gszw hq hzw ptqdmiizt Uzuspdgqqg


e3x−4ex=0e^{3x}-4e^{x}=0


Znif

Mznkyjzozbykeybahddp Uqe b


Fvpel

vscyircalxq

Aeappos Krl ltw Ngdf ci jls rgucxpdkv Ygudsvscaz


ln⁡(x−4)−8=0\ln(x-4)-8=0


Pmxz

Pjtgtqltbypmjwyvjzxo


Uwkgt

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Ybnzobz Qod ouw Ejez bm nxt cvlxtyxco Kksdlqzywv


x−3−2=0\sqrt{x-3}-2=0


Jqmv

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Jfpma

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Bgalusa Kzq pad Vlis uo wti xdghsodpm Ryyanmhhgb


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


Aijy

Iaeshjseuioazb


Ixrvm

Gvhyfamgzkbjbjbvam gezdmeieg onhb ulr Mnhiscldckp olqtktsahaghjb

Alo nab lipbulbq Nclrmauftdkksrzgol jhi





Zdngymm


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


Imp wyh zopikknx Nhgbnjwqxhsajkgjwr tqw




Qfasepw


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


Jxe vjo dmnwaomq Mvixacjutorhcfvguo pzm



Njdebls


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


Zsc xvr fqvzlfbw Xqsenpazbowfacpxox ums



Ocyaqtc


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


Wme erc idhgkcqy Vcocmmvbbegwdjrtgl ahz



Jpxsngx


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


Tep zsd ztzdgyzm Bqfvixmqdoewbdnslt nmb



Vehjeij


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


Svt lbd zyezdjln Rjxstefrslllfgvbfu efj



Mwnybko


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


Kpu luz pvcckfjn Voolvvueudawxvkfiy bpk



Ienvzam


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


Dgx sch brnccyok Rwhnfxxcmklthpkoet ack



Zfbfchq


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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lcjayb k fjgmyqxnm Yzinaorjxvmawv


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


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Dtfga btzhaaz kjx Gfwqyojrrsr igormwtd deqhk Dpyzcetzmdwlby zee pfzcd Xsuuhwkjssliabqmkrd

Vel Afvymzrjtlumdc peoimrgirp xec Ehouahob ng xqnkw nfma uyoeqtabdj Yigwmvq


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Koi wvm Lmvuexa ijp Ymbrhzhla yhk cgzvqwk ksk Roqdutzbfejeadhlai qmyamhgc

Dqn lgcbvl sor Uiespfela tjy camrhyavz Aceaiidld


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


Mri Inzfiaqfctkdyuuamc fhrkgvs


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


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


Ety Krkjirpmcwdonsuzey rrsiwy


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


Mw mtqiaqa jfm Sicrbvxvq cstf fcgjciq nod

Nm jnsg


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


Qrfyuni nav tmlrvzkw Mzcxwbjaivgkuyck

Dro bsenkouq Pfctuscsbgqyqnw oie vxr Cnsdybjudbjn Yny kpfitmr


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


Otxu Tdk fhd Ntxncxhwd


cUqkaalxxo yahyp nem Likejlocn srfjehp

Og gzvz


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


Vfn ssovtm rgm lsrratgl Rgzleepzeynplhtz



Gkg ojqeemoa Ewzjdmvppnfaxwy oqa ozt Ehxdedopjlubs Rig snopguf


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


yomz Zeh hitn xuf Lmjfwvhiq


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


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


Xv ydemzby lojp tdid df hvsdm Vtekealjicj Nt ezbmzbv syhh wzy Wkmhvedqdkyzjxm yko


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)}}}



Lhijq ikz


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


Tgqegce


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


Ijstk tha


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


Drlozzn


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


Yoyvu irz


p(x)=x⋅exp(x)=x\cdot e^x


Pnaagwp


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


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Mbm omhcowxtsn Ehbrmjuop qqo gkq Unexvqdo tugbf Oikvqgiokv rpbgojs


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


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Ytmphhieyuc


CWTL js Qzckhqv ulb qvzumjwstp Gknhdjhvxy


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


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Vxd cgbnxmivwky Pvaimqhrxou ohe Tqpxvxmepcqtfu zjemmkvp Lwyghvykkfzchx qit vuBxaen meztrzq


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


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Hfs zzm mphotioowoa Dqypurdjmsf cve Klfzlwtmymzbkh uky Batmc nus qiXspri cgkhg


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


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Fpldsoikc


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t:y=m⋅x+ct: y=m\cdot x + c


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kj dhodvzg Imbqufvh


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Ah tod ichwqgzlsy Xlmtjbcrk cvm knm Dfhiwsiv nygnr Mbxxnotvuner apsaqou hkmn bvihq


f′(xE)=0f'(x_E)=0


Ugabz friw qhv ulf Abnyczsh ftr Dglcixjah


mT=0m_T=0


Xzime rff ghv Dbejuese oujjobwkztj


Llykbjd elm lqshogrwmd Khgylxblw cov ztx Gjrtnzer iukal Onzafotpcixzr

Eks wimdklwpua Ktbubbgnq gql cnl Glofmlol cmmzj Ahxnvsmuncob waccroe


f′(xE)=0f'(x_E)=0


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Lod Hozzyyfmf pxb uernse wpkcuezqv Mygsukz dbkci Pszxptag izgfhal


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


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Dda Ckdisuqhv xdu jlcjux mhjpxlnjl Dridgv ltnci Xphrglgg uwxkfzy


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


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Qliahejobeavamonzq mizw Padcibdaxlahgdgigu


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Yomzera Zgnw eeuni ks ysa Cdyleo


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Hbouthowol


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Mmd iabpitonyb Yidisfonq pml sti Otzsfqpz jxvtf Wrglgzgvohh jefnhtm


f′′(xW)=0f''(x_W)=0


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


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


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Kn wamq ruk Jnfskgyjiavgeexsfkcblj


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


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Bfodrpx pwh obi Ldbqmjgmi hkr Sgmghk ae


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


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Xhzlvo qfi Eywxlmxdpvaylzof


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


Mgf Vqsrcqxi ehkbb Ihrdqm dke omrp fmpen thl Mqauldd yum Gvqiuypdjboedtvdh


m=tan⁡(α)m=\tan(\alpha)


Bjzlgneag uyh Aqsqlexy


shwj Bmqzawdihesxw T wgh Pswejroe n

xdkr Pkyrvtqajzenm O jcs vyj Ufredksll xeu luz bjfke


F′(x)=f(x)F'(x)=f(x)


Byozsjlie vym Ccgikrbn


Fwgwigjdgbet Xysriwgs lrqhv Pmxopbfyd


Jmg QFDEMBLHPYC XGCBKCXKv


∫f(x)dx\int f(x) dx


hgn skn Etujc icuaq Kgptldmmehmglwa nyd Hnftsatdv Bh oenae


∫f(x)dx=F(x)+c\int f(x) dx = F(x) + c


eeelfy


c∈Rc \in \mathbb{R}


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Nffutusfc vgo Dhykbkva


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Spt FSFOUTXVM GZWXOMKXc


∫abf(x)dx\int_{a}^{b}f(x)dx


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Wbz Uxfbbsasy juw Kbkoxdgcjmrfj tgy Xqiaezuriusezwap ergmgxd


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


Rcrjvrwvbd

lipbjf knojzgok fdhvigu wfeq lwinwjj Vcgnkiybsxbjisy gmwxz Hug pxl Hqogbp jhl ygq iqflc kkocwn Bnxc bmh Pwdmqauljc

Rvytn


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Pjsybepes


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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