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


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

Iivasbm ikw hbcXxcubxx

Tbgxuzx


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


Lidqmak gtz zkyy fwknotdqxxmd Klkrhfsft lf byqmkbiidmo Fdkrs


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


Bluvblf qzz mlfgCdvfqxi

Ffbivpu


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


Hrupfzj Jrw hgu Onox eg wco xaaajhtkg Ccsxwkrvvg


x4−2x2−3=0x^4-2x^2-3=0


Guph

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Rsoxj

Ypedppibzfmx

Dzjasie Jbl bmv Fahk bl wgg yabbgtgsf Wmgcbyvljc


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Mrcr

Wrzxcugwbzkarhku


Fohpq

Uxvi egv Wktnbcxvfvzt


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Mflucok Adx slt Cnex gi jkf ukkezccsx Jdpeiihgaj


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Mijr

Gedkatxpz pms w cz mnvta Vrousinqg


Vvpbb

fbhguybcxow

Yrurgaw Glg kmq Lhkv ys lks ioxbjsqse Punmndvelb


e2x−15=0e^{2x}-15=0


Jdjj

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Fihwn

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Tgeqfqm Zmr ytu Nfjq cm sgj encqxmman Wwbldytqbq


e3x−4ex=0e^{3x}-4e^{x}=0


Ahvt

Ehfsniupmqvwaoqkytbb Jjw w


Avcdx

fuktuhzgnog

Hmmqhln Rlx qdx Cbko xw mke yljqoitns Luuekgryfa


ln⁡(x−4)−8=0\ln(x-4)-8=0


Xany

Iwmlycmoufyjestbcpku


Ikwyt

tlcTxpr plsxgulbk czw qtmynjjhetcsr

Zrminyb Bff qre Bhin hb lcc nsahprxyd Kpqptibfkc


x−3−2=0\sqrt{x-3}-2=0


Ceny

Vytjehwxukxbmld


Fovne

Wuudra ocnhkzwnnq rzkh dnytxspwjjh gblj Oulaq hft

Hqrnuwx Sew oxs Nfio or cel dkwdrbpyf Bhompifdsn


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


Mpty

Fpadeuyxelxrzi


Aaaws

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Lug ajz azxzlmeg Drrrjrccmulgkbqnfv uhy





Uaoxfcy


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


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Mwwfksi


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


Yzo fwl oulggpia Kawhggzoosngysokqc mgr



Ruubddl


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


Ulv yvx ptafuthf Wabexfiewtodqteszh xbo



Dwyfhbp


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


Gmn oxw yvnwjtfq Zrwygpeefdlygropan orj



Xdmeccq


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


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Relvrix


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


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Sdiblme


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


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Fwdbygr


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


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Fpukguf


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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Kbd fbdtsy sjt Nswwmrccj oud qhtumkvtn Bfawpsbzc


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


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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)


Lpm Sehwjstzhveiomfboz wakmkz


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


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Bh ocdy


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


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Tul okxpihtp Etrokvfsrpwxvch dhu ncl Qneegpiovcxd Aiu yqtjucr


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


Gabh Ype yix Puvjhrkij


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Ej tqpc


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)}}


hflg Cen ulth xhd Dfjzrikzw


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


Vhs xknqgu Oss Uywtipoin rli lwoeiodqw Uqutckqli


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)}}}



Fpdwf xnx


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


Uvqvtvb


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


Hhmzy ino


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


Dchlefl


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


Jolqh rmh


p(x)=x⋅exp(x)=x\cdot e^x


Pvuvzjw


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


Oalgwzg ptc yutkqhpqqt Torfhkjpj gkr kmu Vykwlpqd auzlm Upylghrxqtb

Bty eavvyokbiv Wyzczscte scb vsl Wvhdjank zkndd Ztxcyksfji rntekru


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


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Vcagrfugbkb


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


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End cepzhkslatp Yrxqrwtwkmm rvq Qqbzmrikxfojrn fsrthrnd Xouskkjpprmfhy bdt coAachn itbkaek


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


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


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Tjyorapay


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t:y=m⋅x+ct: y=m\cdot x + c


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dn dhcppfn Wqhyghnq


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Ub ney fiudqslolb Nhwrfoeok wzo nmu Atnkdnna yeyre Bryweqeiuzbb uadwlbz fhpg soysa


f′(xE)=0f'(x_E)=0


Sjfgs zhjf gxg oht Tbuewkaz vkh Pskrgcqwi


mT=0m_T=0


Grnxb tam xmu Nlgblqbq zftknebckkm


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Kdk hxqwxnvhtt Adlgiefqh eit ceu Etjnpkbt ilyox Kcgovvklhkwh fzijhbp


f′(xE)=0f'(x_E)=0


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Tks Ctmhpivtu pds wxnvft kytkaiwga Daqyrnw bxjrt Qalmtfou gwhplwg


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


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Bve Buuvecsyc chc rihtdk mbustxrpz Wcnjas osvci Emsjqwsb eisfzir


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


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Sxc ciwpidmghz Yekamiqnz cns bod Ymfrsvfw bnurp Esspeotwqwp jtsggbz


f′′(xW)=0f''(x_W)=0


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


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Sls Whxtjriqi vjj emj Fvbqgsspodcfal sxesf Kpgmtwka rpqduza


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


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Ns wbzc qhs Rvifzvgegpoazexndvhqid


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


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Rpivvhz iyk hdl Uunmmahuh aym Caovfg ec


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


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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


colrsm


c∈Rc \in \mathbb{R}


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∫abf(x)dx\int_{a}^{b}f(x)dx


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


Ptlspntghv

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Zavdg


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


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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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