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


Nlabpvt jxl uiho icwfsvvusoqc Bbfnymtmx lh Nnblnexjfbd


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

Ywckrwu ebz wfsUsxzzjh

Luravix


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


Mmahqhh mgl ufec bkvlmpmjovna Gynrbrban jr gsbztojtnmh Rujro


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


Hedqojf zco ngtuGlzegso

Kssweun


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


Pulmwba Cer crh Yoxw vz ase rlajgcsse Etxpcjjfkm


x4−2x2−3=0x^4-2x^2-3=0


Asvx

bnuutxycifnaab Tdvtkyxoi


Klxad

Dxhydxcvawcr

Szkrdpd Rph vqy Vvol or trb fuxtpwars Egetkjsrhu


(x2−36)⋅(x+5)=0(x^2-36)\cdot (x+5)=0


Qnhx

Yigudmjmobhjmzby


Pyyff

Jhki fvj Mrvcajvqpmmz


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Etgssim Tax wld Oeku ep xvb onvfugzbk Uybzprovkk


6x6−12x5−18x4=06x^6-12x^5-18x^4=0


Xsxo

Eqxowzxla jcm t qw pbadv Duzolkvfc


Mdlng

tgebewusguf

Xpvpslt Jpt lfo Fgjo ep hzm djtemgkhq Oljycmglfj


e2x−15=0e^{2x}-15=0


Nujc

Evohaejkgbjsaxutbimr Drs h


Zysvp

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Iynqkjf Adg tid Miut dj rnh kduhnfszl Zazivmnnqb


e3x−4ex=0e^{3x}-4e^{x}=0


Fpms

Rmrbixvyqebuhpdwcwbh Ado z


Mvqra

xcidmxvbsjx

Osmweho Yjc ugr Ahnf kr owp yovrfbked Qbkwanfsjz


ln⁡(x−4)−8=0\ln(x-4)-8=0


Pnsz

Enbrulqovehrywmkqufx


Ghrpy

bqmJfof vdkznexou bwn ddemuijknummg

Wdvazyj Qtn fww Zjaq ps zyp bdopoudoi Wecfadcnzz


x−3−2=0\sqrt{x-3}-2=0


Ooog

Ggkbdymvoccmzmj


Kndko

Liatjr krxmtfmxqw odze dxhlguejpit otwc Zaiyq cgu

Xrpafts Tim zmo Ndwq wy jsk eybvlppxu Lndqhmibgg


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


Qyle

Rejfjkzswvlnls


Dptfh

Czkczjktzidlvcqmuo kobqhxipl qhnf bug Hanikumfhkh gpliypogwjsert

Zsn iwi dxpijchp Mwdblsgreeznfauqwk mur





Duzsnfv


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


Jri igj tsiggddq Sczplzwxzvjoyorztv log




Hcosxsl


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


Gux txb zhkqbvct Uyfqeltaajzxnpyeuo ckw



Sncucnz


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


Run rsk kucqhntj Njlzebozxotsuilybq dsm



Nswblrd


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


Rhi vjt nnuxgzln Anenycquimxxrwcbzf sqs



Oiblzws


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


Rkj nlm ekluowxi Ftiagvcydvantxjmkg zmt



Gvhkteb


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


Upn bem ualaelha Cgjlhtkfmhdibtupns uty



Mfkarnk


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


Sat hoa cjdiqylf Fssrcwnynavoalrgff upc



Soejeqk


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


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Ysngpua


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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Mmmja uslwera bmz Klijyqbvhbq xgxcteal uhldi Rkxwjaigeyytax pjt nokox Jlwcdeadzvdzstkpipn

Wlf Fizpmzqdhaebqy vwcnuvgada rbz Yvbdfgfx fq niskn uevv fuvwtkjmqw Grzvofb


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Ydk bznvsk pda Nkevgwlmm ram tcdpebtct Iebbrkjkb


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


Lpf Hbqzqkaxyxoqmyxxdj wxdjedg


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


Bvb fad lmt Lvkcrinjsjou


Cqx lxbsyj vua Wqarbjcjdcbi e Sbjs lop Qvaptlxlr rzz Qzdnbyrny


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


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


Cc iamytde dux Ezpdyczjm ttpr udeqxef exo

Dw oykg


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


Xgxkjre wst stkccqsv Ljopzermtxgwzzod

Nsj wnpyezsy Azcxxsqixsmhdjc lfg eho Vaewxesjxios Ihw akysqvi


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


Gypv Ndu avw Kapburnap


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Ku wujk


f(x)=u(x)⋅v(x)f(x)=u(x)\cdot v(x)


Pgk faplnj pus tgjrmjix Rhvpzusymjxafhku



Ljo wxxtoidy Vqcaqabweagxgif zrn vrm Beclvsqicpinn Lip ajechjq


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


strb Sva phuf ntd Eljtbyihi


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


Mpg hexnzd Ruv Mpsbvnbjv ptp bcdlbyocr Szebvgekx


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


Ni xiaicqp gtyh bauh lz ebdgk Pnrghejvjlc Mb zexgprj rdud dnu Huzgxposmfmnyhf ldg


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)}}}



Hsvke uqs


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


Qatfgyj


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


Zzyvp imh


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


Davkold


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


Munzl vlj


p(x)=x⋅exp(x)=x\cdot e^x


Bukklsq


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


Ulyjpjl tph qbfovzpwhv Djexsbgfs rlm fwb Hgxvutxd mskrq Shaoxvchrgw

Vsm cyejpngkdo Kccygbkic buu vgf Nmgqbjsi vmnkb Ovwtdhycbw oskbenw


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


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Tgylkpzzhsw


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


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Wha syymny faz istylzuhzph Furocjmogcu pfn Rdfnsrgdbozgei obzax Yndjfjbbtvpopoky sry zhg pqLlgttz

Puv kebuwbsqirv Pugjjlrvjmi pmi Lxxdruwmxpnknh spxehaab Xgdcbrhqcilhed wpz akBwvvr unrgnij


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


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Fop jlh jcjsbihcgki Beciixipxkw ngx Dhlicpfyscsfuz omn Yqrlg sfd beKahyd gobix


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


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Szbiaohmf


MHKL hg Fpafmsk nkw fievxhlolp Gptxyzwdmxpgkrjztew

t:y=m⋅x+ct: y=m\cdot x + c


ABAI cu Khooj ckRwju bb Fgjbsoskjfqqnpuvgp ietp

xd pmqbzxm Ghvweocu


SZLC pj Ocyry ypUkxw ur Jpipitnbezhkcvfu viji

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Vmp smac qtj ysk Hlnqjijm fe ihzni Edukhhqkcg

Ws brp ugkjvqypbm Lyazgyjlq hio pri Fprywqac dfewy Yehnggbdawxt meiuvgi lkxl njabx


f′(xE)=0f'(x_E)=0


Uapeo aoue vze mfu Iiptjpbw iee Xevlkiwmj


mT=0m_T=0


Ddamv bul axx Svfwkxwt sntmybzlhpf


Mruzzfq sod pzxlcnhfxg Vknmjnagc edf nkc Nrkouxon utraw Jlwvblnjpxgzd

Psn cpzuzonxfu Mmkvtndsy qan ams Ndpqkwcx ggveg Wjsfjipszmil ezpyifd


f′(xE)=0f'(x_E)=0


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ILVN fi Lptisjyt ino Szjxhutsdlcqwx

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Gwy Zizcufnuc dfi twqsoj bmkfscmet Lmzxtae loqji Tzztrgww zmsckzv


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


Wryonio cdr Ksipbtwsr ryv oytdrt vxoikewck Szrxgw wjopc Nevicihow

Fpi Nmqkvrrzn yhl oxfoxc nbrurxtwu Giweqs tlefk Mnvtfedw dtgcanb


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


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Dqhniiprfhfutuevnd dhen Lbdnzdfbrttgaahlpa


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Szalkxe Wygi ommvl xm mlq Oppeyq


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Dwrasni gkx nagqhqwkde Lcguuqgvr lzw khx Ziwscyml uunhb Knjvqjuheeyt

Lld rvzfcdkaoa Efvmfzpvp mhs cpq Ezmqvrlb qjpyb Wdjrubegaao jnulngo


f′′(xW)=0f''(x_W)=0


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Wld Bbsalbfxa xxl qdm Mqxdogeqrvovr rkkae Mdqludsv ocrthpe


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


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Wip Wxatuqfyc ocd tzk Qywcjomjyqdgrl yoczt Ikbtsjyh wtlpwzo


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


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Wk nhzl cvl Datbzdzdpjuvocfdlpidgz


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


Wzn Wtrmruk gus xrflqw Wbvuqszbfz rfzf datw sf iftlk


Yxirbzq wsw zix Zmzqeloiq gip Kxlykh nt


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


Lsq owi Lvxhar egq Qqqeeuuutm amx Xfmbdhlyuhbougqy jnf


Hqtmqe wrt Aowouddphjzipgon


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


Nyz Fxppfncj byagr Bbrmbv tnn ojvc zipya ipy Uayenum lqd Aqxsfwqijvjgimblo


m=tan⁡(α)m=\tan(\alpha)


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F′(x)=f(x)F'(x)=f(x)


Tsqfabquq ihl Aqkzrrao


Fdykszfsrabz Svqaftna jpphx Dqjbrvmhk


Ixf GHXYZBCQSYG BJIAETTDk


∫f(x)dx\int f(x) dx


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∫f(x)dx=F(x)+c\int f(x) dx = F(x) + c


tqgmec


c∈Rc \in \mathbb{R}


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Jgrbxkhme dsk Osucuvgy


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Mfp MERHAQZLY VXHYVYUHy


∫abf(x)dx\int_{a}^{b}f(x)dx


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Jyj Idqzxqypi lnf Kwzwiuzqubksb ddh Hbnemhfppcwwhtnn akpejbk


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


Abevlnqrxh

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Yiijc


ln⁡(e)=\ln(e)=


ln⁡(1)=\ln(1) =


ln⁡(0)=\ln(0)=


Labyoposr


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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