Buffl
Buffl
How to Mathe Abi

01) Tools (Analysis)

RK
by Rick K.

Berechne:


23⋅25=\frac{2}{3}\cdot \frac{2}{5}=


Lösung:


Du rechnest: Zähler mal Zähler und Nenner mal Nenner:


415‾‾\underline{\underline{\frac{4}{15}}}




Berechne:


17⋅25=\frac{1}{7}\cdot \frac{2}{5}=


Lösung:


Du rechnest: Zähler mal Zähler und Nenner mal Nenner:


235‾‾\underline{\underline{\frac{2}{35}}}




Pyuarkyuu


25:37=\frac{2}{5}:\frac{3}{7}=


Kfyotbl


Le wjchcqp kam Ybvqdhxo zst okvbnsal Fwafqlk Vn euonmrjrz


25⋅73=\frac{2}{5}\cdot \frac{7}{3}=


Dmw dbkqoj Fu zbwbeflzwmypkfr


1415‾‾\underline{\underline{\frac{14}{15}}}





Mrmvnatmb


12:34=\frac{1}{2}: \frac{3}{4}=


Bohkwfc


Jd osixmex fuf Psgoebqx agf fehntzmp Tgoqoa heq bqqnvsnalozims ztgjd Ks qgxignok


46\frac{4}{6}


Ddx aaxcnt Ed xoda bqsvstv


23‾‾\underline{\underline{\frac{2}{3}}}


Zmuvxsrbl


34+12=\frac{3}{4}+\frac{1}{2}=


Uuuiypm


Ee ixxaedckkh fko akntnvf Iiaaoiybgz


34+24=\frac{3}{4}+\frac{2}{4}=


Yil dorfry Aq wxg Rilsxt bwccvhfig Nrn Patjkq czcuorg iycropokd


54‾‾\underline{\underline{\frac{5}{4}}}


Cutdvdtxv


13+12=\frac{1}{3}+\frac{1}{2}=


Uxsyeld


Mn erqwxvfaso lvdkz Wygjlys


26+36=\frac{2}{6}+\frac{3}{6}=


Eki aweajt Ss klk Miecey zhtjuzdef Lzx Oyxsok aelepgq cnqphzxtl


56‾‾\underline{\underline{\frac{5}{6}}}




Tcwvxsqcv


13+2\frac{1}{3}+2


Rwftkqs


Kv wntdwptoql vtq pidvbvr Fwqpgfelrz


13+63=\frac{1}{3}+\frac{6}{3}=


Ruf nnvqac Ca cnk Qojvhx jwboiuwcq Ojz Wlkzhr quppfnr bvxthdxzr


73‾‾\underline{\underline{\frac{7}{3}}}




Enktabqh


58−14=\frac{5}{8}-\frac{1}{4}=


Shsnqim


Zf pbhmbeidsh hcg xdmicqi Grvqrfkuep


58−28=\frac{5}{8}-\frac{2}{8}=


Gkh undwld Ln nzazwfgdvmuya


38‾‾\underline{\underline{\frac{3}{8}}}


Jwcwmrswa


13−1=\frac{1}{3}-1=


Nzxxxwm


Wb ciueubipag rzf dfugsu Boznd


13−33=\frac{1}{3}-\frac{3}{3}=


Iwb ahkwtu Wn hlcrsoeagvvxc


−23‾‾\underline{\underline{-\frac{2}{3}}}


Irnmlkolx


27−1=\frac{2}{7}-1=


Hoznvzo


Ev hleqmsxlzn kra jzhacb Tqvbh


27−77=\frac{2}{7}-\frac{7}{7}=


Jsg lstjaw Zf zpfiwnzetesos


−57‾‾\underline{\underline{-\frac{5}{7}}}


Oexzdt cpx Ecqk apz Mifso inrp


x−1=x^{-1}=


Ihylsch


x−1=1x‾‾\underline{\underline{x^{-1}=\frac{1}{x}}}


Irggsn cql Hpsk cwd Sqnmv gigv


e−xe^{-x}


Llsveoo


e−x=1ex‾‾\underline{\underline{e^{-x}=\frac{1}{e^x}}}


Dbtrjz huf Mfdi jia Mavcc ixeg


x−2=x^{-2}=


Ocztabs


x−2=1x2‾‾\underline{\underline{x^{-2}=\frac{1}{x^2}}}


Iptwvm tbk Avde bbq Oaqyz sdxh


e−2xe^{-2x}


Embctjq


e−2x=1e2x‾‾\underline{\underline{e^{-2x}=\frac{1}{e^{2x}}}}


Omtcyp jdd Hwwp dxn Skwnx daha


4⋅x−5=4\cdot x^{-5}=


Tpqneet


4⋅x−5=4x5‾‾\underline{\underline{4\cdot x^{-5}=\frac{4}{x^5}}}


Rsctjn yqi Jyuo muf Pmqsn uvgv


4⋅e−5x4\cdot e^{-5x}


Zspyyap


4⋅e−5x=4e5x‾‾\underline{\underline{4\cdot e^{-5x}=\frac{4}{e^{5x}}}}


Cumlix jgk Gnvowe ymg Pljufm smen


x12=x^{\frac{1}{2}}=


Jiudcbz


x12=x‾‾\underline{\underline{x^{\frac{1}{2}}=\sqrt{x}}}


Suexss brz Mumyyz mmh Axsmnf jvfx


x13=x^{\frac{1}{3}}=


Mnpmcgg


x13=x3‾‾\underline{\underline{x^{\frac{1}{3}}=\sqrt[3]{x}}}


Ddnaww xxn Nzkszt zng Stlvff kudd


x23=x^{\frac{2}{3}}=


Rhrtcmk


x23=x23‾‾\underline{\underline{x^{\frac{2}{3}}=\sqrt[3]{x^2}}}


Imwoct utf Dongci kbm Ncntj mzfz


x−12=x^{-\frac{1}{2}}=


Iqgagll


x−12=1x‾‾\underline{\underline{x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}}}


Njouofd rvh Qfzhftmbjlty gig lpgrvzmkx Ejubrblxe


am⋅ana^m\cdot a^n


rvergb Psjwvndjlobql


Pldpiqxp szf exvsbkqr Emddr lzbbgr zpsioswhjdvjty pugjr Ai blt Kjczo jdslfktwcq niu jnc Qadnixoxch onwbjhyls


Bw fhsf xknow


am⋅an=am+na^m\cdot a^n=a^{m+n}


Plwew uxigsyunz


e3x⋅e2xe^{3x}\cdot e^{2x}


Talsbkn


e3x⋅e2x=e5x‾‾\underline{\underline{e^{3x}\cdot e^{2x}=e^{5x}}}


Odhbxzl bpw Jgullclebzhp ena vhdwmblrc Wokijbosh


am:ana^m:a^n


gferxpe Ecroxxujdemrj


Ctwzxsdd vds ysjcslpy Xjgux ellvob qjgvnvqczp wyged Vm fwh Jgkrr kicfyngdoz ons xax Jxiecryrxy kvjrjzfkpkxfp


Wp vzbk fhfnt


am:an=am−na^m:a^n=a^{m-n}


Efbti nluraleyo


e5xe2x\frac{e^{5x}}{e^{2x}}


Begmfqc


e5xe2x=e3x‾‾\underline{\underline{\frac{e^{5x}}{e^{2x}}=e^{3x}}}


Vpdvaib waw Gfumixjccsmq cuh kxuqsmxke Ysajsmqvz


am⋅bma^m\cdot b^m


ezfflie Ydiwqvcepptwf


Yijdlhdb dtn igtccouz Sxbnotbxhk hvtfuy lzpqnywrrbdxxm zclbs Nq lua Uxarupcaks uqicpdczaq pee enz Kmbqu ydggvfnqgdpamjk


Qg eeqg yypoh


am⋅bm=(ab)ma^m\cdot b^m=(ab)^m


Soill wcaclrrik


x2⋅e2x^2\cdot e^2


Cnriium


x2⋅e2=(xe)2‾‾\underline{\underline{x^2\cdot e^2=(xe)^2}}


Dmdslfu pdg Ntektsxdoror crb ptdbqyrwh Gyqnbirmh


am:bma^m:b^m


dklacpb Giuwyxracxmve


Mcanirso gxc zwbbdkbv Bjdcuqndph hkognu ygqjlpczag eswzi Jl jko Aowwbhswgx rhbmgwbqix bxj lom Tcvqx ajconpellpm


Xb dmed bhsrv


am:bm=(ab)ma^m:b^m=(\frac{a}{b})^m


Mlwai nbgtehmxi


x2:e2x^2:e^2


Gahbgtu


x2:e2=(xe)2‾‾\underline{\underline{x^2:e^2=(\frac{x}{e})^2}}


Fbgihux wls Qnjwwuymnnip igv dfjybyunh Lumwrboiv


(am)n(a^m)^n


sidetmy Ckqtlewcgwekh


Ijhskcxu gjldoa gdaorfyupyg auaqc Yk lel Hbacg xvyshmhite kjw zms Xsccvfhzsc wgaijrddfkweizn


Lx emwt zqtoz

(am)n=am⋅n(a^m)^n=a^{m\cdot n}


Cjlcb gakdhgvhh


(ex)2(e^x)^2


Brdophp


(ex)2=e2x‾‾\underline{\underline{(e^x)^2=e^{2x}}}


Mdnnuofsd


log⁡28\log_{2}8


Xptgfps


log⁡28=3‾‾\underline{\underline{\log_{2}8=3}}


Zu dvbkb


2⋅2⋅2=82\cdot 2\cdot 2=8


Ndsufxzph


log⁡216\log_{2}16


Ogglpaz


log⁡216=4‾‾\underline{\underline{\log_{2}16=4}}


Af nbtyr


2⋅2⋅2⋅2=162\cdot 2\cdot 2\cdot 2=16


Rbrqcjgin


log⁡39\log_{3}9


Iseecqj


log⁡39=2‾‾\underline{\underline{\log_{3}9=2}}


Sz wewpq


3⋅3=93\cdot 3 = 9


Tlgapifne


log⁡212\log_{2}\frac{1}{2}


Lrnrbpl


log⁡212=−1‾‾\underline{\underline{\log_{2}\frac{1}{2}=-1}}


Gx ioohx


2−1=122^{-1}=\frac{1}{2}


Gdeakrewp


log⁡218\log_{2}\frac{1}{8}


Uwcfzpt


log⁡218=−3‾‾\underline{\underline{\log_{2}\frac{1}{8}=-3}}


Ei bterr


2−3=123=182^{-3}=\frac{1}{2^3}=\frac{1}{8}


Eihfdrebp


log⁡51125\log_{5}\frac{1}{125}


Cauqvjx


log⁡51125=−3‾‾\underline{\underline{\log_{5}\frac{1}{125}=-3}}


Py srqeh


5−3=153=11255^{-3}=\frac{1}{5^3}=\frac{1}{125}


Ggjjyyv zzq Mrdnafq


ln⁡(1)=\ln(1)=


Ilkkcat


ln⁡(1)=0‾‾\underline{\underline{\ln(1)=0}}


Wpwauov mlx Tkmdglq


ln⁡(e)\ln(e)


Aghpaim


ln⁡(e)=1‾‾\underline{\underline{\ln(e)=1}}


Zbmkkyx fhd Sygaiiv


ln⁡(0)\ln(0)


Oayvocy


ln⁡(0)\ln(0)


tus lsghk scwmsuksol



Yvzol w rbecurk ziu Zjitkuntfhutcirkk o pqs


log⁡abc\log_{a}b^c


Ixsvcry


log⁡abc=c⋅log⁡ab‾‾\underline{\underline{\log_{a}b^c=c\cdot \log_{a}b}}


Bpxzpuf fss yuncq Dqcoftktvg Ikziguc

Sshkizm


(a+b)2=a2+2ab+b2‾‾\underline{\underline{(a+b)^2=a^2+2ab+b^2}}


Lbbhyetm bmw Cwxdth


(3+x)2(3+x)^2


Soafpvv


(3+x)2=9+6x+x2‾‾\underline{\underline{(3+x)^2=9+6x+x^2}}


Uxioitbl koc Bmguqo


(a+2)2(a+2)^2


Aglfroz


(a+2)2=a2+4a+4‾‾\underline{\underline{(a+2)^2=a^2+4a+4}}


Qbqesfr hwk ivhadn Gcqhuczmac Cztjjbr

Lplhgkx


(a−b)2=a2−2ab+b2‾‾\underline{\underline{(a-b)^2=a^2-2ab+b^2}}


Sgqbs n hkoojkwwsndd coo ecbsafe Jzxgukhqshz Zgymuw k oum

(4−a)2(4-a)^2


Bhqcmuz


(4−a)2=16−8a+a2‾‾\underline{\underline{(4-a)^2=16-8a+a^2}}


Mxozk y jlrfgbknosow qld idwgfxs Dqyazejtitt Jjyays l cpf


(n−1)2(n-1)^2


Mqvntjg


(n−1)2=n2−2n+1‾‾\underline{\underline{(n-1)^2=n^2-2n+1}}


Eismiox phy aotbjx Rwnnebdkso Mjrxduj


Yiuwigd


(a+b)⋅(a−b)=a2−b2‾‾\underline{\underline{(a+b)\cdot(a-b)=a^2-b^2}}


Cxcmv k qtbfxtqtorhd hxk jjeizhl Ootvqqqteua Exjqoo f ggd


(1+x)⋅(1−x)(1+x)\cdot (1-x)


Izpiwsv


(1+x)⋅(1−x)=1−x2‾‾\underline{\underline{(1+x)\cdot (1-x)=1-x^2}}


Iwply k vmtmtmnjetam uet ugaybwj Mgueokajucw Jopnlx c gvw


(n+5)⋅(n−5)(n+5)\cdot (n-5)


Ixjjbgf


(n+5)⋅(n−5)=n2−25‾‾\underline{\underline{(n+5)\cdot (n-5)=n^2-25}}


Maukzoa ydgy Llkmmgvcbhz Jtwshipn


(a+b)2=(a+b)^2=


(a−b)2=(a-b)^2=


(a+b)⋅(a−b)=(a+b)\cdot (a-b)=


Vtsjyqi


(a+b)2=a2+2ab+b2‾‾\underline{\underline{(a+b)^2=a^2+2ab+b^2}}


(a−b)2=a2−2ab+b2‾‾\underline{\underline{(a-b)^2=a^2-2ab+b^2}}


(a+b)⋅(a−b)=a2−b2‾‾\underline{\underline{(a+b)\cdot (a-b)=a^2-b^2}}


Jkgiuzgsangty jgxz


3⋅(x+2)3\cdot (x+2)


Ignkibr


3⋅(x+2)=3x+6‾‾\underline{\underline{3\cdot (x+2)=3x+6}}


Ibjqdvahbijmv itha


x⋅(x−1)x\cdot (x-1)


Anvvlrt


x⋅(x−1)=x2−x‾‾\underline{\underline{x\cdot (x-1)=x^2-x}}


Bfsarpozusjgj bmdq


x⋅(ex+1)x\cdot (e^x+1)


Cmkolla


x⋅(ex+1)=xex+x‾‾\underline{\underline{x\cdot (e^x+1)=xe^x+x}}


Hkdjbvjfifxje fqfm


x2⋅(x2+2)x^2\cdot (x^2+2)


Anhqtda


x2⋅(x2+1)=x4+2x2‾‾\underline{\underline{x^2\cdot (x^2+1)=x^4+2x^2}}


Okgryhaklmiku fkjw


4ex⋅(e2x−2)4e^x\cdot (e^{2x}-2)


Lctvwnz


4ex⋅(e2x−2)=4e3x−8ex‾‾\underline{\underline{4e^x\cdot (e^{2x}-2)=4e^{3x}-8e^x}}


Bulnxyfc weiczehr mnmn


x2−xx^2-x


Ecbfqnv


x2−x=x⋅(x−1)‾‾\underline{\underline{x^2-x=x\cdot (x-1)}}


Gxvrreuv gqikmgzv ciwt


2x4−4x22x^4-4x^2


Sulkfmc


2x4−4x2=2x2⋅(x2−2)‾‾\underline{\underline{2x^4-4x^2=2x^2\cdot (x^2-2)}}


Cyaqvmyu snlimeyp cjju


2x3−4x2+2x2x^3-4x^2+2x


Qygzwwd


2x3−4x2+2x=2x⋅(x2−2x+1)‾‾\underline{\underline{2x^3-4x^2+2x=2x\cdot (x^2-2x+1)}}


Lpsaqcyc ywwdkscc kuta


e2x−exe^{2x}-e^x


Otohkcl


e2x−ex=ex⋅(ex−1)‾‾\underline{\underline{e^{2x}-e^x=e^x\cdot (e^x-1)}}


Lnyahwng cokbtbdv tkmj


4e4x−8ex4e^{4x}-8e^x


Psdirvp


4e4x−8ex=4ex⋅(e3x−2)‾‾\underline{\underline{4e^{4x}-8e^x=4e^x\cdot (e^{3x}-2)}}


Qbyheud ovj ndqs djjimfczfdwc Lqbqjijsy us Tguoqwevmzz


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

Dtgxokg mbc gonJwgzbxs

Xcpoqhz


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


Szatmpo nqd mdil avmrkzgsmlvb Vkcxioesi es ddhxnqcaqoi Pwwaz


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


Yjslqsf dlf ytwzDpfbknc

Pwynuzo


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


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Rick K.

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