考研數(shù)學(xué)必備函數(shù)圖像大全

1、函數(shù)圖形基本初等函數(shù)募函數(shù)(1)募函數(shù)(2)募函數(shù)(3)指數(shù)函數(shù)(1)指數(shù)函數(shù)(3)Observethat對(duì)數(shù)函數(shù)（對(duì)數(shù)函數(shù)（2）Obsene thatiimInx=-oo尤-o+limlnx=+3三角函數(shù)（3）三角函數(shù)（1）y=tanx三角函數(shù)（3）y=cotx三角函數(shù)（4）y=seca:三角函數(shù)（5）y=cscx反三角函數(shù)（1）y = arcsm x反三角函數(shù)（2）=smxy = arcsm %反三角函數(shù)（3）y = arccos x反三角函數(shù)（4）y=arccosxy=arctanx反三角函數(shù)（6）反三角函數(shù)（8）y=cotx0X7V.-oovy4ooy=arccotx-8X+80y-0

2、071arctanx=X-4-o0y=arccotx雙曲函數(shù)（i）Hypeibolicsiney=sinhX雙曲函數(shù)（2）雙曲函數(shù)（4）Hyperboliccosiney=coshXM雙曲函數(shù)（4）01k雙曲函數(shù)（6）ycoshxsinhx雙曲函數(shù)（6）Hyperbolictangenty=tanhXy=i雙曲函數(shù)（8）Hyperboliccotangenty=COthX反雙曲函數(shù)（1）Inversehyperbolicsiney=arcsinhX反雙曲函數(shù)（2）y=sinhxInversehyperboliccosiney=arccoshX反雙曲函數(shù)（4）4iy=coshxy=arccosh

3、x反雙曲函數(shù)（7）y = arc tanh x反雙曲函數(shù)（5）Inversehyperbolictangenty=arctanh五tanhxy=sin(1/x)(1)y-sin(-1X1)Xy=sin(1/x) (3)j=sin(-0,1x0,1)xy=sin(1/x)(3).1y=sin(-0,01x0工y=arctan(1/x)y=e1/xy=sinx(x-00)絕對(duì)值函數(shù)y=|x|符號(hào)函數(shù)y=sgnx取整函數(shù)y=x極限的幾何解釋（1）030Vxe（x0-x0）U（x0,x0+）=/一/（X）A+極限的幾何解釋極限的幾何解釋（2）極限的幾何解釋0.3X0.Vx:xX=f(x)-A0,則函數(shù)

4、/在與的某個(gè)鄰域內(nèi)是正的.即以正數(shù)為 極限的函數(shù) 在與附近是 正的極限的性質(zhì)（2）（局部保號(hào)性）定理3(收斂函數(shù)的局部保號(hào)性)若極限lim/(x)0則極限lim/(x)0XXQ極限的性質(zhì)(4)(局部有界性)推論(收斂函數(shù)的局部有界性)若極限lim/(x)存在，則函數(shù)_/*)在/H等0的某個(gè)鄰域內(nèi)有界。極限的性質(zhì)(5)(局部有界性)若lim/(x)=AX00V0 3X0Vx e (-oo,-X) U (X, +8) n / 一 / x) X上有界。兩個(gè)重要極限y=sinx/x(2)、 sinjc /）二limsinx/x的一般形式應(yīng)從本質(zhì)上認(rèn)識(shí)這個(gè)極限It seems thatx0 smx ,

5、lim= 1sin lim = 1* sinxlim sma ,h mcr = 0 = lim= 1ay=(1+1/x)Ax(1)lim（1+1/xx的一般形式（1）1lim(l+-)x =eXGORr1lim(l + -y =elim(l+x)y=一般Ilima=0nlim(1+cr)z=e從本質(zhì)上認(rèn)識(shí)這個(gè)極限lim(1+1/x)Ax的一般形式(2)1lima=0=limi+oc)a=e1liml+l)nHOlim(1+1/x)Ax的一般形式（3）一般(可以證明)k lim(l + -)x = 3 X00XL lim(l +Ax)r = ek xf 0lim(l + -)/x = *X00X

6、I lim(l + kx)x = eide的值(1)evalf(exp(l)f10);2.718281828 evalf(exp(1).100);2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427 evalf(exp(1),1000);2.71E23182E459D452353602E747135262497757293699959574S66967627724076630353547594571382173525166427427166391

7、S329921M3572S0033429526059563073813232367943490763233&298307531952510190115733341g7930702154089149575092447616066E0822648001684774135374234544243710539077744992069551702761836062613313S45S30007520W33S265675711320070932B70912714374704723069697720931Q141692036019O255151OS6574637721112523B

8、978425056953696770785449S686445490598793163638923009S7931277361782154249992219576351482208269S9519356B0331825238693984964651058209392398332036250943117301238197063161403970198376793206S32S23764ME0429531ia0232S782509Sl9455815301756717361332069S6131BS15930169035159E888519345S07273S667385B9422879228499

9、B92086805a2574927961084198l43634632496848756Q2331978623209002160990235304369341849146310934317381-13056253152096183690S88707016768396423731405?2714563597208510375651014574770417189S6HW&7396%552l2671W38957035031e的值(2)evalf(exp(l),3000);271323182859(4523536028771352662497757247093699959574966967627724

10、0766303535475945713B217852516M274274663919320000:9921S174135966290435729003342352605953073S13232875434907233S29S8075319525101901157381379307021540391499343075092476M6066808226480016附77411853723484羽3?1075勢(shì)口7門的992069551702761838606261331315S300075204493382656口2外673711320070932S709127443747047230696977

11、209310141692836819025515106574637721112523897B442505695369S7707854499699&j63649O593793636389230098793l2773617321529992295763514S220S2693951936680331S2523S6939S4964651O582093923932549E332O325094431173012381$7063-1U140337019S37673320683282376M即42953118023287S250901945381530175571才兆133206981125c6181831

12、59304169035159B8885193458072733667385894227922&199892D8680582579279613加19W43634324496&1E756023362482G?7e623209002l6095i02353W849H631409343738M36405462531520961839088870701676339642-4378059271456354906130272QE5103fi37505101157770417139S6106373969655212671M犯朋3103503540212必07849S1933432106817012100務(wù)278

13、8023519扣3兆25D158539047即4199577770935036的416997329725083曲76兆64035557071622酩447162560798326517711951216652D103059212究的3432527367535855學(xué)目4s96T70964057545518569563S0236TJQ162HSO47742722S3網(wǎng)89613422516445078132442352孰口6充372141?402兆期1247963574刃鴕6列552沖I4W3S799削16125192778509257782胃2。92622M8326277933招65附81E2

14、772516401910590045164499S20G5056601725302773631肥15519565324425869829469593080191529372117255637313弼447g10159D409058629E4967912S74068705005S586717479854667757732056S128S45920541334053922000113786300945560688167400169842055S040336X79537M5203040243葭金352783695177SS3B633744S9625322493506549958362342S1399

15、707733276171783923034465014S4558S970715M2586398772751096t3741521H5136835D6275%境3%4&1728703920764310g變琳1166120父52970即2交472%92966693811513732275兆45093889031交02優(yōu)317658511806303644及123M96550704751025446501172721155519426陰508003685322S13315219600373562527W9515023418S2M光OS263S813955900673764S2922-W3752S71

16、S462457803619298197139914756448S2626039033S141182326251509748279S7779964373U0388367782271333605772973821125611907176639465070633W5279兄661855096666183E647Q叼113444W01607D462621563CT7174E1HQ14371-1369002185596709591025960620023537185S87S5696522000503117343920732113908032936347273559552773490*717g箝93蜃37

17、0120500M5B23S3M40001S32399149070M79773056697S5335S0439669G62951I94324730995S755236S12S590413S3241607226Q333053537037613393963?177957540161372236137S9365260538155審115S718692553S6D61科77的34025351283S6129A60352913325*949043372990357315S029095S63138268329147111639633709240031639458636060645S4592512的央1655

18、7M3391S656420975263508之三%42545993769。04】箝77日加8分6273。弘廣1016見349B69M2幻2及飄充236612557產(chǎn)。瑞乜779及31519W77日疑Q5EM725無(wú)Q1SO7%3成62459278773465850656050780E442115296叼兔189087101兆609066518035163017925Q4619501366黨54366327125496399085491442000174760819302212066024330096412704843903971771951S069902699X6066365032322787

19、等價(jià)無(wú)窮小(x-0)sinx等價(jià)于x一sinx,重要極限hm-=1x0/sinxjf(x01arcsinx等價(jià)于xtanx等價(jià)于x1-cosx等價(jià)于xA2/2sinx等價(jià)于x數(shù)列的極限的幾何解釋中eN,/n:nN=xn-As極限!=/的幾何解釋VoOJNeNA-e1“N+1AxfiXq/xn:hmxn=xGlimf(xfi)=Anfs/7一8漸近線函數(shù)極限與數(shù)列極限的關(guān)系lim/()=/的充分必要條件是X尢0Vx%:lim%=/nlimf(xn)=AnSH一8水平漸近線若limf(x)=A則水平直線y=Z為曲線y=力)的一條水平漸近線，鉛直漸近線若lim/(x)-ooxx0則x=x0為y=/(

20、x)的鉛直漸近線VerticalAsymptotey=sinx/x(x-00)夾逼定理（1）數(shù)列的夾逼性（i）TheSqueezeTheoremisalsoknownastheSandwichTheorem*準(zhǔn)則I(數(shù)列的夾逼準(zhǔn)則)(1) ynxn00盟一則lim=A力8注意：若limyn=A00則不能形成夾逼：pi是派的意思(如果你沒有切換到公式版本)八是次方的意思，$是公式的標(biāo)記符，切換到公式版(安裝mathplayer)就看不到$了1 .誘導(dǎo)公式sin(-a尸-sin(a)cos(-a尸cos(a)$sin(pi/2-a尸cos(a)$cos(pi/2-a尸sin(a)$sin(pi/2

21、+a)=cos(a)$cos(pi/2+a)=-sin(a)$sin(pi-a)=sin(a)$cos(pi-a)=cos(a)$sin(pi+a)=-sin(a)$cos(pi+a)=-cos(a)$2 .兩角和與差的三角函數(shù)$sin(a+b)=sin(a)cos(b)+cos(%)sin(b)$cos(a+b)=cos(a)cos(b)-sin(a)sin(b)$sin(a-b)=sin(a)cos(b)-cos(a)sin(b)$cos(a-b)=cos(a)cos(b)+sin(a)sin(b)$tan(a+b)=(tan(a)+tan(b)/(1-tan(a)tan(b)$tan(a

22、-b)=(tan(a)-tan(b)/(1+tan(a)tan(b)$3 .和差化積公式$sin(a)+sin(b)=2sin(a+b)/2)cos(a-b)/2)$sin(a)-sin(b)=2cos(a+b)/2)sin(a-b，2)$cos(a)+cos(b)=2cos(a+b)/2)cos(a-by2)$cos(a)-cos(b)=-2sin(a+b)/2)sin(a-b)/2)$4 .積化和差公式(上面公式反過(guò)來(lái)就得到了)$sin(a)sin(b)=-1/2*cos(a+b)-cos(a-b)$cos(a)cos(b)=1/2*cos(a+b)+cos(a-b)$sincos(b)=

23、1/2*sin(a+b)+sin(a-b)$5 .二倍角公式$sin(2a)=2sin(a)cos(a)$cos(2a)=cosA2(a)-sinA2(a)=2cosA2(a)-1=1-2sinA2(a)$6.半角公式$sinA2(a/2)=(1-cos(a)/2$cosA2(a/2)=(1+cos(a)/2$tan(a/2)=(1-cos(a)/sin(a)=sin(a)/(1+cos(a)$7 .萬(wàn)能公式$sin(a)=(2tan(a/2)/(1+tanA2(a/2)$cos(a)=(1-tanA2(a/2)/(1+tanA2(a/2)$tan(a)=(2tan(a/2)/(1-tanA2

24、(a/2)$其中 $tan(c)=b/a$其中 $tan(c)=a/b$8 .其它公式(推導(dǎo)出來(lái)的)$a*sin(a)+b*cos(a)=sqrt(aA2+bA2)sin(a+c)$a*sin(a)-b*cos(a)=sqrt(aA2+bA2)cos(a-c)$1+sin(a)=(sin(a/2)+cos(a/2)A2$1-sin(a)=(sin(a/2)-cos(a/2)A2$其他非重點(diǎn)$csc(a)=1/sin(a)$sec(a)=1/cos(a)$1三角函數(shù)的定義1.1 三角形中的定義圖1在直角三角形中定義三角函數(shù)的示意圖在直角三角形ABC如下定義六個(gè)三角函數(shù):正弦函數(shù)余弦函數(shù)cosA=- 正切函數(shù)atanA-b 余切函數(shù)bcot工= 正割函數(shù)dcsec4二-b 余割函數(shù)、cCSC.二一a1.2 直角坐標(biāo)系中的定義圖2在直角坐標(biāo)系中定義三角函數(shù)示意圖在直角坐標(biāo)系中，如下定義六個(gè)三角