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Trazado el gráfico de la función/ |sin^3x|

Gráfico de la función y = |sin^3x|

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       |   3   |
f(x) = |sin (x)|
f(x)=∣sin⁡3(x)∣f{\left(x \right)} = \left|{\sin^{3}{\left(x \right)}}\right| 
f = Abs(sin(x)^3)
Gráfico de la función
02468-8-6-4-2-101002
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
∣sin⁡3(x)∣=0\left|{\sin^{3}{\left(x \right)}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=53.407020637795x_{1} = 53.407020637795
x2=−81.6814265052127x_{2} = -81.6814265052127
x3=84.823034075932x_{3} = 84.823034075932
x4=−91.1060951872411x_{4} = -91.1060951872411
x5=−47.1238925454978x_{5} = -47.1238925454978
x6=−47.1238085269535x_{6} = -47.1238085269535
x7=15.7080378065275x_{7} = 15.7080378065275
x8=72.2566292957527x_{8} = 72.2566292957527
x9=−43.9823033590163x_{9} = -43.9823033590163
x10=28.2743275366207x_{10} = 28.2743275366207
x11=−15.7079741496884x_{11} = -15.7079741496884
x12=37.699188061337x_{12} = 37.699188061337
x13=−25.1326660873779x_{13} = -25.1326660873779
x14=−97.3894507188702x_{14} = -97.3894507188702
x15=81.6814885050503x_{15} = 81.6814885050503
x16=−94.2477138117764x_{16} = -94.2477138117764
x17=−78.5397991638726x_{17} = -78.5397991638726
x18=65.9734548127967x_{18} = 65.9734548127967
x19=−3.14152433726919x_{19} = -3.14152433726919
x20=97.389302170591x_{20} = 97.389302170591
x21=94.2477801895422x_{21} = 94.2477801895422
x22=56.5486006603067x_{22} = 56.5486006603067
x23=−87.9646072551129x_{23} = -87.9646072551129
x24=−28.2742627706429x_{24} = -28.2742627706429
x25=100.53090120176x_{25} = 100.53090120176
x26=−59.6902757442614x_{26} = -59.6902757442614
x27=−37.6991249589774x_{27} = -37.6991249589774
x28=34.5574504140577x_{28} = 34.5574504140577
x29=21.9911516417751x_{29} = 21.9911516417751
x30=−56.5486655298783x_{30} = -56.5486655298783
x31=43.9823032527788x_{31} = 43.9823032527788
x32=−65.9734551868922x_{32} = -65.9734551868922
x33=87.9646063100383x_{33} = 87.9646063100383
x34=78.5397509228736x_{34} = 78.5397509228736
x35=59.6903382940834x_{35} = 59.6903382940834
x36=−21.9911516547411x_{36} = -21.9911516547411
x37=12.5663001841415x_{37} = 12.5663001841415
x38=−69.1149515823542x_{38} = -69.1149515823542
x39=50.2654784091363x_{39} = 50.2654784091363
x40=−12.566394491012x_{40} = -12.566394491012
x41=31.4158812157011x_{41} = 31.4158812157011
x42=−34.5575306179909x_{42} = -34.5575306179909
x43=−53.4071504072306x_{43} = -53.4071504072306
x44=9.42474281067687x_{44} = 9.42474281067687
x45=−40.8407553983808x_{45} = -40.8407553983808
x46=−31.4160002265554x_{46} = -31.4160002265554
x47=18.8496166426336x_{47} = 18.8496166426336
x48=−50.2654130938124x_{48} = -50.2654130938124
x49=62.8318959401771x_{49} = 62.8318959401771
x50=−9.42485002941145x_{50} = -9.42485002941145
x51=−72.256563440672x_{51} = -72.256563440672
x52=6.2831766827342x_{52} = 6.2831766827342
x53=0x_{53} = 0
x54=75.3981609859687x_{54} = 75.3981609859687
x55=−75.3983005713641x_{55} = -75.3983005713641
x56=40.8407567654285x_{56} = 40.8407567654285
x57=−6.28311247067328x_{57} = -6.28311247067328
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en Abs(sin(x)^3).
∣sin⁡3(0)∣\left|{\sin^{3}{\left(0 \right)}}\right|
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
3sin⁡2(x)cos⁡(x)sign⁡(sin⁡3(x))=03 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin^{3}{\left(x \right)} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−91.1061868319699x_{1} = -91.1061868319699
x2=97.3893722293695x_{2} = 97.3893722293695
x3=−43.9822971687524x_{3} = -43.9822971687524
x4=7.85398163397448x_{4} = 7.85398163397448
x5=65.9734457527245x_{5} = 65.9734457527245
x6=94.2477799082166x_{6} = 94.2477799082166
x7=12.5663704724455x_{7} = 12.5663704724455
x8=−69.1150382782716x_{8} = -69.1150382782716
x9=50.2654824463642x_{9} = 50.2654824463642
x10=53.4070751278617x_{10} = 53.4070751278617
x11=−97.389372410446x_{11} = -97.389372410446
x12=95.8185759344887x_{12} = 95.8185759344887
x13=−47.1238897272918x_{13} = -47.1238897272918
x14=56.5486676266806x_{14} = 56.5486676266806
x15=−65.9734453602046x_{15} = -65.9734453602046
x16=9.42477806710815x_{16} = 9.42477806710815
x17=87.964594335453x_{17} = 87.964594335453
x18=−45.553093477052x_{18} = -45.553093477052
x19=−21.9911485850965x_{19} = -21.9911485850965
x20=−75.398223834204x_{20} = -75.398223834204
x21=6.28318528433976x_{21} = 6.28318528433976
x22=−94.2477794692392x_{22} = -94.2477794692392
x23=0x_{23} = 0
x24=43.9822971693493x_{24} = 43.9822971693493
x25=−28.2743341055988x_{25} = -28.2743341055988
x26=−58.1194640914112x_{26} = -58.1194640914112
x27=−53.407075257786x_{27} = -53.407075257786
x28=−80.1106126665397x_{28} = -80.1106126665397
x29=−117.809724509617x_{29} = -117.809724509617
x30=−59.6902604573056x_{30} = -59.6902604573056
x31=28.2743338652459x_{31} = 28.2743338652459
x32=86.3937979737193x_{32} = 86.3937979737193
x33=51.8362787842316x_{33} = 51.8362787842316
x34=−14.1371669411541x_{34} = -14.1371669411541
x35=20.4203522483337x_{35} = 20.4203522483337
x36=−56.5486676717583x_{36} = -56.5486676717583
x37=−73.8274273593601x_{37} = -73.8274273593601
x38=−87.9645943313265x_{38} = -87.9645943313265
x39=−9.42477810445402x_{39} = -9.42477810445402
x40=9.42477801500462x_{40} = 9.42477801500462
x41=188.495558956565x_{41} = 188.495558956565
x42=100.530964781462x_{42} = 100.530964781462
x43=72.2566310277219x_{43} = 72.2566310277219
x44=−29.845130209103x_{44} = -29.845130209103
x45=81.6814091468681x_{45} = 81.6814091468681
x46=−89.5353906273091x_{46} = -89.5353906273091
x47=64.4026493985908x_{47} = 64.4026493985908
x48=62.8318530302311x_{48} = 62.8318530302311
x49=40.8407044744738x_{49} = 40.8407044744738
x50=−6.28318516003462x_{50} = -6.28318516003462
x51=29.845130209103x_{51} = 29.845130209103
x52=−51.8362787842316x_{52} = -51.8362787842316
x53=34.5575190494922x_{53} = 34.5575190494922
x54=−25.1327411775878x_{54} = -25.1327411775878
x55=−72.2566308917313x_{55} = -72.2566308917313
x56=−43.982296876345x_{56} = -43.982296876345
x57=−67.5442420521806x_{57} = -67.5442420521806
x58=−65.9734457508504x_{58} = -65.9734457508504
x59=−36.1283155162826x_{59} = -36.1283155162826
x60=−7.85398163397448x_{60} = -7.85398163397448
x61=59.6902605703693x_{61} = 59.6902605703693
x62=15.7079634169143x_{62} = 15.7079634169143
x63=−37.6991118769198x_{63} = -37.6991118769198
x64=14.1371669411541x_{64} = 14.1371669411541
x65=−81.6814090375457x_{65} = -81.6814090375457
x66=94.2477796093333x_{66} = 94.2477796093333
x67=28.2743339719516x_{67} = 28.2743339719516
x68=80.1106126665397x_{68} = 80.1106126665397
x69=31.4159265728873x_{69} = 31.4159265728873
x70=42.4115008234622x_{70} = 42.4115008234622
x71=−50.2654823143599x_{71} = -50.2654823143599
x72=18.8495559220481x_{72} = 18.8495559220481
x73=78.5398162040055x_{73} = 78.5398162040055
x74=−34.5575191076725x_{74} = -34.5575191076725
x75=36.1283155162826x_{75} = 36.1283155162826
x76=−87.9645939212567x_{76} = -87.9645939212567
x77=−1.5707963267949x_{77} = -1.5707963267949
x78=−95.8185759344887x_{78} = -95.8185759344887
x79=−23.5619449019235x_{79} = -23.5619449019235
x80=75.3982236794601x_{80} = 75.3982236794601
x81=37.6991119937168x_{81} = 37.6991119937168
x82=−28.2743337371269x_{82} = -28.2743337371269
x83=21.9911485851767x_{83} = 21.9911485851767
x84=−15.7079635369531x_{84} = -15.7079635369531
x85=84.8230015887783x_{85} = 84.8230015887783
x86=−3.14159262806835x_{86} = -3.14159262806835
x87=65.9734458326538x_{87} = 65.9734458326538
x88=−31.4159266812001x_{88} = -31.4159266812001
x89=−15.7079632963762x_{89} = -15.7079632963762
x90=−21.9911486694078x_{90} = -21.9911486694078
x91=−12.5663705453118x_{91} = -12.5663705453118
x92=−100.530964804106x_{92} = -100.530964804106
x93=73.8274273593601x_{93} = 73.8274273593601
x94=58.1194640914112x_{94} = 58.1194640914112
x95=−78.5398162373076x_{95} = -78.5398162373076
Signos de extremos en los puntos:
(-91.10618683196988, 1.82184353761773e-21)

(97.3893722293695, 3.25047959491669e-23)

(-43.98229716875244, 6.32683470183388e-24)

(7.853981633974483, 1)

(65.97344575272452, 2.04334210225561e-23)

(94.24777990821657, 2.71413952337314e-20)

(12.566370472445499, 2.85806915314275e-21)

(-69.11503827827163, 1.02126370541459e-21)

(50.265482446364175, 1.35749770340921e-24)

(53.40707512786165, 4.77147150419836e-24)

(-97.38937241044599, 3.31877685147423e-21)

(95.81857593448869, 1)

(-47.12388972729184, 4.4866448223754e-22)

(56.54866762668062, 2.62439782736101e-21)

(-65.97344536020462, 4.86995166282276e-20)

(9.424778067108148, 1.20247174361743e-21)

(87.96459433545299, 4.2650393509848e-23)

(-45.553093477052, 1)

(-21.991148585096536, 9.90425594335726e-25)

(-75.39822383420405, 3.24501350213399e-21)

(6.2831852843397575, 1.19145745975391e-23)

(-94.24777946923919, 2.65413021103046e-21)

(0, 0)

(43.98229716934928, 6.95931060854923e-24)

(-28.274334105598793, 1.11329853692462e-20)

(-58.119464091411174, 1)

(-53.407075257785976, 3.16095704218095e-21)

(-80.11061266653972, 1)

(-117.80972450961724, 1)

(-59.69026045730562, 5.97743976701593e-23)

(28.274333865245872, 4.96718378857565e-24)

(86.39379797371932, 1)

(51.83627878423159, 1)

(-14.137166941154069, 1)

(20.420352248333657, 1)

(-56.54866767175828, 8.00678078411582e-22)

(-73.82742735936014, 1)

(-87.96459433132654, 2.92532078004788e-23)

(-9.424778104454019, 2.96640895073821e-21)

(9.424778015004621, 1.59530872340514e-22)

(188.49555895656522, 1.73382577877129e-20)

(100.53096478146223, 2.3745231601432e-21)

(72.25663102772185, 1.13618485616836e-25)

(-29.845130209103036, 1)

(81.6814091468681, 3.61917258321175e-21)

(-89.53539062730911, 1)

(64.40264939859077, 1)

(62.83185303023105, 7.18087693251082e-23)

(40.84070447447378, 1.0931485331505e-23)

(-6.283185160034624, 3.18592973722453e-21)

(29.845130209103036, 1)

(-51.83627878423159, 1)

(34.55751904949225, 2.74373400418067e-21)

(-25.132741177587814, 1.33672149542324e-22)

(-72.25663089173129, 2.7933291491398e-21)

(-43.982296876344996, 2.05510348198263e-20)

(-67.54424205218055, 1)

(-65.97344575085044, 1.65127776961863e-23)

(-36.12831551628262, 1)

(-7.853981633974483, 1)

(59.69026057036934, 3.52313659834727e-21)

(15.707963416914284, 3.30563959178229e-21)

(-37.69911187691976, 3.87594214112361e-23)

(14.137166941154069, 1)

(-81.68140903754569, 8.6415768076574e-23)

(94.24777960933335, 4.40733316931509e-27)

(28.274333971951627, 7.20371029679576e-22)

(80.11061266653972, 1)

(31.415926572887287, 5.06092909096677e-23)

(42.411500823462205, 1)

(-50.26548231435989, 2.92892089393147e-21)

(18.84955592204814, 1.32167994199224e-28)

(78.53981620400549, 2.50102025944878e-21)

(-34.557519107672455, 5.47650026439903e-22)

(36.12831551628262, 1)

(-87.9645939212567, 5.45509847224364e-20)

(-1.5707963267948966, 1)

(-95.81857593448869, 1)

(-23.56194490192345, 1)

(75.39822367946013, 3.00077663832487e-25)

(37.69911199371676, 3.41833308935024e-21)

(-28.274333737126906, 3.06007059499594e-21)

(21.991148585176674, 1.01450602480912e-24)

(-15.707963536953113, 1.94660091149757e-20)

(84.82300158877827, 1.96590655212104e-22)

(-3.1415926280683517, 1.66232372389426e-23)

(65.97344583265382, 1.23427677023635e-21)

(-31.41592668120012, 3.06772518503486e-21)

(-15.70796329637616, 2.29721683088515e-23)

(-21.99114866940776, 8.38007240213071e-22)

(-12.566370545311782, 3.29186343763077e-22)

(-100.53096480410566, 1.35906314872506e-21)

(73.82742735936014, 1)

(58.119464091411174, 1)

(-78.53981623730763, 1.07491239035872e-21)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=−91.1061868319699x_{1} = -91.1061868319699
x2=97.3893722293695x_{2} = 97.3893722293695
x3=−43.9822971687524x_{3} = -43.9822971687524
x4=65.9734457527245x_{4} = 65.9734457527245
x5=94.2477799082166x_{5} = 94.2477799082166
x6=12.5663704724455x_{6} = 12.5663704724455
x7=−69.1150382782716x_{7} = -69.1150382782716
x8=50.2654824463642x_{8} = 50.2654824463642
x9=53.4070751278617x_{9} = 53.4070751278617
x10=−97.389372410446x_{10} = -97.389372410446
x11=−47.1238897272918x_{11} = -47.1238897272918
x12=56.5486676266806x_{12} = 56.5486676266806
x13=−65.9734453602046x_{13} = -65.9734453602046
x14=9.42477806710815x_{14} = 9.42477806710815
x15=87.964594335453x_{15} = 87.964594335453
x16=−21.9911485850965x_{16} = -21.9911485850965
x17=−75.398223834204x_{17} = -75.398223834204
x18=6.28318528433976x_{18} = 6.28318528433976
x19=−94.2477794692392x_{19} = -94.2477794692392
x20=0x_{20} = 0
x21=43.9822971693493x_{21} = 43.9822971693493
x22=−28.2743341055988x_{22} = -28.2743341055988
x23=−53.407075257786x_{23} = -53.407075257786
x24=−59.6902604573056x_{24} = -59.6902604573056
x25=28.2743338652459x_{25} = 28.2743338652459
x26=−56.5486676717583x_{26} = -56.5486676717583
x27=−87.9645943313265x_{27} = -87.9645943313265
x28=−9.42477810445402x_{28} = -9.42477810445402
x29=9.42477801500462x_{29} = 9.42477801500462
x30=188.495558956565x_{30} = 188.495558956565
x31=100.530964781462x_{31} = 100.530964781462
x32=72.2566310277219x_{32} = 72.2566310277219
x33=81.6814091468681x_{33} = 81.6814091468681
x34=62.8318530302311x_{34} = 62.8318530302311
x35=40.8407044744738x_{35} = 40.8407044744738
x36=−6.28318516003462x_{36} = -6.28318516003462
x37=34.5575190494922x_{37} = 34.5575190494922
x38=−25.1327411775878x_{38} = -25.1327411775878
x39=−72.2566308917313x_{39} = -72.2566308917313
x40=−43.982296876345x_{40} = -43.982296876345
x41=−65.9734457508504x_{41} = -65.9734457508504
x42=59.6902605703693x_{42} = 59.6902605703693
x43=15.7079634169143x_{43} = 15.7079634169143
x44=−37.6991118769198x_{44} = -37.6991118769198
x45=−81.6814090375457x_{45} = -81.6814090375457
x46=94.2477796093333x_{46} = 94.2477796093333
x47=28.2743339719516x_{47} = 28.2743339719516
x48=31.4159265728873x_{48} = 31.4159265728873
x49=−50.2654823143599x_{49} = -50.2654823143599
x50=18.8495559220481x_{50} = 18.8495559220481
x51=78.5398162040055x_{51} = 78.5398162040055
x52=−34.5575191076725x_{52} = -34.5575191076725
x53=−87.9645939212567x_{53} = -87.9645939212567
x54=75.3982236794601x_{54} = 75.3982236794601
x55=37.6991119937168x_{55} = 37.6991119937168
x56=−28.2743337371269x_{56} = -28.2743337371269
x57=21.9911485851767x_{57} = 21.9911485851767
x58=−15.7079635369531x_{58} = -15.7079635369531
x59=84.8230015887783x_{59} = 84.8230015887783
x60=−3.14159262806835x_{60} = -3.14159262806835
x61=65.9734458326538x_{61} = 65.9734458326538
x62=−31.4159266812001x_{62} = -31.4159266812001
x63=−15.7079632963762x_{63} = -15.7079632963762
x64=−21.9911486694078x_{64} = -21.9911486694078
x65=−12.5663705453118x_{65} = -12.5663705453118
x66=−100.530964804106x_{66} = -100.530964804106
x67=−78.5398162373076x_{67} = -78.5398162373076
Puntos máximos de la función:
x67=7.85398163397448x_{67} = 7.85398163397448
x67=95.8185759344887x_{67} = 95.8185759344887
x67=−45.553093477052x_{67} = -45.553093477052
x67=−58.1194640914112x_{67} = -58.1194640914112
x67=−80.1106126665397x_{67} = -80.1106126665397
x67=−117.809724509617x_{67} = -117.809724509617
x67=86.3937979737193x_{67} = 86.3937979737193
x67=51.8362787842316x_{67} = 51.8362787842316
x67=−14.1371669411541x_{67} = -14.1371669411541
x67=20.4203522483337x_{67} = 20.4203522483337
x67=−73.8274273593601x_{67} = -73.8274273593601
x67=−29.845130209103x_{67} = -29.845130209103
x67=−89.5353906273091x_{67} = -89.5353906273091
x67=64.4026493985908x_{67} = 64.4026493985908
x67=29.845130209103x_{67} = 29.845130209103
x67=−51.8362787842316x_{67} = -51.8362787842316
x67=−67.5442420521806x_{67} = -67.5442420521806
x67=−36.1283155162826x_{67} = -36.1283155162826
x67=−7.85398163397448x_{67} = -7.85398163397448
x67=14.1371669411541x_{67} = 14.1371669411541
x67=80.1106126665397x_{67} = 80.1106126665397
x67=42.4115008234622x_{67} = 42.4115008234622
x67=36.1283155162826x_{67} = 36.1283155162826
x67=−1.5707963267949x_{67} = -1.5707963267949
x67=−95.8185759344887x_{67} = -95.8185759344887
x67=−23.5619449019235x_{67} = -23.5619449019235
x67=73.8274273593601x_{67} = 73.8274273593601
x67=58.1194640914112x_{67} = 58.1194640914112
Decrece en los intervalos
[188.495558956565,∞)\left[188.495558956565, \infty\right)
Crece en los intervalos
(−∞,−100.530964804106]\left(-\infty, -100.530964804106\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
3(6sin⁡3(x)cos⁡2(x)δ(sin⁡3(x))−sin⁡2(x)sign⁡(sin⁡3(x))+2cos⁡2(x)sign⁡(sin⁡3(x)))sin⁡(x)=03 \left(6 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} \delta\left(\sin^{3}{\left(x \right)}\right) - \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\sin^{3}{\left(x \right)} \right)} + 2 \cos^{2}{\left(x \right)} \operatorname{sign}{\left(\sin^{3}{\left(x \right)} \right)}\right) \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞∣sin⁡3(x)∣=⟨0,1⟩∣⟨−1,1⟩∣\lim_{x \to -\infty} \left|{\sin^{3}{\left(x \right)}}\right| = \left\langle 0, 1\right\rangle \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨0,1⟩∣⟨−1,1⟩∣y = \left\langle 0, 1\right\rangle \left|{\left\langle -1, 1\right\rangle}\right|
lim⁡x→∞∣sin⁡3(x)∣=⟨0,1⟩∣⟨−1,1⟩∣\lim_{x \to \infty} \left|{\sin^{3}{\left(x \right)}}\right| = \left\langle 0, 1\right\rangle \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨0,1⟩∣⟨−1,1⟩∣y = \left\langle 0, 1\right\rangle \left|{\left\langle -1, 1\right\rangle}\right|
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(sin(x)^3), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(∣sin⁡3(x)∣x)=0\lim_{x \to -\infty}\left(\frac{\left|{\sin^{3}{\left(x \right)}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(∣sin⁡3(x)∣x)=0\lim_{x \to \infty}\left(\frac{\left|{\sin^{3}{\left(x \right)}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
∣sin⁡3(x)∣=sin⁡2(x)∣sin⁡(x)∣\left|{\sin^{3}{\left(x \right)}}\right| = \sin^{2}{\left(x \right)} \left|{\sin{\left(x \right)}}\right|
- No
∣sin⁡3(x)∣=−sin⁡2(x)∣sin⁡(x)∣\left|{\sin^{3}{\left(x \right)}}\right| = - \sin^{2}{\left(x \right)} \left|{\sin{\left(x \right)}}\right|
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор