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Trazado el gráfico de la función/ lnx*sin(x)^2

Gráfico de la función y = lnx*sin(x)^2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                 2   
f(x) = log(x)*sin (x)
f(x)=log⁡(x)sin⁡2(x)f{\left(x \right)} = \log{\left(x \right)} \sin^{2}{\left(x \right)} 
f = log(x)*sin(x)^2
Gráfico de la función
02468-8-6-4-2-10102.5-2.5
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:
log⁡(x)sin⁡2(x)=0\log{\left(x \right)} \sin^{2}{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=1x_{1} = 1
x2=πx_{2} = \pi
Solución numérica
x1=100.530964766714x_{1} = 100.530964766714
x2=56.5486676093942x_{2} = 56.5486676093942
x3=−12.5663703688317x_{3} = -12.5663703688317
x4=62.8318528334018x_{4} = 62.8318528334018
x5=65.9734457529035x_{5} = 65.9734457529035
x6=−87.9645943587859x_{6} = -87.9645943587859
x7=−62.8318528390238x_{7} = -62.8318528390238
x8=−75.398223862187x_{8} = -75.398223862187
x9=75.3982242072123x_{9} = 75.3982242072123
x10=69.1150385904649x_{10} = 69.1150385904649
x11=−21.9911485864536x_{11} = -21.9911485864536
x12=−53.4070752838512x_{12} = -53.4070752838512
x13=−56.5486675197118x_{13} = -56.5486675197118
x14=−91.1061872054414x_{14} = -91.1061872054414
x15=37.699112019774x_{15} = 37.699112019774
x16=53.4070753637887x_{16} = 53.4070753637887
x17=59.6902605980227x_{17} = 59.6902605980227
x18=40.8407042574134x_{18} = 40.8407042574134
x19=−91.1061872017085x_{19} = -91.1061872017085
x20=47.1238895923028x_{20} = 47.1238895923028
x21=−84.8230018275441x_{21} = -84.8230018275441
x22=47.1238900212775x_{22} = 47.1238900212775
x23=−43.9822971745836x_{23} = -43.9822971745836
x24=91.1061867326316x_{24} = 91.1061867326316
x25=−40.8407042678506x_{25} = -40.8407042678506
x26=−97.3893724404962x_{26} = -97.3893724404962
x27=−47.1238900499755x_{27} = -47.1238900499755
x28=−25.1327414743941x_{28} = -25.1327414743941
x29=−18.8495556986729x_{29} = -18.8495556986729
x30=−59.6902604576489x_{30} = -59.6902604576489
x31=21.9911485851996x_{31} = 21.9911485851996
x32=18.8495556834211x_{32} = 18.8495556834211
x33=34.5575190309907x_{33} = 34.5575190309907
x34=−69.1150386258394x_{34} = -69.1150386258394
x35=25.1327414538853x_{35} = 25.1327414538853
x36=3.14159296679403x_{36} = 3.14159296679403
x37=−9.42477812775273x_{37} = -9.42477812775273
x38=−65.9734457650256x_{38} = -65.9734457650256
x39=84.8230014098108x_{39} = 84.8230014098108
x40=72.2566310277192x_{40} = 72.2566310277192
x41=78.5398161880055x_{41} = 78.5398161880055
x42=−94.2477794530841x_{42} = -94.2477794530841
x43=81.6814091763464x_{43} = 81.6814091763464
x44=−47.1238901634649x_{44} = -47.1238901634649
x45=−84.8230014108525x_{45} = -84.8230014108525
x46=−69.1150386812732x_{46} = -69.1150386812732
x47=−50.26548229554x_{47} = -50.26548229554
x48=−15.7079632965444x_{48} = -15.7079632965444
x49=−81.6814090380142x_{49} = -81.6814090380142
x50=−28.2743337169939x_{50} = -28.2743337169939
x51=−78.5398160961768x_{51} = -78.5398160961768
x52=−34.5575189435564x_{52} = -34.5575189435564
x53=9.42477821969831x_{53} = 9.42477821969831
x54=−18.849556125498x_{54} = -18.849556125498
x55=25.1327410259853x_{55} = 25.1327410259853
x56=28.274333865208x_{56} = 28.274333865208
x57=31.4159267885251x_{57} = 31.4159267885251
x58=15.7079634423521x_{58} = 15.7079634423521
x59=87.9645943357646x_{59} = 87.9645943357646
x60=75.398223939555x_{60} = 75.398223939555
x61=−62.8318532599408x_{61} = -62.8318532599408
x62=18.849555467321x_{62} = 18.849555467321
x63=43.9822971694319x_{63} = 43.9822971694319
x64=69.1150381619555x_{64} = 69.1150381619555
x65=97.3893727189685x_{65} = 97.3893727189685
x66=−72.2566308742628x_{66} = -72.2566308742628
x67=6.28318528435388x_{67} = 6.28318528435388
x68=94.2477796093525x_{68} = 94.2477796093525
x69=−100.530964672801x_{69} = -100.530964672801
x70=−31.4159267055451x_{70} = -31.4159267055451
x71=12.5663704539928x_{71} = 12.5663704539928
x72=−25.132741657845x_{72} = -25.132741657845
x73=40.8407039438721x_{73} = 40.8407039438721
x74=−3.1415929030096x_{74} = -3.1415929030096
x75=97.3893725153965x_{75} = 97.3893725153965
x76=−40.8407046921536x_{76} = -40.8407046921536
x77=−6.28318513957697x_{77} = -6.28318513957697
x78=91.1061871597628x_{78} = 91.1061871597628
x79=−37.6991118771621x_{79} = -37.6991118771621
x80=50.2654824463487x_{80} = 50.2654824463487
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 log(x)*sin(x)^2.
log⁡(0)sin⁡2(0)\log{\left(0 \right)} \sin^{2}{\left(0 \right)}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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
2log⁡(x)sin⁡(x)cos⁡(x)+sin⁡2(x)x=02 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sin^{2}{\left(x \right)}}{x} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=95.8197196421744x_{1} = 95.8197196421744
x2=80.1120364968984x_{2} = 80.1120364968984
x3=70.6874957987652x_{3} = 70.6874957987652
x4=−6.28318530717959x_{4} = -6.28318530717959
x5=−31.4159265358979x_{5} = -31.4159265358979
x6=67.5459991590417x_{6} = 67.5459991590417
x7=21.9911485751286x_{7} = 21.9911485751286
x8=43.9822971502571x_{8} = 43.9822971502571
x9=15.707963267949x_{9} = 15.707963267949
x10=42.4146464836393x_{10} = 42.4146464836393
x11=7.88468215226503x_{11} = 7.88468215226503
x12=−53.4070751110265x_{12} = -53.4070751110265
x13=92.6781744605177x_{13} = 92.6781744605177
x14=58.1215816459086x_{14} = 58.1215816459086
x15=−9.42477796076938x_{15} = -9.42477796076938
x16=78.5398163397448x_{16} = 78.5398163397448
x17=−81.6814089933346x_{17} = -81.6814089933346
x18=−94.2477796076938x_{18} = -94.2477796076938
x19=36.1321731425561x_{19} = 36.1321731425561
x20=26.7092361429331x_{20} = 26.7092361429331
x21=94.2477796076938x_{21} = 94.2477796076938
x22=12.5663706143592x_{22} = 12.5663706143592
x23=81.6814089933346x_{23} = 81.6814089933346
x24=29.8500622839131x_{24} = 29.8500622839131
x25=−50.2654824574367x_{25} = -50.2654824574367
x26=23.5686584612553x_{26} = 23.5686584612553
x27=−15.707963267949x_{27} = -15.707963267949
x28=64.4045132832651x_{28} = 64.4045132832651
x29=−59.6902604182061x_{29} = -59.6902604182061
x30=270.176968208722x_{30} = 270.176968208722
x31=51.8387217793455x_{31} = 51.8387217793455
x32=6.28318530717959x_{32} = 6.28318530717959
x33=48.697328558041x_{33} = 48.697328558041
x34=73.829001694965x_{34} = 73.829001694965
x35=−87.9645943005142x_{35} = -87.9645943005142
x36=34.5575191894877x_{36} = 34.5575191894877
x37=65.9734457253857x_{37} = 65.9734457253857
x38=−40.8407044966673x_{38} = -40.8407044966673
x39=−37.6991118430775x_{39} = -37.6991118430775
x40=72.2566310325652x_{40} = 72.2566310325652
x41=−43.9822971502571x_{41} = -43.9822971502571
x42=20.4284648400094x_{42} = 20.4284648400094
x43=14.1505011586627x_{43} = 14.1505011586627
x44=−100.530964914873x_{44} = -100.530964914873
x45=45.5559674357001x_{45} = 45.5559674357001
x46=−75.398223686155x_{46} = -75.398223686155
x47=1.94119311490964x_{47} = 1.94119311490964
x48=−97.3893722612836x_{48} = -97.3893722612836
x49=87.9645943005142x_{49} = 87.9645943005142
x50=59.6902604182061x_{50} = 59.6902604182061
x51=100.530964914873x_{51} = 100.530964914873
x52=28.2743338823081x_{52} = 28.2743338823081
x53=−72.2566310325652x_{53} = -72.2566310325652
x54=−21.9911485751286x_{54} = -21.9911485751286
x55=56.5486677646163x_{55} = 56.5486677646163
x56=89.5366330613754x_{56} = 89.5366330613754
x57=−28.2743338823081x_{57} = -28.2743338823081
x58=50.2654824574367x_{58} = 50.2654824574367
x59=−65.9734457253857x_{59} = -65.9734457253857
x60=37.6991118430775x_{60} = 37.6991118430775
x61=86.3950958997003x_{61} = 86.3950958997003
Signos de extremos en los puntos:
(95.81971964217442, 4.56246253755753)

(80.11203649689836, 4.38341722467833)

(70.68749579876517, 4.25825694491077)

(-6.283185307179586, 1.10254964387092e-31 + 5.99903913064743e-32*pi*I)

(-31.41592653589793, 5.17014436343721e-30 + 1.49975978266186e-30*pi*I)

(67.54599915904168, 4.21279582809083)

(21.991148575128552, 2.27125663724702e-30)

(43.982297150257104, 1.11225529081318e-29)

(15.707963267948966, 1.03264752464199e-30)

(42.414646483639295, 3.74745665652845)

(7.884682152265031, 2.06297628658956)

(-53.40707511102649, 8.60546142301337e-30 + 2.16329417632678e-30*pi*I)

(92.67817446051765, 4.52912657571395)

(58.12158164590861, 4.06251883524572)

(-9.42477796076938, 3.0280269348815e-31 + 1.34978380439567e-31*pi*I)

(78.53981633974483, 1.05239675280611e-30)

(-81.68140899333463, 6.77020503227825e-29 + 1.53769519406264e-29*pi*I)

(-94.2477796076938, 5.35287607041647e-29 + 1.17751027577409e-29*pi*I)

(36.132173142556084, 3.5871303095993)

(26.709236142933094, 3.28490275263666)

(94.2477796076938, 5.35287607041647e-29)

(12.566370614359172, 6.07348539927449e-31)

(81.68140899333463, 6.77020503227825e-29)

(29.85006228391305, 3.39610431359338)

(-50.26548245743669, 1.50400944749698e-29 + 3.83938504361436e-30*pi*I)

(23.568658461255307, 3.15977537682115)

(-15.707963267948966, 1.03264752464199e-30 + 3.74939945665464e-31*pi*I)

(64.40451328326512, 4.16516924258626)

(-59.69026041820607, 6.14517616924322e-30 + 1.5027934458313e-30*pi*I)

(270.1769682087222, 1.7417470442363e-27)

(51.838721779345526, 3.94811383137987)

(6.283185307179586, 1.10254964387092e-31)

(48.69732855804098, 3.88559704250618)

(73.82900169496496, 4.30174096928494)

(-87.96459430051421, 5.26403170691023e-29 + 1.1758116696069e-29*pi*I)

(34.55751918948773, 1.72337415243203e-29)

(65.97344572538566, 4.03120648719441e-30)

(-40.840704496667314, 1.42608898598829e-29 + 3.84423798515659e-30*pi*I)

(-37.69911184307752, 7.83875937863388e-30 + 2.15965408703307e-30*pi*I)

(72.25663103256524, 1.73645580663874e-28)

(-43.982297150257104, 1.11225529081318e-29 + 2.93952917401724e-30*pi*I)

(20.428464840009365, 3.01673071130889)

(14.150501158662737, 2.64927893980534)

(-100.53096491487338, 7.08054135721405e-29 + 1.53575401744574e-29*pi*I)

(45.55596743570007, 3.81891008060303)

(-75.39822368615503, 3.73428700801825e-29 + 8.6386163481323e-30*pi*I)

(1.9411931149096389, 0.576387980778498)

(-97.3893722612836, 2.15581661527067e-28 + 4.70834203716472e-29*pi*I)

(87.96459430051421, 5.26403170691023e-29)

(59.69026041820607, 6.14517616924322e-30)

(100.53096491487338, 7.08054135721405e-29)

(28.274333882308138, 4.0598244084922e-30)

(-72.25663103256524, 1.73645580663874e-28 + 4.05692731349557e-29*pi*I)

(-21.991148575128552, 2.27125663724702e-30 + 7.3488229350431e-31*pi*I)

(56.548667764616276, 1.96074534521452e-29)

(89.53663306137544, 4.49464091136003)

(-28.274333882308138, 4.0598244084922e-30 + 1.2148054239561e-30*pi*I)

(50.26548245743669, 1.50400944749698e-29)

(-65.97344572538566, 4.03120648719441e-30 + 9.62273497948765e-31*pi*I)

(37.69911184307752, 7.83875937863388e-30)

(86.39509589970032, 4.45892340221529)


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=−6.28318530717959x_{1} = -6.28318530717959
x2=−31.4159265358979x_{2} = -31.4159265358979
x3=21.9911485751286x_{3} = 21.9911485751286
x4=43.9822971502571x_{4} = 43.9822971502571
x5=15.707963267949x_{5} = 15.707963267949
x6=−53.4070751110265x_{6} = -53.4070751110265
x7=−9.42477796076938x_{7} = -9.42477796076938
x8=78.5398163397448x_{8} = 78.5398163397448
x9=−81.6814089933346x_{9} = -81.6814089933346
x10=−94.2477796076938x_{10} = -94.2477796076938
x11=94.2477796076938x_{11} = 94.2477796076938
x12=12.5663706143592x_{12} = 12.5663706143592
x13=81.6814089933346x_{13} = 81.6814089933346
x14=−50.2654824574367x_{14} = -50.2654824574367
x15=−15.707963267949x_{15} = -15.707963267949
x16=−59.6902604182061x_{16} = -59.6902604182061
x17=270.176968208722x_{17} = 270.176968208722
x18=6.28318530717959x_{18} = 6.28318530717959
x19=−87.9645943005142x_{19} = -87.9645943005142
x20=34.5575191894877x_{20} = 34.5575191894877
x21=65.9734457253857x_{21} = 65.9734457253857
x22=−40.8407044966673x_{22} = -40.8407044966673
x23=−37.6991118430775x_{23} = -37.6991118430775
x24=72.2566310325652x_{24} = 72.2566310325652
x25=−43.9822971502571x_{25} = -43.9822971502571
x26=−100.530964914873x_{26} = -100.530964914873
x27=−75.398223686155x_{27} = -75.398223686155
x28=−97.3893722612836x_{28} = -97.3893722612836
x29=87.9645943005142x_{29} = 87.9645943005142
x30=59.6902604182061x_{30} = 59.6902604182061
x31=100.530964914873x_{31} = 100.530964914873
x32=28.2743338823081x_{32} = 28.2743338823081
x33=−72.2566310325652x_{33} = -72.2566310325652
x34=−21.9911485751286x_{34} = -21.9911485751286
x35=56.5486677646163x_{35} = 56.5486677646163
x36=−28.2743338823081x_{36} = -28.2743338823081
x37=50.2654824574367x_{37} = 50.2654824574367
x38=−65.9734457253857x_{38} = -65.9734457253857
x39=37.6991118430775x_{39} = 37.6991118430775
Puntos máximos de la función:
x39=95.8197196421744x_{39} = 95.8197196421744
x39=80.1120364968984x_{39} = 80.1120364968984
x39=70.6874957987652x_{39} = 70.6874957987652
x39=67.5459991590417x_{39} = 67.5459991590417
x39=42.4146464836393x_{39} = 42.4146464836393
x39=7.88468215226503x_{39} = 7.88468215226503
x39=92.6781744605177x_{39} = 92.6781744605177
x39=58.1215816459086x_{39} = 58.1215816459086
x39=36.1321731425561x_{39} = 36.1321731425561
x39=26.7092361429331x_{39} = 26.7092361429331
x39=29.8500622839131x_{39} = 29.8500622839131
x39=23.5686584612553x_{39} = 23.5686584612553
x39=64.4045132832651x_{39} = 64.4045132832651
x39=51.8387217793455x_{39} = 51.8387217793455
x39=48.697328558041x_{39} = 48.697328558041
x39=73.829001694965x_{39} = 73.829001694965
x39=20.4284648400094x_{39} = 20.4284648400094
x39=14.1505011586627x_{39} = 14.1505011586627
x39=45.5559674357001x_{39} = 45.5559674357001
x39=1.94119311490964x_{39} = 1.94119311490964
x39=89.5366330613754x_{39} = 89.5366330613754
x39=86.3950958997003x_{39} = 86.3950958997003
Decrece en los intervalos
[270.176968208722,∞)\left[270.176968208722, \infty\right)
Crece en los intervalos
(−∞,−100.530964914873]\left(-\infty, -100.530964914873\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
−2(sin⁡2(x)−cos⁡2(x))log⁡(x)+4sin⁡(x)cos⁡(x)x−sin⁡2(x)x2=0- 2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \log{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} - \frac{\sin^{2}{\left(x \right)}}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=24.3538383764564x_{1} = 24.3538383764564
x2=96.6051094036356x_{2} = 96.6051094036356
x3=69.9021146690577x_{3} = 69.9021146690577
x4=68.3313786837675x_{4} = 68.3313786837675
x5=46.3413193708802x_{5} = 46.3413193708802
x6=49.4826871182256x_{6} = 49.4826871182256
x7=16.5039986039154x_{7} = 16.5039986039154
x8=32.2057609130582x_{8} = 32.2057609130582
x9=2.56372347785954x_{9} = 2.56372347785954
x10=74.6143846512062x_{10} = 74.6143846512062
x11=109.171322870945x_{11} = 109.171322870945
x12=63.6191362325953x_{12} = 63.6191362325953
x13=77.7558999415355x_{13} = 77.7558999415355
x14=5.55222612151163x_{14} = 5.55222612151163
x15=85.6097084865142x_{15} = 85.6097084865142
x16=41.6293042263401x_{16} = 41.6293042263401
x17=47.911970825717x_{17} = 47.911970825717
x18=30.6353359960064x_{18} = 30.6353359960064
x19=4.00943109513867x_{19} = 4.00943109513867
x20=25.9240063903879x_{20} = 25.9240063903879
x21=82.4681770421537x_{21} = 82.4681770421537
x22=40.0587094975312x_{22} = 40.0587094975312
x23=88.7512448059522x_{23} = 88.7512448059522
x24=99.7466585671434x_{24} = 99.7466585671434
x25=76.1851314475436x_{25} = 76.1851314475436
x26=33.7763575468426x_{26} = 33.7763575468426
x27=55.7655092736559x_{27} = 55.7655092736559
x28=66.7606199103709x_{28} = 66.7606199103709
x29=98.1758779372257x_{29} = 98.1758779372257
x30=90.3220214249147x_{30} = 90.3220214249147
x31=10.2306466686845x_{31} = 10.2306466686845
x32=18.0738438609999x_{32} = 18.0738438609999
x33=52.6240856735649x_{33} = 52.6240856735649
x34=93.4635635620593x_{34} = 93.4635635620593
x35=91.8927854554234x_{35} = 91.8927854554234
x36=19.643390684436x_{36} = 19.643390684436
x37=8.66679695828245x_{37} = 8.66679695828245
x38=38.4880455188002x_{38} = 38.4880455188002
x39=60.4776655555505x_{39} = 60.4776655555505
x40=84.0389501054096x_{40} = 84.0389501054096
x41=11.7984879147268x_{41} = 11.7984879147268
x42=54.1947733288452x_{42} = 54.1947733288452
x43=27.4944723337379x_{43} = 27.4944723337379
x44=62.048414862195x_{44} = 62.048414862195

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[109.171322870945,∞)\left[109.171322870945, \infty\right)
Convexa en los intervalos
(−∞,2.56372347785954]\left(-\infty, 2.56372347785954\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(log⁡(x)sin⁡2(x))=⟨0,∞⟩\lim_{x \to -\infty}\left(\log{\left(x \right)} \sin^{2}{\left(x \right)}\right) = \left\langle 0, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨0,∞⟩y = \left\langle 0, \infty\right\rangle
lim⁡x→∞(log⁡(x)sin⁡2(x))=⟨0,∞⟩\lim_{x \to \infty}\left(\log{\left(x \right)} \sin^{2}{\left(x \right)}\right) = \left\langle 0, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨0,∞⟩y = \left\langle 0, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función log(x)*sin(x)^2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(log⁡(x)sin⁡2(x)x)=0\lim_{x \to -\infty}\left(\frac{\log{\left(x \right)} \sin^{2}{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(log⁡(x)sin⁡2(x)x)=0\lim_{x \to \infty}\left(\frac{\log{\left(x \right)} \sin^{2}{\left(x \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:
log⁡(x)sin⁡2(x)=log⁡(−x)sin⁡2(x)\log{\left(x \right)} \sin^{2}{\left(x \right)} = \log{\left(- x \right)} \sin^{2}{\left(x \right)}
- No
log⁡(x)sin⁡2(x)=−log⁡(−x)sin⁡2(x)\log{\left(x \right)} \sin^{2}{\left(x \right)} = - \log{\left(- x \right)} \sin^{2}{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор