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Trazado el gráfico de la función/ sin(x)*atan(x)

Gráfico de la función y = sin(x)*atan(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = sin(x)*atan(x)
f(x)=sin⁡(x)atan⁡(x)f{\left(x \right)} = \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} 
f = sin(x)*atan(x)
Gráfico de la función
02468-8-6-4-2-10105-5
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:
sin⁡(x)atan⁡(x)=0\sin{\left(x \right)} \operatorname{atan}{\left(x \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=69.1150383789755x_{1} = 69.1150383789755
x2=65.9734457253857x_{2} = 65.9734457253857
x3=−91.106186954104x_{3} = -91.106186954104
x4=163.362817986669x_{4} = 163.362817986669
x5=−59.6902604182061x_{5} = -59.6902604182061
x6=−21.9911485751286x_{6} = -21.9911485751286
x7=12.5663706143592x_{7} = 12.5663706143592
x8=21.9911485751286x_{8} = 21.9911485751286
x9=−69.1150383789755x_{9} = -69.1150383789755
x10=−100.530964914873x_{10} = -100.530964914873
x11=3.14159265358979x_{11} = 3.14159265358979
x12=−3.14159265358979x_{12} = -3.14159265358979
x13=−25.1327412287183x_{13} = -25.1327412287183
x14=−15.707963267949x_{14} = -15.707963267949
x15=−53.4070751110265x_{15} = -53.4070751110265
x16=−72.2566310325652x_{16} = -72.2566310325652
x17=84.8230016469244x_{17} = 84.8230016469244
x18=−81.6814089933346x_{18} = -81.6814089933346
x19=−94.2477796076938x_{19} = -94.2477796076938
x20=18.8495559215388x_{20} = 18.8495559215388
x21=−65.9734457253857x_{21} = -65.9734457253857
x22=94.2477796076938x_{22} = 94.2477796076938
x23=9.42477796076938x_{23} = 9.42477796076938
x24=−40.8407044966673x_{24} = -40.8407044966673
x25=−122.522113490002x_{25} = -122.522113490002
x26=34.5575191894877x_{26} = 34.5575191894877
x27=292.168116783851x_{27} = 292.168116783851
x28=0x_{28} = 0
x29=53.4070751110265x_{29} = 53.4070751110265
x30=97.3893722612836x_{30} = 97.3893722612836
x31=−62.8318530717959x_{31} = -62.8318530717959
x32=59.6902604182061x_{32} = 59.6902604182061
x33=−28.2743338823081x_{33} = -28.2743338823081
x34=−56.5486677646163x_{34} = -56.5486677646163
x35=91.106186954104x_{35} = 91.106186954104
x36=15.707963267949x_{36} = 15.707963267949
x37=−18.8495559215388x_{37} = -18.8495559215388
x38=6.28318530717959x_{38} = 6.28318530717959
x39=56.5486677646163x_{39} = 56.5486677646163
x40=87.9645943005142x_{40} = 87.9645943005142
x41=31.4159265358979x_{41} = 31.4159265358979
x42=25.1327412287183x_{42} = 25.1327412287183
x43=43.9822971502571x_{43} = 43.9822971502571
x44=−47.1238898038469x_{44} = -47.1238898038469
x45=72.2566310325652x_{45} = 72.2566310325652
x46=−34.5575191894877x_{46} = -34.5575191894877
x47=−97.3893722612836x_{47} = -97.3893722612836
x48=−50.2654824574367x_{48} = -50.2654824574367
x49=100.530964914873x_{49} = 100.530964914873
x50=1030.44239037745x_{50} = 1030.44239037745
x51=81.6814089933346x_{51} = 81.6814089933346
x52=−75.398223686155x_{52} = -75.398223686155
x53=40.8407044966673x_{53} = 40.8407044966673
x54=−9.42477796076938x_{54} = -9.42477796076938
x55=78.5398163397448x_{55} = 78.5398163397448
x56=−87.9645943005142x_{56} = -87.9645943005142
x57=37.6991118430775x_{57} = 37.6991118430775
x58=−78.5398163397448x_{58} = -78.5398163397448
x59=−6.28318530717959x_{59} = -6.28318530717959
x60=50.2654824574367x_{60} = 50.2654824574367
x61=−37.6991118430775x_{61} = -37.6991118430775
x62=−43.9822971502571x_{62} = -43.9822971502571
x63=47.1238898038469x_{63} = 47.1238898038469
x64=28.2743338823081x_{64} = 28.2743338823081
x65=62.8318530717959x_{65} = 62.8318530717959
x66=−31.4159265358979x_{66} = -31.4159265358979
x67=−12.5663706143592x_{67} = -12.5663706143592
x68=75.398223686155x_{68} = 75.398223686155
x69=−84.8230016469244x_{69} = -84.8230016469244
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 sin(x)*atan(x).
sin⁡(0)atan⁡(0)\sin{\left(0 \right)} \operatorname{atan}{\left(0 \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
cos⁡(x)atan⁡(x)+sin⁡(x)x2+1=0\cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin{\left(x \right)}}{x^{2} + 1} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−61.2612281128569x_{1} = -61.2612281128569
x2=73.827545153735x_{2} = 73.827545153735
x3=1.79103397776014x_{3} = 1.79103397776014
x4=−4.74359618362999x_{4} = -4.74359618362999
x5=−1.79103397776014x_{5} = -1.79103397776014
x6=54.9780844551589x_{6} = 54.9780844551589
x7=−11.0011109024118x_{7} = -11.0011109024118
x8=4.74359618362999x_{8} = 4.74359618362999
x9=17.2809654364073x_{9} = 17.2809654364073
x10=−76.9691283508747x_{10} = -76.9691283508747
x11=−45.5534044627264x_{11} = -45.5534044627264
x12=29.8458596412272x_{12} = 29.8458596412272
x13=95.8186457300403x_{13} = 95.8186457300403
x14=39.2703275097022x_{14} = 39.2703275097022
x15=45.5534044627264x_{15} = 45.5534044627264
x16=−86.3938838884988x_{16} = -86.3938838884988
x17=11.0011109024118x_{17} = 11.0011109024118
x18=20.4219240188353x_{18} = 20.4219240188353
x19=26.7044507808002x_{19} = 26.7044507808002
x20=98.9602340090719x_{20} = 98.9602340090719
x21=−80.1107126426188x_{21} = -80.1107126426188
x22=32.987318864864x_{22} = 32.987318864864
x23=−32.987318864864x_{23} = -32.987318864864
x24=−89.5354705986824x_{24} = -89.5354705986824
x25=−64.4028043800929x_{25} = -64.4028043800929
x26=−51.8365185642119x_{26} = -51.8365185642119
x27=67.5443828898684x_{27} = 67.5443828898684
x28=48.694958052076x_{28} = 48.694958052076
x29=−70.6859632509207x_{29} = -70.6859632509207
x30=51.8365185642119x_{30} = 51.8365185642119
x31=−54.9780844551589x_{31} = -54.9780844551589
x32=0x_{32} = 0
x33=−92.6770579048997x_{33} = -92.6770579048997
x34=−42.4118599365484x_{34} = -42.4118599365484
x35=83.2522978663322x_{35} = 83.2522978663322
x36=−14.1404840184881x_{36} = -14.1404840184881
x37=−98.9602340090719x_{37} = -98.9602340090719
x38=−95.8186457300403x_{38} = -95.8186457300403
x39=−23.5631212086715x_{39} = -23.5631212086715
x40=7.8649958747173x_{40} = 7.8649958747173
x41=89.5354705986824x_{41} = 89.5354705986824
x42=−73.827545153735x_{42} = -73.827545153735
x43=80.1107126426188x_{43} = 80.1107126426188
x44=92.6770579048997x_{44} = 92.6770579048997
x45=61.2612281128569x_{45} = 61.2612281128569
x46=23.5631212086715x_{46} = 23.5631212086715
x47=−36.1288116046131x_{47} = -36.1288116046131
x48=−26.7044507808002x_{48} = -26.7044507808002
x49=−29.8458596412272x_{49} = -29.8458596412272
x50=−58.1196545885159x_{50} = -58.1196545885159
x51=−7.8649958747173x_{51} = -7.8649958747173
x52=−48.694958052076x_{52} = -48.694958052076
x53=−39.2703275097022x_{53} = -39.2703275097022
x54=76.9691283508747x_{54} = 76.9691283508747
x55=64.4028043800929x_{55} = 64.4028043800929
x56=42.4118599365484x_{56} = 42.4118599365484
x57=−20.4219240188353x_{57} = -20.4219240188353
x58=−67.5443828898684x_{58} = -67.5443828898684
x59=−17.2809654364073x_{59} = -17.2809654364073
x60=36.1288116046131x_{60} = 36.1288116046131
x61=70.6859632509207x_{61} = 70.6859632509207
x62=86.3938838884988x_{62} = 86.3938838884988
x63=−83.2522978663322x_{63} = -83.2522978663322
x64=14.1404840184881x_{64} = 14.1404840184881
x65=58.1196545885159x_{65} = 58.1196545885159
Signos de extremos en los puntos:
(-61.26122811285691, -1.5544742153389)

(73.82754515373497, -1.5572520643401)

(1.7910339777601358, 1.03593336473382)

(-4.7435961836299905, -1.36236430357899)

(-1.7910339777601358, 1.03593336473382)

(54.97808445515894, -1.55260923119595)

(-11.001110902411808, -1.4801228582299)

(4.7435961836299905, -1.36236430357899)

(17.280965436407328, -1.51298997049872)

(-76.96912835087466, 1.55780482663327)

(-45.553404462726384, 1.54884752107669)

(29.84585964122719, -1.53730296241164)

(95.8186457300403, 1.56036031976415)

(39.270327509702184, 1.54533717389503)

(45.553404462726384, 1.54884752107669)

(-86.39388388849885, -1.55922194448498)

(11.001110902411808, -1.4801228582299)

(20.42192401883534, 1.52186654514573)

(26.704450780800197, 1.53336623503182)

(98.96023400907185, -1.56069159831347)

(-80.11071264261882, -1.55831424223611)

(32.98731886486398, 1.54049065473337)

(-32.98731886486398, 1.54049065473337)

(-89.53547059868244, 1.55962802821361)

(-64.4028043800929, 1.5552702816364)

(-51.83651856421186, 1.55150725579965)

(67.54438288986843, -1.55599231281641)

(48.694958052076046, -1.55026314860543)

(-70.68596325092066, 1.55665017729342)

(51.83651856421186, 1.55150725579965)

(-54.97808445515894, -1.55260923119595)

(0, 0)

(-92.6770579048997, -1.5600065842339)

(-42.41185993654844, -1.54722228447912)

(83.25229786633224, 1.55878521728754)

(-14.140484018488104, 1.50018667629801)

(-98.96023400907185, -1.56069159831347)

(-95.8186457300403, 1.56036031976415)

(-23.56312120867149, -1.52838152134177)

(7.864995874717303, 1.44424164730901)

(89.53547059868244, 1.55962802821361)

(-73.82754515373497, -1.5572520643401)

(80.11071264261882, -1.55831424223611)

(92.6770579048997, -1.5600065842339)

(61.26122811285691, -1.5544742153389)

(23.56312120867149, -1.52838152134177)

(-36.128811604613105, -1.54312446153498)

(-26.704450780800197, 1.53336623503182)

(-29.84585964122719, -1.53730296241164)

(-58.119654588515886, 1.55359211279627)

(-7.864995874717303, 1.44424164730901)

(-48.694958052076046, -1.55026314860543)

(-39.270327509702184, 1.54533717389503)

(76.96912835087466, 1.55780482663327)

(64.4028043800929, 1.5552702816364)

(42.41185993654844, -1.54722228447912)

(-20.42192401883534, 1.52186654514573)

(-67.54438288986843, -1.55599231281641)

(-17.280965436407328, -1.51298997049872)

(36.128811604613105, -1.54312446153498)

(70.68596325092066, 1.55665017729342)

(86.39388388849885, -1.55922194448498)

(-83.25229786633224, 1.55878521728754)

(14.140484018488104, 1.50018667629801)

(58.119654588515886, 1.55359211279627)


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=−61.2612281128569x_{1} = -61.2612281128569
x2=73.827545153735x_{2} = 73.827545153735
x3=−4.74359618362999x_{3} = -4.74359618362999
x4=54.9780844551589x_{4} = 54.9780844551589
x5=−11.0011109024118x_{5} = -11.0011109024118
x6=4.74359618362999x_{6} = 4.74359618362999
x7=17.2809654364073x_{7} = 17.2809654364073
x8=29.8458596412272x_{8} = 29.8458596412272
x9=−86.3938838884988x_{9} = -86.3938838884988
x10=11.0011109024118x_{10} = 11.0011109024118
x11=98.9602340090719x_{11} = 98.9602340090719
x12=−80.1107126426188x_{12} = -80.1107126426188
x13=67.5443828898684x_{13} = 67.5443828898684
x14=48.694958052076x_{14} = 48.694958052076
x15=−54.9780844551589x_{15} = -54.9780844551589
x16=0x_{16} = 0
x17=−92.6770579048997x_{17} = -92.6770579048997
x18=−42.4118599365484x_{18} = -42.4118599365484
x19=−98.9602340090719x_{19} = -98.9602340090719
x20=−23.5631212086715x_{20} = -23.5631212086715
x21=−73.827545153735x_{21} = -73.827545153735
x22=80.1107126426188x_{22} = 80.1107126426188
x23=92.6770579048997x_{23} = 92.6770579048997
x24=61.2612281128569x_{24} = 61.2612281128569
x25=23.5631212086715x_{25} = 23.5631212086715
x26=−36.1288116046131x_{26} = -36.1288116046131
x27=−29.8458596412272x_{27} = -29.8458596412272
x28=−48.694958052076x_{28} = -48.694958052076
x29=42.4118599365484x_{29} = 42.4118599365484
x30=−67.5443828898684x_{30} = -67.5443828898684
x31=−17.2809654364073x_{31} = -17.2809654364073
x32=36.1288116046131x_{32} = 36.1288116046131
x33=86.3938838884988x_{33} = 86.3938838884988
Puntos máximos de la función:
x33=1.79103397776014x_{33} = 1.79103397776014
x33=−1.79103397776014x_{33} = -1.79103397776014
x33=−76.9691283508747x_{33} = -76.9691283508747
x33=−45.5534044627264x_{33} = -45.5534044627264
x33=95.8186457300403x_{33} = 95.8186457300403
x33=39.2703275097022x_{33} = 39.2703275097022
x33=45.5534044627264x_{33} = 45.5534044627264
x33=20.4219240188353x_{33} = 20.4219240188353
x33=26.7044507808002x_{33} = 26.7044507808002
x33=32.987318864864x_{33} = 32.987318864864
x33=−32.987318864864x_{33} = -32.987318864864
x33=−89.5354705986824x_{33} = -89.5354705986824
x33=−64.4028043800929x_{33} = -64.4028043800929
x33=−51.8365185642119x_{33} = -51.8365185642119
x33=−70.6859632509207x_{33} = -70.6859632509207
x33=51.8365185642119x_{33} = 51.8365185642119
x33=83.2522978663322x_{33} = 83.2522978663322
x33=−14.1404840184881x_{33} = -14.1404840184881
x33=−95.8186457300403x_{33} = -95.8186457300403
x33=7.8649958747173x_{33} = 7.8649958747173
x33=89.5354705986824x_{33} = 89.5354705986824
x33=−26.7044507808002x_{33} = -26.7044507808002
x33=−58.1196545885159x_{33} = -58.1196545885159
x33=−7.8649958747173x_{33} = -7.8649958747173
x33=−39.2703275097022x_{33} = -39.2703275097022
x33=76.9691283508747x_{33} = 76.9691283508747
x33=64.4028043800929x_{33} = 64.4028043800929
x33=−20.4219240188353x_{33} = -20.4219240188353
x33=70.6859632509207x_{33} = 70.6859632509207
x33=−83.2522978663322x_{33} = -83.2522978663322
x33=14.1404840184881x_{33} = 14.1404840184881
x33=58.1196545885159x_{33} = 58.1196545885159
Decrece en los intervalos
[98.9602340090719,∞)\left[98.9602340090719, \infty\right)
Crece en los intervalos
(−∞,−98.9602340090719]\left(-\infty, -98.9602340090719\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
−2xsin⁡(x)(x2+1)2−sin⁡(x)atan⁡(x)+2cos⁡(x)x2+1=0- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−28.2759609016006x_{1} = -28.2759609016006
x2=21.9938531789562x_{2} = 21.9938531789562
x3=−18.8532519435147x_{3} = -18.8532519435147
x4=15.7133138949299x_{4} = 15.7133138949299
x5=−72.256877018428x_{5} = -72.256877018428
x6=75.3984495204372x_{6} = 75.3984495204372
x7=18.8532519435147x_{7} = 18.8532519435147
x8=−21.9938531789562x_{8} = -21.9938531789562
x9=43.9829646343884x_{9} = 43.9829646343884
x10=87.9647600263064x_{10} = 87.9647600263064
x11=−53.4075267137478x_{11} = -53.4075267137478
x12=−87.9647600263064x_{12} = -87.9647600263064
x13=−56.5490703302555x_{13} = -56.5490703302555
x14=−81.6816012996122x_{14} = -81.6816012996122
x15=65.9737410345762x_{15} = 65.9737410345762
x16=56.5490703302555x_{16} = 56.5490703302555
x17=40.8414794224676x_{17} = 40.8414794224676
x18=78.5400244008501x_{18} = 78.5400244008501
x19=72.256877018428x_{19} = 72.256877018428
x20=−43.9829646343884x_{20} = -43.9829646343884
x21=31.4172417711937x_{21} = 31.4172417711937
x22=3.27025559384994x_{22} = 3.27025559384994
x23=−94.2479239057106x_{23} = -94.2479239057106
x24=−15.7133138949299x_{24} = -15.7133138949299
x25=−3.27025559384994x_{25} = -3.27025559384994
x26=84.8231799223075x_{26} = 84.8231799223075
x27=−12.5747920390384x_{27} = -12.5747920390384
x28=−37.7000223964691x_{28} = -37.7000223964691
x29=−97.3895073712924x_{29} = -97.3895073712924
x30=−50.2659926334542x_{30} = -50.2659926334542
x31=−84.8231799223075x_{31} = -84.8231799223075
x32=−78.5400244008501x_{32} = -78.5400244008501
x33=12.5747920390384x_{33} = 12.5747920390384
x34=−25.134805522921x_{34} = -25.134805522921
x35=−59.690621520068x_{35} = -59.690621520068
x36=28.2759609016006x_{36} = 28.2759609016006
x37=−31.4172417711937x_{37} = -31.4172417711937
x38=−75.3984495204372x_{38} = -75.3984495204372
x39=62.8321788004678x_{39} = 62.8321788004678
x40=37.7000223964691x_{40} = 37.7000223964691
x41=6.31756549582733x_{41} = 6.31756549582733
x42=147.654913369085x_{42} = 147.654913369085
x43=69.1153073388908x_{43} = 69.1153073388908
x44=−47.1244707319001x_{44} = -47.1244707319001
x45=91.1063414102081x_{45} = 91.1063414102081
x46=0.777864066729225x_{46} = 0.777864066729225
x47=−100.531091687256x_{47} = -100.531091687256
x48=34.558604347829x_{48} = 34.558604347829
x49=100.531091687256x_{49} = 100.531091687256
x50=−62.8321788004678x_{50} = -62.8321788004678
x51=97.3895073712924x_{51} = 97.3895073712924
x52=−65.9737410345762x_{52} = -65.9737410345762
x53=59.690621520068x_{53} = 59.690621520068
x54=25.134805522921x_{54} = 25.134805522921
x55=53.4075267137478x_{55} = 53.4075267137478
x56=−34.558604347829x_{56} = -34.558604347829
x57=81.6816012996122x_{57} = 81.6816012996122
x58=50.2659926334542x_{58} = 50.2659926334542
x59=−40.8414794224676x_{59} = -40.8414794224676
x60=9.43990010438496x_{60} = 9.43990010438496
x61=−6.31756549582733x_{61} = -6.31756549582733
x62=94.2479239057106x_{62} = 94.2479239057106
x63=47.1244707319001x_{63} = 47.1244707319001
x64=−9.43990010438496x_{64} = -9.43990010438496
x65=−69.1153073388908x_{65} = -69.1153073388908
x66=−91.1063414102081x_{66} = -91.1063414102081
x67=−103.672676751813x_{67} = -103.672676751813

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
[147.654913369085,∞)\left[147.654913369085, \infty\right)
Convexa en los intervalos
(−∞,−100.531091687256]\left(-\infty, -100.531091687256\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(x)atan⁡(x))=⟨−12,12⟩π\lim_{x \to -\infty}\left(\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−12,12⟩πy = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
lim⁡x→∞(sin⁡(x)atan⁡(x))=⟨−12,12⟩π\lim_{x \to \infty}\left(\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−12,12⟩πy = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x)*atan(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x)atan⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(x)atan⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \operatorname{atan}{\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:
sin⁡(x)atan⁡(x)=sin⁡(x)atan⁡(x)\sin{\left(x \right)} \operatorname{atan}{\left(x \right)} = \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}
- No
sin⁡(x)atan⁡(x)=−sin⁡(x)atan⁡(x)\sin{\left(x \right)} \operatorname{atan}{\left(x \right)} = - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор