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(sinx)/x
Trazado el gráfico de la función/ (sinx)/x

Gráfico de la función y = (sinx)/x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       sin(x)
f(x) = ------
         x
f(x)=sin⁡(x)xf{\left(x \right)} = \frac{\sin{\left(x \right)}}{x} 
f = sin(x)/x
Gráfico de la función
02468-8-6-4-2-10102-1
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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)x=0\frac{\sin{\left(x \right)}}{x} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=πx_{1} = \pi
Solución numérica
x1=−59.6902604182061x_{1} = -59.6902604182061
x2=−62.8318530717959x_{2} = -62.8318530717959
x3=−97.3893722612836x_{3} = -97.3893722612836
x4=87.9645943005142x_{4} = 87.9645943005142
x5=−56.5486677646163x_{5} = -56.5486677646163
x6=31.4159265358979x_{6} = 31.4159265358979
x7=69.1150383789755x_{7} = 69.1150383789755
x8=−370.707933123596x_{8} = -370.707933123596
x9=−37.6991118430775x_{9} = -37.6991118430775
x10=−81.6814089933346x_{10} = -81.6814089933346
x11=153.9380400259x_{11} = 153.9380400259
x12=−84.8230016469244x_{12} = -84.8230016469244
x13=−21.9911485751286x_{13} = -21.9911485751286
x14=47.1238898038469x_{14} = 47.1238898038469
x15=−113.097335529233x_{15} = -113.097335529233
x16=−223.053078404875x_{16} = -223.053078404875
x17=−12.5663706143592x_{17} = -12.5663706143592
x18=−15.707963267949x_{18} = -15.707963267949
x19=12.5663706143592x_{19} = 12.5663706143592
x20=−87.9645943005142x_{20} = -87.9645943005142
x21=53.4070751110265x_{21} = 53.4070751110265
x22=72.2566310325652x_{22} = 72.2566310325652
x23=−100.530964914873x_{23} = -100.530964914873
x24=−3.14159265358979x_{24} = -3.14159265358979
x25=34.5575191894877x_{25} = 34.5575191894877
x26=−94.2477796076938x_{26} = -94.2477796076938
x27=6.28318530717959x_{27} = 6.28318530717959
x28=−69.1150383789755x_{28} = -69.1150383789755
x29=97.3893722612836x_{29} = 97.3893722612836
x30=65.9734457253857x_{30} = 65.9734457253857
x31=590.619418874881x_{31} = 590.619418874881
x32=−50.2654824574367x_{32} = -50.2654824574367
x33=15.707963267949x_{33} = 15.707963267949
x34=3.14159265358979x_{34} = 3.14159265358979
x35=−25.1327412287183x_{35} = -25.1327412287183
x36=−18.8495559215388x_{36} = -18.8495559215388
x37=40.8407044966673x_{37} = 40.8407044966673
x38=−53.4070751110265x_{38} = -53.4070751110265
x39=37.6991118430775x_{39} = 37.6991118430775
x40=−43.9822971502571x_{40} = -43.9822971502571
x41=18.8495559215388x_{41} = 18.8495559215388
x42=−78.5398163397448x_{42} = -78.5398163397448
x43=−6.28318530717959x_{43} = -6.28318530717959
x44=−40.8407044966673x_{44} = -40.8407044966673
x45=43.9822971502571x_{45} = 43.9822971502571
x46=56.5486677646163x_{46} = 56.5486677646163
x47=−65.9734457253857x_{47} = -65.9734457253857
x48=25.1327412287183x_{48} = 25.1327412287183
x49=78.5398163397448x_{49} = 78.5398163397448
x50=−28.2743338823081x_{50} = -28.2743338823081
x51=75.398223686155x_{51} = 75.398223686155
x52=59.6902604182061x_{52} = 59.6902604182061
x53=−34.5575191894877x_{53} = -34.5575191894877
x54=81.6814089933346x_{54} = 81.6814089933346
x55=−47.1238898038469x_{55} = -47.1238898038469
x56=100.530964914873x_{56} = 100.530964914873
x57=−9.42477796076938x_{57} = -9.42477796076938
x58=−75.398223686155x_{58} = -75.398223686155
x59=−72.2566310325652x_{59} = -72.2566310325652
x60=−31.4159265358979x_{60} = -31.4159265358979
x61=28.2743338823081x_{61} = 28.2743338823081
x62=−91.106186954104x_{62} = -91.106186954104
x63=21.9911485751286x_{63} = 21.9911485751286
x64=62.8318530717959x_{64} = 62.8318530717959
x65=9.42477796076938x_{65} = 9.42477796076938
x66=50.2654824574367x_{66} = 50.2654824574367
x67=94.2477796076938x_{67} = 94.2477796076938
x68=91.106186954104x_{68} = 91.106186954104
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)/x.
sin⁡(0)0\frac{\sin{\left(0 \right)}}{0}
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
cos⁡(x)x−sin⁡(x)x2=0\frac{\cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=17.2207552719308x_{1} = 17.2207552719308
x2=−80.0981286289451x_{2} = -80.0981286289451
x3=−83.2401924707234x_{3} = -83.2401924707234
x4=98.9500628243319x_{4} = 98.9500628243319
x5=−45.5311340139913x_{5} = -45.5311340139913
x6=−86.3822220347287x_{6} = -86.3822220347287
x7=7.72525183693771x_{7} = 7.72525183693771
x8=−394.267341680887x_{8} = -394.267341680887
x9=−4.49340945790906x_{9} = -4.49340945790906
x10=4.49340945790906x_{10} = 4.49340945790906
x11=108.375719651675x_{11} = 108.375719651675
x12=39.2444323611642x_{12} = 39.2444323611642
x13=−70.6716857116195x_{13} = -70.6716857116195
x14=10.9041216594289x_{14} = 10.9041216594289
x15=−42.3879135681319x_{15} = -42.3879135681319
x16=80.0981286289451x_{16} = 80.0981286289451
x17=89.5242209304172x_{17} = 89.5242209304172
x18=−48.6741442319544x_{18} = -48.6741442319544
x19=14.0661939128315x_{19} = 14.0661939128315
x20=−36.1006222443756x_{20} = -36.1006222443756
x21=−95.8081387868617x_{21} = -95.8081387868617
x22=64.3871195905574x_{22} = 64.3871195905574
x23=61.2447302603744x_{23} = 61.2447302603744
x24=−54.9596782878889x_{24} = -54.9596782878889
x25=76.9560263103312x_{25} = 76.9560263103312
x26=−76.9560263103312x_{26} = -76.9560263103312
x27=−98.9500628243319x_{27} = -98.9500628243319
x28=−7.72525183693771x_{28} = -7.72525183693771
x29=−20.3713029592876x_{29} = -20.3713029592876
x30=−39.2444323611642x_{30} = -39.2444323611642
x31=−14.0661939128315x_{31} = -14.0661939128315
x32=−32.9563890398225x_{32} = -32.9563890398225
x33=54.9596782878889x_{33} = 54.9596782878889
x34=73.8138806006806x_{34} = 73.8138806006806
x35=26.6660542588127x_{35} = 26.6660542588127
x36=−26.6660542588127x_{36} = -26.6660542588127
x37=−61.2447302603744x_{37} = -61.2447302603744
x38=−67.5294347771441x_{38} = -67.5294347771441
x39=29.811598790893x_{39} = 29.811598790893
x40=51.8169824872797x_{40} = 51.8169824872797
x41=23.519452498689x_{41} = 23.519452498689
x42=−58.1022547544956x_{42} = -58.1022547544956
x43=67.5294347771441x_{43} = 67.5294347771441
x44=−10.9041216594289x_{44} = -10.9041216594289
x45=−89.5242209304172x_{45} = -89.5242209304172
x46=86.3822220347287x_{46} = 86.3822220347287
x47=−23.519452498689x_{47} = -23.519452498689
x48=−17.2207552719308x_{48} = -17.2207552719308
x49=−4355.81798462425x_{49} = -4355.81798462425
x50=58.1022547544956x_{50} = 58.1022547544956
x51=−92.6661922776228x_{51} = -92.6661922776228
x52=−29.811598790893x_{52} = -29.811598790893
x53=92.6661922776228x_{53} = 92.6661922776228
x54=−64.3871195905574x_{54} = -64.3871195905574
x55=32.9563890398225x_{55} = 32.9563890398225
x56=20.3713029592876x_{56} = 20.3713029592876
x57=48.6741442319544x_{57} = 48.6741442319544
x58=45.5311340139913x_{58} = 45.5311340139913
x59=36.1006222443756x_{59} = 36.1006222443756
x60=70.6716857116195x_{60} = 70.6716857116195
x61=83.2401924707234x_{61} = 83.2401924707234
x62=95.8081387868617x_{62} = 95.8081387868617
x63=−73.8138806006806x_{63} = -73.8138806006806
x64=42.3879135681319x_{64} = 42.3879135681319
x65=−51.8169824872797x_{65} = -51.8169824872797
Signos de extremos en los puntos:
(17.22075527193077, -0.0579718023461539)

(-80.09812862894512, -0.012483713321779)

(-83.2401924707234, 0.0120125604820527)

(98.95006282433188, -0.010105591736504)

(-45.53113401399128, 0.0219576982284824)

(-86.38222203472871, -0.0115756804584678)

(7.725251836937707, 0.128374553525899)

(-394.26734168088706, -0.00253634191261283)

(-4.493409457909064, -0.217233628211222)

(4.493409457909064, -0.217233628211222)

(108.37571965167469, 0.00922676625078197)

(39.24443236116419, 0.0254730530928808)

(-70.6716857116195, 0.0141485220648664)

(10.904121659428899, -0.0913252028230577)

(-42.38791356813192, -0.0235850682290164)

(80.09812862894512, -0.012483713321779)

(89.52422093041719, 0.0111694646341736)

(-48.674144231954386, -0.0205404540417537)

(14.066193912831473, 0.0709134594504622)

(-36.10062224437561, -0.0276897323011492)

(-95.8081387868617, 0.0104369581345658)

(64.38711959055742, 0.0155291838074613)

(61.2447302603744, -0.0163257593209978)

(-54.959678287888934, -0.0181921463218031)

(76.95602631033118, 0.0129933369870427)

(-76.95602631033118, 0.0129933369870427)

(-98.95006282433188, -0.010105591736504)

(-7.725251836937707, 0.128374553525899)

(-20.37130295928756, 0.0490296240140742)

(-39.24443236116419, 0.0254730530928808)

(-14.066193912831473, 0.0709134594504622)

(-32.956389039822476, 0.0303291711863103)

(54.959678287888934, -0.0181921463218031)

(73.81388060068065, -0.01354634434514)

(26.666054258812675, 0.0374745199939312)

(-26.666054258812675, 0.0374745199939312)

(-61.2447302603744, -0.0163257593209978)

(-67.52943477714412, -0.0148067339465492)

(29.81159879089296, -0.0335251350213988)

(51.81698248727967, 0.019295099487588)

(23.519452498689006, -0.0424796169776126)

(-58.10225475449559, 0.0172084874716279)

(67.52943477714412, -0.0148067339465492)

(-10.904121659428899, -0.0913252028230577)

(-89.52422093041719, 0.0111694646341736)

(86.38222203472871, -0.0115756804584678)

(-23.519452498689006, -0.0424796169776126)

(-17.22075527193077, -0.0579718023461539)

(-4355.817984624248, 0.000229577998248987)

(58.10225475449559, 0.0172084874716279)

(-92.66619227762284, -0.0107907938495342)

(-29.81159879089296, -0.0335251350213988)

(92.66619227762284, -0.0107907938495342)

(-64.38711959055742, 0.0155291838074613)

(32.956389039822476, 0.0303291711863103)

(20.37130295928756, 0.0490296240140742)

(48.674144231954386, -0.0205404540417537)

(45.53113401399128, 0.0219576982284824)

(36.10062224437561, -0.0276897323011492)

(70.6716857116195, 0.0141485220648664)

(83.2401924707234, 0.0120125604820527)

(95.8081387868617, 0.0104369581345658)

(-73.81388060068065, -0.01354634434514)

(42.38791356813192, -0.0235850682290164)

(-51.81698248727967, 0.019295099487588)


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=17.2207552719308x_{1} = 17.2207552719308
x2=−80.0981286289451x_{2} = -80.0981286289451
x3=98.9500628243319x_{3} = 98.9500628243319
x4=−86.3822220347287x_{4} = -86.3822220347287
x5=−394.267341680887x_{5} = -394.267341680887
x6=−4.49340945790906x_{6} = -4.49340945790906
x7=4.49340945790906x_{7} = 4.49340945790906
x8=10.9041216594289x_{8} = 10.9041216594289
x9=−42.3879135681319x_{9} = -42.3879135681319
x10=80.0981286289451x_{10} = 80.0981286289451
x11=−48.6741442319544x_{11} = -48.6741442319544
x12=−36.1006222443756x_{12} = -36.1006222443756
x13=61.2447302603744x_{13} = 61.2447302603744
x14=−54.9596782878889x_{14} = -54.9596782878889
x15=−98.9500628243319x_{15} = -98.9500628243319
x16=54.9596782878889x_{16} = 54.9596782878889
x17=73.8138806006806x_{17} = 73.8138806006806
x18=−61.2447302603744x_{18} = -61.2447302603744
x19=−67.5294347771441x_{19} = -67.5294347771441
x20=29.811598790893x_{20} = 29.811598790893
x21=23.519452498689x_{21} = 23.519452498689
x22=67.5294347771441x_{22} = 67.5294347771441
x23=−10.9041216594289x_{23} = -10.9041216594289
x24=86.3822220347287x_{24} = 86.3822220347287
x25=−23.519452498689x_{25} = -23.519452498689
x26=−17.2207552719308x_{26} = -17.2207552719308
x27=−92.6661922776228x_{27} = -92.6661922776228
x28=−29.811598790893x_{28} = -29.811598790893
x29=92.6661922776228x_{29} = 92.6661922776228
x30=48.6741442319544x_{30} = 48.6741442319544
x31=36.1006222443756x_{31} = 36.1006222443756
x32=−73.8138806006806x_{32} = -73.8138806006806
x33=42.3879135681319x_{33} = 42.3879135681319
Puntos máximos de la función:
x33=−83.2401924707234x_{33} = -83.2401924707234
x33=−45.5311340139913x_{33} = -45.5311340139913
x33=7.72525183693771x_{33} = 7.72525183693771
x33=108.375719651675x_{33} = 108.375719651675
x33=39.2444323611642x_{33} = 39.2444323611642
x33=−70.6716857116195x_{33} = -70.6716857116195
x33=89.5242209304172x_{33} = 89.5242209304172
x33=14.0661939128315x_{33} = 14.0661939128315
x33=−95.8081387868617x_{33} = -95.8081387868617
x33=64.3871195905574x_{33} = 64.3871195905574
x33=76.9560263103312x_{33} = 76.9560263103312
x33=−76.9560263103312x_{33} = -76.9560263103312
x33=−7.72525183693771x_{33} = -7.72525183693771
x33=−20.3713029592876x_{33} = -20.3713029592876
x33=−39.2444323611642x_{33} = -39.2444323611642
x33=−14.0661939128315x_{33} = -14.0661939128315
x33=−32.9563890398225x_{33} = -32.9563890398225
x33=26.6660542588127x_{33} = 26.6660542588127
x33=−26.6660542588127x_{33} = -26.6660542588127
x33=51.8169824872797x_{33} = 51.8169824872797
x33=−58.1022547544956x_{33} = -58.1022547544956
x33=−89.5242209304172x_{33} = -89.5242209304172
x33=−4355.81798462425x_{33} = -4355.81798462425
x33=58.1022547544956x_{33} = 58.1022547544956
x33=−64.3871195905574x_{33} = -64.3871195905574
x33=32.9563890398225x_{33} = 32.9563890398225
x33=20.3713029592876x_{33} = 20.3713029592876
x33=45.5311340139913x_{33} = 45.5311340139913
x33=70.6716857116195x_{33} = 70.6716857116195
x33=83.2401924707234x_{33} = 83.2401924707234
x33=95.8081387868617x_{33} = 95.8081387868617
x33=−51.8169824872797x_{33} = -51.8169824872797
Decrece en los intervalos
[98.9500628243319,∞)\left[98.9500628243319, \infty\right)
Crece en los intervalos
(−∞,−394.267341680887]\left(-\infty, -394.267341680887\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
−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x=0\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−12.404445021902x_{1} = -12.404445021902
x2=−47.0813974121542x_{2} = -47.0813974121542
x3=−18.7426455847748x_{3} = -18.7426455847748
x4=−91.0842274914688x_{4} = -91.0842274914688
x5=9.20584014293667x_{5} = 9.20584014293667
x6=−84.7994143922025x_{6} = -84.7994143922025
x7=21.8996964794928x_{7} = 21.8996964794928
x8=−342.42775856009x_{8} = -342.42775856009
x9=−87.9418500396598x_{9} = -87.9418500396598
x10=−1288.05143523817x_{10} = -1288.05143523817
x11=−59.6567290035279x_{11} = -59.6567290035279
x12=100.511065295271x_{12} = 100.511065295271
x13=−43.9367614714198x_{13} = -43.9367614714198
x14=91.0842274914688x_{14} = 91.0842274914688
x15=−15.5792364103872x_{15} = -15.5792364103872
x16=43.9367614714198x_{16} = 43.9367614714198
x17=31.3520917265645x_{17} = 31.3520917265645
x18=53.3695918204908x_{18} = 53.3695918204908
x19=59.6567290035279x_{19} = 59.6567290035279
x20=34.499514921367x_{20} = 34.499514921367
x21=131.931731514843x_{21} = 131.931731514843
x22=47.0813974121542x_{22} = 47.0813974121542
x23=−50.2256516491831x_{23} = -50.2256516491831
x24=94.2265525745684x_{24} = 94.2265525745684
x25=−78.5143405319308x_{25} = -78.5143405319308
x26=−40.7916552312719x_{26} = -40.7916552312719
x27=75.3716854092873x_{27} = 75.3716854092873
x28=69.0860849466452x_{28} = 69.0860849466452
x29=−9.20584014293667x_{29} = -9.20584014293667
x30=65.9431119046552x_{30} = 65.9431119046552
x31=−28.2033610039524x_{31} = -28.2033610039524
x32=−81.6569138240367x_{32} = -81.6569138240367
x33=25.052825280993x_{33} = 25.052825280993
x34=−2.0815759778181x_{34} = -2.0815759778181
x35=−62.8000005565198x_{35} = -62.8000005565198
x36=−94.2265525745684x_{36} = -94.2265525745684
x37=−25.052825280993x_{37} = -25.052825280993
x38=−34.499514921367x_{38} = -34.499514921367
x39=−37.6459603230864x_{39} = -37.6459603230864
x40=28.2033610039524x_{40} = 28.2033610039524
x41=81.6569138240367x_{41} = 81.6569138240367
x42=78.5143405319308x_{42} = 78.5143405319308
x43=56.5132704621986x_{43} = 56.5132704621986
x44=15.5792364103872x_{44} = 15.5792364103872
x45=50.2256516491831x_{45} = 50.2256516491831
x46=97.368830362901x_{46} = 97.368830362901
x47=62.8000005565198x_{47} = 62.8000005565198
x48=−1790.70669566846x_{48} = -1790.70669566846
x49=−65.9431119046552x_{49} = -65.9431119046552
x50=87.9418500396598x_{50} = 87.9418500396598
x51=40.7916552312719x_{51} = 40.7916552312719
x52=18.7426455847748x_{52} = 18.7426455847748
x53=84.7994143922025x_{53} = 84.7994143922025
x54=−56.5132704621986x_{54} = -56.5132704621986
x55=37.6459603230864x_{55} = 37.6459603230864
x56=72.2289377620154x_{56} = 72.2289377620154
x57=−100.511065295271x_{57} = -100.511065295271
x58=−53.3695918204908x_{58} = -53.3695918204908
x59=−5.94036999057271x_{59} = -5.94036999057271
x60=−31.3520917265645x_{60} = -31.3520917265645
x61=2.0815759778181x_{61} = 2.0815759778181
x62=5.94036999057271x_{62} = 5.94036999057271
x63=12.404445021902x_{63} = 12.404445021902
x64=−97.368830362901x_{64} = -97.368830362901
x65=−21.8996964794928x_{65} = -21.8996964794928
x66=−69.0860849466452x_{66} = -69.0860849466452
x67=−72.2289377620154x_{67} = -72.2289377620154
x68=−75.3716854092873x_{68} = -75.3716854092873
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=0x_{1} = 0

lim⁡x→0−(−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x)=−13\lim_{x \to 0^-}\left(\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x}\right) = - \frac{1}{3}
lim⁡x→0+(−sin⁡(x)−2cos⁡(x)x+2sin⁡(x)x2x)=−13\lim_{x \to 0^+}\left(\frac{- \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{2 \sin{\left(x \right)}}{x^{2}}}{x}\right) = - \frac{1}{3}
- los límites son iguales, es decir omitimos el punto correspondiente

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
[97.368830362901,∞)\left[97.368830362901, \infty\right)
Convexa en los intervalos
(−∞,−1790.70669566846]\left(-\infty, -1790.70669566846\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(sin⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x)/x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x)x2)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{2}}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(x)x2)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{2}}\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)x=sin⁡(x)x\frac{\sin{\left(x \right)}}{x} = \frac{\sin{\left(x \right)}}{x}
- No
sin⁡(x)x=−sin⁡(x)x\frac{\sin{\left(x \right)}}{x} = - \frac{\sin{\left(x \right)}}{x}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = (sinx)/x
    © Sr Examen – Калькулятор