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

Gráfico de la función y = sin(x)/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=−43.9822971502571x_{1} = -43.9822971502571
x2=−31.4159265358979x_{2} = -31.4159265358979
x3=84.8230016469244x_{3} = 84.8230016469244
x4=−91.106186954104x_{4} = -91.106186954104
x5=−97.3893722612836x_{5} = -97.3893722612836
x6=91.106186954104x_{6} = 91.106186954104
x7=6.28318530717959x_{7} = 6.28318530717959
x8=−72.2566310325652x_{8} = -72.2566310325652
x9=−47.1238898038469x_{9} = -47.1238898038469
x10=−113.097335529233x_{10} = -113.097335529233
x11=94.2477796076938x_{11} = 94.2477796076938
x12=50.2654824574367x_{12} = 50.2654824574367
x13=56.5486677646163x_{13} = 56.5486677646163
x14=43.9822971502571x_{14} = 43.9822971502571
x15=47.1238898038469x_{15} = 47.1238898038469
x16=−50.2654824574367x_{16} = -50.2654824574367
x17=37.6991118430775x_{17} = 37.6991118430775
x18=−28.2743338823081x_{18} = -28.2743338823081
x19=−223.053078404875x_{19} = -223.053078404875
x20=65.9734457253857x_{20} = 65.9734457253857
x21=15.707963267949x_{21} = 15.707963267949
x22=28.2743338823081x_{22} = 28.2743338823081
x23=−62.8318530717959x_{23} = -62.8318530717959
x24=−40.8407044966673x_{24} = -40.8407044966673
x25=−6.28318530717959x_{25} = -6.28318530717959
x26=−81.6814089933346x_{26} = -81.6814089933346
x27=−15.707963267949x_{27} = -15.707963267949
x28=−59.6902604182061x_{28} = -59.6902604182061
x29=72.2566310325652x_{29} = 72.2566310325652
x30=3.14159265358979x_{30} = 3.14159265358979
x31=−25.1327412287183x_{31} = -25.1327412287183
x32=21.9911485751286x_{32} = 21.9911485751286
x33=−75.398223686155x_{33} = -75.398223686155
x34=153.9380400259x_{34} = 153.9380400259
x35=−56.5486677646163x_{35} = -56.5486677646163
x36=−69.1150383789755x_{36} = -69.1150383789755
x37=−84.8230016469244x_{37} = -84.8230016469244
x38=78.5398163397448x_{38} = 78.5398163397448
x39=9.42477796076938x_{39} = 9.42477796076938
x40=590.619418874881x_{40} = 590.619418874881
x41=−53.4070751110265x_{41} = -53.4070751110265
x42=62.8318530717959x_{42} = 62.8318530717959
x43=−18.8495559215388x_{43} = -18.8495559215388
x44=40.8407044966673x_{44} = 40.8407044966673
x45=25.1327412287183x_{45} = 25.1327412287183
x46=100.530964914873x_{46} = 100.530964914873
x47=−87.9645943005142x_{47} = -87.9645943005142
x48=−9.42477796076938x_{48} = -9.42477796076938
x49=75.398223686155x_{49} = 75.398223686155
x50=81.6814089933346x_{50} = 81.6814089933346
x51=87.9645943005142x_{51} = 87.9645943005142
x52=12.5663706143592x_{52} = 12.5663706143592
x53=−34.5575191894877x_{53} = -34.5575191894877
x54=69.1150383789755x_{54} = 69.1150383789755
x55=−3.14159265358979x_{55} = -3.14159265358979
x56=−21.9911485751286x_{56} = -21.9911485751286
x57=−370.707933123596x_{57} = -370.707933123596
x58=−37.6991118430775x_{58} = -37.6991118430775
x59=31.4159265358979x_{59} = 31.4159265358979
x60=−78.5398163397448x_{60} = -78.5398163397448
x61=−12.5663706143592x_{61} = -12.5663706143592
x62=−94.2477796076938x_{62} = -94.2477796076938
x63=97.3893722612836x_{63} = 97.3893722612836
x64=−100.530964914873x_{64} = -100.530964914873
x65=59.6902604182061x_{65} = 59.6902604182061
x66=53.4070751110265x_{66} = 53.4070751110265
x67=34.5575191894877x_{67} = 34.5575191894877
x68=−65.9734457253857x_{68} = -65.9734457253857
x69=18.8495559215388x_{69} = 18.8495559215388
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=−86.3822220347287x_{1} = -86.3822220347287
x2=−4.49340945790906x_{2} = -4.49340945790906
x3=−42.3879135681319x_{3} = -42.3879135681319
x4=−32.9563890398225x_{4} = -32.9563890398225
x5=−67.5294347771441x_{5} = -67.5294347771441
x6=−20.3713029592876x_{6} = -20.3713029592876
x7=23.519452498689x_{7} = 23.519452498689
x8=61.2447302603744x_{8} = 61.2447302603744
x9=7.72525183693771x_{9} = 7.72525183693771
x10=−92.6661922776228x_{10} = -92.6661922776228
x11=14.0661939128315x_{11} = 14.0661939128315
x12=−45.5311340139913x_{12} = -45.5311340139913
x13=48.6741442319544x_{13} = 48.6741442319544
x14=70.6716857116195x_{14} = 70.6716857116195
x15=64.3871195905574x_{15} = 64.3871195905574
x16=36.1006222443756x_{16} = 36.1006222443756
x17=95.8081387868617x_{17} = 95.8081387868617
x18=−29.811598790893x_{18} = -29.811598790893
x19=−76.9560263103312x_{19} = -76.9560263103312
x20=−10.9041216594289x_{20} = -10.9041216594289
x21=98.9500628243319x_{21} = 98.9500628243319
x22=76.9560263103312x_{22} = 76.9560263103312
x23=45.5311340139913x_{23} = 45.5311340139913
x24=39.2444323611642x_{24} = 39.2444323611642
x25=−98.9500628243319x_{25} = -98.9500628243319
x26=−89.5242209304172x_{26} = -89.5242209304172
x27=−61.2447302603744x_{27} = -61.2447302603744
x28=17.2207552719308x_{28} = 17.2207552719308
x29=92.6661922776228x_{29} = 92.6661922776228
x30=4.49340945790906x_{30} = 4.49340945790906
x31=54.9596782878889x_{31} = 54.9596782878889
x32=−394.267341680887x_{32} = -394.267341680887
x33=−48.6741442319544x_{33} = -48.6741442319544
x34=67.5294347771441x_{34} = 67.5294347771441
x35=−7.72525183693771x_{35} = -7.72525183693771
x36=−17.2207552719308x_{36} = -17.2207552719308
x37=−4355.81798462425x_{37} = -4355.81798462425
x38=86.3822220347287x_{38} = 86.3822220347287
x39=32.9563890398225x_{39} = 32.9563890398225
x40=−26.6660542588127x_{40} = -26.6660542588127
x41=26.6660542588127x_{41} = 26.6660542588127
x42=80.0981286289451x_{42} = 80.0981286289451
x43=108.375719651675x_{43} = 108.375719651675
x44=−95.8081387868617x_{44} = -95.8081387868617
x45=20.3713029592876x_{45} = 20.3713029592876
x46=−83.2401924707234x_{46} = -83.2401924707234
x47=10.9041216594289x_{47} = 10.9041216594289
x48=83.2401924707234x_{48} = 83.2401924707234
x49=89.5242209304172x_{49} = 89.5242209304172
x50=29.811598790893x_{50} = 29.811598790893
x51=58.1022547544956x_{51} = 58.1022547544956
x52=−54.9596782878889x_{52} = -54.9596782878889
x53=−64.3871195905574x_{53} = -64.3871195905574
x54=−39.2444323611642x_{54} = -39.2444323611642
x55=−14.0661939128315x_{55} = -14.0661939128315
x56=−70.6716857116195x_{56} = -70.6716857116195
x57=−73.8138806006806x_{57} = -73.8138806006806
x58=73.8138806006806x_{58} = 73.8138806006806
x59=−36.1006222443756x_{59} = -36.1006222443756
x60=−58.1022547544956x_{60} = -58.1022547544956
x61=42.3879135681319x_{61} = 42.3879135681319
x62=−51.8169824872797x_{62} = -51.8169824872797
x63=−23.519452498689x_{63} = -23.519452498689
x64=51.8169824872797x_{64} = 51.8169824872797
x65=−80.0981286289451x_{65} = -80.0981286289451
Signos de extremos en los puntos:
(-86.38222203472871, -0.0115756804584678)

(-4.493409457909064, -0.217233628211222)

(-42.38791356813192, -0.0235850682290164)

(-32.956389039822476, 0.0303291711863103)

(-67.52943477714412, -0.0148067339465492)

(-20.37130295928756, 0.0490296240140742)

(23.519452498689006, -0.0424796169776126)

(61.2447302603744, -0.0163257593209978)

(7.725251836937707, 0.128374553525899)

(-92.66619227762284, -0.0107907938495342)

(14.066193912831473, 0.0709134594504622)

(-45.53113401399128, 0.0219576982284824)

(48.674144231954386, -0.0205404540417537)

(70.6716857116195, 0.0141485220648664)

(64.38711959055742, 0.0155291838074613)

(36.10062224437561, -0.0276897323011492)

(95.8081387868617, 0.0104369581345658)

(-29.81159879089296, -0.0335251350213988)

(-76.95602631033118, 0.0129933369870427)

(-10.904121659428899, -0.0913252028230577)

(98.95006282433188, -0.010105591736504)

(76.95602631033118, 0.0129933369870427)

(45.53113401399128, 0.0219576982284824)

(39.24443236116419, 0.0254730530928808)

(-98.95006282433188, -0.010105591736504)

(-89.52422093041719, 0.0111694646341736)

(-61.2447302603744, -0.0163257593209978)

(17.22075527193077, -0.0579718023461539)

(92.66619227762284, -0.0107907938495342)

(4.493409457909064, -0.217233628211222)

(54.959678287888934, -0.0181921463218031)

(-394.26734168088706, -0.00253634191261283)

(-48.674144231954386, -0.0205404540417537)

(67.52943477714412, -0.0148067339465492)

(-7.725251836937707, 0.128374553525899)

(-17.22075527193077, -0.0579718023461539)

(-4355.817984624248, 0.000229577998248987)

(86.38222203472871, -0.0115756804584678)

(32.956389039822476, 0.0303291711863103)

(-26.666054258812675, 0.0374745199939312)

(26.666054258812675, 0.0374745199939312)

(80.09812862894512, -0.012483713321779)

(108.37571965167469, 0.00922676625078197)

(-95.8081387868617, 0.0104369581345658)

(20.37130295928756, 0.0490296240140742)

(-83.2401924707234, 0.0120125604820527)

(10.904121659428899, -0.0913252028230577)

(83.2401924707234, 0.0120125604820527)

(89.52422093041719, 0.0111694646341736)

(29.81159879089296, -0.0335251350213988)

(58.10225475449559, 0.0172084874716279)

(-54.959678287888934, -0.0181921463218031)

(-64.38711959055742, 0.0155291838074613)

(-39.24443236116419, 0.0254730530928808)

(-14.066193912831473, 0.0709134594504622)

(-70.6716857116195, 0.0141485220648664)

(-73.81388060068065, -0.01354634434514)

(73.81388060068065, -0.01354634434514)

(-36.10062224437561, -0.0276897323011492)

(-58.10225475449559, 0.0172084874716279)

(42.38791356813192, -0.0235850682290164)

(-51.81698248727967, 0.019295099487588)

(-23.519452498689006, -0.0424796169776126)

(51.81698248727967, 0.019295099487588)

(-80.09812862894512, -0.012483713321779)


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