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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=69.1150383789755x_{1} = 69.1150383789755
x2=65.9734457253857x_{2} = 65.9734457253857
x3=−91.106186954104x_{3} = -91.106186954104
x4=590.619418874881x_{4} = 590.619418874881
x5=−59.6902604182061x_{5} = -59.6902604182061
x6=−21.9911485751286x_{6} = -21.9911485751286
x7=−370.707933123596x_{7} = -370.707933123596
x8=12.5663706143592x_{8} = 12.5663706143592
x9=21.9911485751286x_{9} = 21.9911485751286
x10=−69.1150383789755x_{10} = -69.1150383789755
x11=−100.530964914873x_{11} = -100.530964914873
x12=−223.053078404875x_{12} = -223.053078404875
x13=3.14159265358979x_{13} = 3.14159265358979
x14=−3.14159265358979x_{14} = -3.14159265358979
x15=−25.1327412287183x_{15} = -25.1327412287183
x16=−15.707963267949x_{16} = -15.707963267949
x17=−53.4070751110265x_{17} = -53.4070751110265
x18=−72.2566310325652x_{18} = -72.2566310325652
x19=153.9380400259x_{19} = 153.9380400259
x20=84.8230016469244x_{20} = 84.8230016469244
x21=−81.6814089933346x_{21} = -81.6814089933346
x22=−94.2477796076938x_{22} = -94.2477796076938
x23=18.8495559215388x_{23} = 18.8495559215388
x24=−65.9734457253857x_{24} = -65.9734457253857
x25=94.2477796076938x_{25} = 94.2477796076938
x26=9.42477796076938x_{26} = 9.42477796076938
x27=−40.8407044966673x_{27} = -40.8407044966673
x28=34.5575191894877x_{28} = 34.5575191894877
x29=97.3893722612836x_{29} = 97.3893722612836
x30=53.4070751110265x_{30} = 53.4070751110265
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=47.1238898038469x_{47} = 47.1238898038469
x48=−97.3893722612836x_{48} = -97.3893722612836
x49=−50.2654824574367x_{49} = -50.2654824574367
x50=100.530964914873x_{50} = 100.530964914873
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=−113.097335529233x_{63} = -113.097335529233
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)/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=−64.3871195905574x_{1} = -64.3871195905574
x2=−61.2447302603744x_{2} = -61.2447302603744
x3=−26.6660542588127x_{3} = -26.6660542588127
x4=−86.3822220347287x_{4} = -86.3822220347287
x5=54.9596782878889x_{5} = 54.9596782878889
x6=−20.3713029592876x_{6} = -20.3713029592876
x7=95.8081387868617x_{7} = 95.8081387868617
x8=−36.1006222443756x_{8} = -36.1006222443756
x9=20.3713029592876x_{9} = 20.3713029592876
x10=−73.8138806006806x_{10} = -73.8138806006806
x11=−67.5294347771441x_{11} = -67.5294347771441
x12=70.6716857116195x_{12} = 70.6716857116195
x13=−92.6661922776228x_{13} = -92.6661922776228
x14=64.3871195905574x_{14} = 64.3871195905574
x15=26.6660542588127x_{15} = 26.6660542588127
x16=58.1022547544956x_{16} = 58.1022547544956
x17=−29.811598790893x_{17} = -29.811598790893
x18=32.9563890398225x_{18} = 32.9563890398225
x19=83.2401924707234x_{19} = 83.2401924707234
x20=23.519452498689x_{20} = 23.519452498689
x21=−7.72525183693771x_{21} = -7.72525183693771
x22=−4.49340945790906x_{22} = -4.49340945790906
x23=76.9560263103312x_{23} = 76.9560263103312
x24=89.5242209304172x_{24} = 89.5242209304172
x25=−45.5311340139913x_{25} = -45.5311340139913
x26=108.375719651675x_{26} = 108.375719651675
x27=−83.2401924707234x_{27} = -83.2401924707234
x28=−14.0661939128315x_{28} = -14.0661939128315
x29=7.72525183693771x_{29} = 7.72525183693771
x30=−80.0981286289451x_{30} = -80.0981286289451
x31=80.0981286289451x_{31} = 80.0981286289451
x32=−17.2207552719308x_{32} = -17.2207552719308
x33=−32.9563890398225x_{33} = -32.9563890398225
x34=−4355.81798462425x_{34} = -4355.81798462425
x35=17.2207552719308x_{35} = 17.2207552719308
x36=−48.6741442319544x_{36} = -48.6741442319544
x37=−39.2444323611642x_{37} = -39.2444323611642
x38=−10.9041216594289x_{38} = -10.9041216594289
x39=73.8138806006806x_{39} = 73.8138806006806
x40=98.9500628243319x_{40} = 98.9500628243319
x41=45.5311340139913x_{41} = 45.5311340139913
x42=29.811598790893x_{42} = 29.811598790893
x43=4.49340945790906x_{43} = 4.49340945790906
x44=10.9041216594289x_{44} = 10.9041216594289
x45=−42.3879135681319x_{45} = -42.3879135681319
x46=−23.519452498689x_{46} = -23.519452498689
x47=−98.9500628243319x_{47} = -98.9500628243319
x48=92.6661922776228x_{48} = 92.6661922776228
x49=48.6741442319544x_{49} = 48.6741442319544
x50=−394.267341680887x_{50} = -394.267341680887
x51=36.1006222443756x_{51} = 36.1006222443756
x52=14.0661939128315x_{52} = 14.0661939128315
x53=−76.9560263103312x_{53} = -76.9560263103312
x54=51.8169824872797x_{54} = 51.8169824872797
x55=−58.1022547544956x_{55} = -58.1022547544956
x56=86.3822220347287x_{56} = 86.3822220347287
x57=−89.5242209304172x_{57} = -89.5242209304172
x58=−95.8081387868617x_{58} = -95.8081387868617
x59=−51.8169824872797x_{59} = -51.8169824872797
x60=−70.6716857116195x_{60} = -70.6716857116195
x61=−54.9596782878889x_{61} = -54.9596782878889
x62=42.3879135681319x_{62} = 42.3879135681319
x63=67.5294347771441x_{63} = 67.5294347771441
x64=61.2447302603744x_{64} = 61.2447302603744
x65=39.2444323611642x_{65} = 39.2444323611642
Signos de extremos en los puntos:
(-64.38711959055742, 0.0155291838074613)

(-61.2447302603744, -0.0163257593209978)

(-26.666054258812675, 0.0374745199939312)

(-86.38222203472871, -0.0115756804584678)

(54.959678287888934, -0.0181921463218031)

(-20.37130295928756, 0.0490296240140742)

(95.8081387868617, 0.0104369581345658)

(-36.10062224437561, -0.0276897323011492)

(20.37130295928756, 0.0490296240140742)

(-73.81388060068065, -0.01354634434514)

(-67.52943477714412, -0.0148067339465492)

(70.6716857116195, 0.0141485220648664)

(-92.66619227762284, -0.0107907938495342)

(64.38711959055742, 0.0155291838074613)

(26.666054258812675, 0.0374745199939312)

(58.10225475449559, 0.0172084874716279)

(-29.81159879089296, -0.0335251350213988)

(32.956389039822476, 0.0303291711863103)

(83.2401924707234, 0.0120125604820527)

(23.519452498689006, -0.0424796169776126)

(-7.725251836937707, 0.128374553525899)

(-4.493409457909064, -0.217233628211222)

(76.95602631033118, 0.0129933369870427)

(89.52422093041719, 0.0111694646341736)

(-45.53113401399128, 0.0219576982284824)

(108.37571965167469, 0.00922676625078197)

(-83.2401924707234, 0.0120125604820527)

(-14.066193912831473, 0.0709134594504622)

(7.725251836937707, 0.128374553525899)

(-80.09812862894512, -0.012483713321779)

(80.09812862894512, -0.012483713321779)

(-17.22075527193077, -0.0579718023461539)

(-32.956389039822476, 0.0303291711863103)

(-4355.817984624248, 0.000229577998248987)

(17.22075527193077, -0.0579718023461539)

(-48.674144231954386, -0.0205404540417537)

(-39.24443236116419, 0.0254730530928808)

(-10.904121659428899, -0.0913252028230577)

(73.81388060068065, -0.01354634434514)

(98.95006282433188, -0.010105591736504)

(45.53113401399128, 0.0219576982284824)

(29.81159879089296, -0.0335251350213988)

(4.493409457909064, -0.217233628211222)

(10.904121659428899, -0.0913252028230577)

(-42.38791356813192, -0.0235850682290164)

(-23.519452498689006, -0.0424796169776126)

(-98.95006282433188, -0.010105591736504)

(92.66619227762284, -0.0107907938495342)

(48.674144231954386, -0.0205404540417537)

(-394.26734168088706, -0.00253634191261283)

(36.10062224437561, -0.0276897323011492)

(14.066193912831473, 0.0709134594504622)

(-76.95602631033118, 0.0129933369870427)

(51.81698248727967, 0.019295099487588)

(-58.10225475449559, 0.0172084874716279)

(86.38222203472871, -0.0115756804584678)

(-89.52422093041719, 0.0111694646341736)

(-95.8081387868617, 0.0104369581345658)

(-51.81698248727967, 0.019295099487588)

(-70.6716857116195, 0.0141485220648664)

(-54.959678287888934, -0.0181921463218031)

(42.38791356813192, -0.0235850682290164)

(67.52943477714412, -0.0148067339465492)

(61.2447302603744, -0.0163257593209978)

(39.24443236116419, 0.0254730530928808)


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