Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ cos(x)/x^3

Gráfico de la función y = cos(x)/x^3

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       cos(x)
f(x) = ------
          3  
         x
f(x)=cos⁡(x)x3f{\left(x \right)} = \frac{\cos{\left(x \right)}}{x^{3}} 
f = cos(x)/x^3
Gráfico de la función
02468-8-6-4-2-1010-2000020000
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:
cos⁡(x)x3=0\frac{\cos{\left(x \right)}}{x^{3}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=π2x_{1} = \frac{\pi}{2}
x2=3π2x_{2} = \frac{3 \pi}{2}
Solución numérica
x1=−29.845130209103x_{1} = -29.845130209103
x2=−67.5442420521806x_{2} = -67.5442420521806
x3=−70.6858347057703x_{3} = -70.6858347057703
x4=64.4026493985908x_{4} = 64.4026493985908
x5=−36.1283155162826x_{5} = -36.1283155162826
x6=−92.6769832808989x_{6} = -92.6769832808989
x7=−61.261056745001x_{7} = -61.261056745001
x8=−199.491133502952x_{8} = -199.491133502952
x9=−76.9690200129499x_{9} = -76.9690200129499
x10=−98.9601685880785x_{10} = -98.9601685880785
x11=−95.8185759344887x_{11} = -95.8185759344887
x12=29.845130209103x_{12} = 29.845130209103
x13=80.1106126665397x_{13} = 80.1106126665397
x14=−64.4026493985908x_{14} = -64.4026493985908
x15=36.1283155162826x_{15} = 36.1283155162826
x16=73.8274273593601x_{16} = 73.8274273593601
x17=32.9867228626928x_{17} = 32.9867228626928
x18=−4.71238898038469x_{18} = -4.71238898038469
x19=−39.2699081698724x_{19} = -39.2699081698724
x20=26.7035375555132x_{20} = 26.7035375555132
x21=−7.85398163397448x_{21} = -7.85398163397448
x22=95.8185759344887x_{22} = 95.8185759344887
x23=−17.2787595947439x_{23} = -17.2787595947439
x24=−10.9955742875643x_{24} = -10.9955742875643
x25=98.9601685880785x_{25} = 98.9601685880785
x26=−86.3937979737193x_{26} = -86.3937979737193
x27=92.6769832808989x_{27} = 92.6769832808989
x28=−48.6946861306418x_{28} = -48.6946861306418
x29=54.9778714378214x_{29} = 54.9778714378214
x30=45.553093477052x_{30} = 45.553093477052
x31=23.5619449019235x_{31} = 23.5619449019235
x32=76.9690200129499x_{32} = 76.9690200129499
x33=−89.5353906273091x_{33} = -89.5353906273091
x34=4.71238898038469x_{34} = 4.71238898038469
x35=−26.7035375555132x_{35} = -26.7035375555132
x36=−80.1106126665397x_{36} = -80.1106126665397
x37=7.85398163397448x_{37} = 7.85398163397448
x38=14.1371669411541x_{38} = 14.1371669411541
x39=86.3937979737193x_{39} = 86.3937979737193
x40=−45.553093477052x_{40} = -45.553093477052
x41=−83.2522053201295x_{41} = -83.2522053201295
x42=70.6858347057703x_{42} = 70.6858347057703
x43=83.2522053201295x_{43} = 83.2522053201295
x44=48.6946861306418x_{44} = 48.6946861306418
x45=−20.4203522483337x_{45} = -20.4203522483337
x46=51.8362787842316x_{46} = 51.8362787842316
x47=10.9955742875643x_{47} = 10.9955742875643
x48=20.4203522483337x_{48} = 20.4203522483337
x49=89.5353906273091x_{49} = 89.5353906273091
x50=17.2787595947439x_{50} = 17.2787595947439
x51=58.1194640914112x_{51} = 58.1194640914112
x52=61.261056745001x_{52} = 61.261056745001
x53=−32.9867228626928x_{53} = -32.9867228626928
x54=−51.8362787842316x_{54} = -51.8362787842316
x55=−14.1371669411541x_{55} = -14.1371669411541
x56=−58.1194640914112x_{56} = -58.1194640914112
x57=−42.4115008234622x_{57} = -42.4115008234622
x58=−54.9778714378214x_{58} = -54.9778714378214
x59=−1.5707963267949x_{59} = -1.5707963267949
x60=42.4115008234622x_{60} = 42.4115008234622
x61=39.2699081698724x_{61} = 39.2699081698724
x62=67.5442420521806x_{62} = 67.5442420521806
x63=−23.5619449019235x_{63} = -23.5619449019235
x64=−73.8274273593601x_{64} = -73.8274273593601
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 cos(x)/x^3.
cos⁡(0)03\frac{\cos{\left(0 \right)}}{0^{3}}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
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
−sin⁡(x)x3−3cos⁡(x)x4=0- \frac{\sin{\left(x \right)}}{x^{3}} - \frac{3 \cos{\left(x \right)}}{x^{4}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=12.327655521099x_{1} = 12.327655521099
x2=−100.50112336357x_{2} = -100.50112336357
x3=−47.0602278498565x_{3} = -47.0602278498565
x4=75.3584349525985x_{4} = 75.3584349525985
x5=−84.7876338830228x_{5} = -84.7876338830228
x6=50.2057993706114x_{6} = 50.2057993706114
x7=37.6195344424891x_{7} = 37.6195344424891
x8=56.4956161262601x_{8} = 56.4956161262601
x9=78.50161915521x_{9} = 78.50161915521
x10=94.2159486198017x_{10} = 94.2159486198017
x11=72.2151123545007x_{11} = 72.2151123545007
x12=−380.124819103717x_{12} = -380.124819103717
x13=5.80628149104622x_{13} = 5.80628149104622
x14=100.50112336357x_{14} = 100.50112336357
x15=18.6904032530853x_{15} = 18.6904032530853
x16=−72.2151123545007x_{16} = -72.2151123545007
x17=−62.7841065943838x_{17} = -62.7841065943838
x18=−81.6446809310296x_{18} = -81.6446809310296
x19=91.0732583460488x_{19} = 91.0732583460488
x20=97.3585680793661x_{20} = 97.3585680793661
x21=−31.3204337466541x_{21} = -31.3204337466541
x22=40.7672484166364x_{22} = 40.7672484166364
x23=−25.0133755606323x_{23} = -25.0133755606323
x24=−40.7672484166364x_{24} = -40.7672484166364
x25=65.9279728888237x_{25} = 65.9279728888237
x26=31.3204337466541x_{26} = 31.3204337466541
x27=−34.4707075119921x_{27} = -34.4707075119921
x28=−65.9279728888237x_{28} = -65.9279728888237
x29=21.8547311042253x_{29} = 21.8547311042253
x30=−91.0732583460488x_{30} = -91.0732583460488
x31=−87.9304896708771x_{31} = -87.9304896708771
x32=−59.6400009696211x_{32} = -59.6400009696211
x33=−9.10654133164946x_{33} = -9.10654133164946
x34=87.9304896708771x_{34} = 87.9304896708771
x35=34.4707075119921x_{35} = 34.4707075119921
x36=28.1682308860662x_{36} = 28.1682308860662
x37=69.0716324888295x_{37} = 69.0716324888295
x38=−94.2159486198017x_{38} = -94.2159486198017
x39=−37.6195344424891x_{39} = -37.6195344424891
x40=518.35700038984x_{40} = 518.35700038984
x41=47.0602278498565x_{41} = 47.0602278498565
x42=59.6400009696211x_{42} = 59.6400009696211
x43=81.6446809310296x_{43} = 81.6446809310296
x44=53.3509027906022x_{44} = 53.3509027906022
x45=−2.20452539445172x_{45} = -2.20452539445172
x46=−18.6904032530853x_{46} = -18.6904032530853
x47=−15.5169830019484x_{47} = -15.5169830019484
x48=−97.3585680793661x_{48} = -97.3585680793661
x49=15.5169830019484x_{49} = 15.5169830019484
x50=43.9140879217563x_{50} = 43.9140879217563
x51=−43.9140879217563x_{51} = -43.9140879217563
x52=62.7841065943838x_{52} = 62.7841065943838
x53=−78.50161915521x_{53} = -78.50161915521
x54=−50.2057993706114x_{54} = -50.2057993706114
x55=9.10654133164946x_{55} = 9.10654133164946
x56=−28.1682308860662x_{56} = -28.1682308860662
x57=−12.327655521099x_{57} = -12.327655521099
x58=−75.3584349525985x_{58} = -75.3584349525985
x59=−1083.84669757642x_{59} = -1083.84669757642
x60=2.20452539445172x_{60} = 2.20452539445172
x61=84.7876338830228x_{61} = 84.7876338830228
x62=−5.80628149104622x_{62} = -5.80628149104622
x63=−56.4956161262601x_{63} = -56.4956161262601
x64=−53.3509027906022x_{64} = -53.3509027906022
x65=−103.643620306534x_{65} = -103.643620306534
x66=25.0133755606323x_{66} = 25.0133755606323
x67=−69.0716324888295x_{67} = -69.0716324888295
x68=−21.8547311042253x_{68} = -21.8547311042253
Signos de extremos en los puntos:
(12.327655521098961, 0.000518638886803666)

(-100.50112336356959, -9.84677125634237e-7)

(-47.06022784985651, 9.5754074775838e-6)

(75.35843495259849, 2.33485826727833e-6)

(-84.7876338830228, 1.63957304942886e-6)

(50.20579937061139, 7.88795433540522e-6)

(37.619534442489126, 1.87233345638677e-5)

(56.49561612626008, 5.53788980086548e-6)

(78.50161915520997, -2.0656049051152e-6)

(94.21594861980165, 1.19510667228868e-6)

(72.21511235450072, -2.65302474093483e-6)

(-380.1248191037165, 1.82057173454409e-8)

(5.8062814910462155, 0.00453862470500485)

(100.50112336356959, 9.84677125634237e-7)

(18.690403253085307, 0.000151223874462241)

(-72.21511235450072, 2.65302474093483e-6)

(-62.78410659438384, -4.03604146547336e-6)

(-81.64468093102955, -1.83621412894209e-6)

(91.07325834604883, -1.32309760125654e-6)

(97.3585680793661, -1.08310705206369e-6)

(-31.320433746654114, -3.23991444144119e-5)

(40.767248416636356, -1.47195001853466e-5)

(-25.01337556063232, -6.34427155787386e-5)

(-40.767248416636356, 1.47195001853466e-5)

(65.92797288882375, -3.48611464323845e-6)

(31.320433746654114, 3.23991444144119e-5)

(-34.47070751199214, 2.43226487730105e-5)

(-65.92797288882375, 3.48611464323845e-6)

(21.854731104225348, -9.49095579677938e-5)

(-91.07325834604883, 1.32309760125654e-6)

(-87.93048967087708, -1.47003916834536e-6)

(-59.640000969621056, 4.70802030061175e-6)

(-9.106541331649463, 0.00125766965231332)

(87.93048967087708, 1.47003916834536e-6)

(34.47070751199214, -2.43226487730105e-5)

(28.1682308860662, -4.44909904084811e-5)

(69.07163248882952, 3.03173745311126e-6)

(-94.21594861980165, -1.19510667228868e-6)

(-37.619534442489126, -1.87233345638677e-5)

(518.35700038984, -7.17969214279648e-9)

(47.06022784985651, -9.5754074775838e-6)

(59.640000969621056, -4.70802030061175e-6)

(81.64468093102955, 1.83621412894209e-6)

(53.350902790602206, -6.57489996749211e-6)

(-2.2045253944517174, 0.0552699707829989)

(-18.690403253085307, -0.000151223874462241)

(-15.516983001948434, 0.000262790351635489)

(-97.3585680793661, 1.08310705206369e-6)

(15.516983001948434, -0.000262790351635489)

(43.914087921756334, 1.17808692820516e-5)

(-43.914087921756334, -1.17808692820516e-5)

(62.78410659438384, 4.03604146547336e-6)

(-78.50161915520997, 2.0656049051152e-6)

(-50.20579937061139, -7.88795433540522e-6)

(9.106541331649463, -0.00125766965231332)

(-28.1682308860662, 4.44909904084811e-5)

(-12.327655521098961, -0.000518638886803666)

(-75.35843495259849, -2.33485826727833e-6)

(-1083.846697576425, 7.85406986804821e-10)

(2.2045253944517174, -0.0552699707829989)

(84.7876338830228, -1.63957304942886e-6)

(-5.8062814910462155, -0.00453862470500485)

(-56.49561612626008, -5.53788980086548e-6)

(-53.350902790602206, 6.57489996749211e-6)

(-103.64362030653376, 8.97822364178806e-7)

(25.01337556063232, 6.34427155787386e-5)

(-69.07163248882952, -3.03173745311126e-6)

(-21.854731104225348, 9.49095579677938e-5)


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=−100.50112336357x_{1} = -100.50112336357
x2=78.50161915521x_{2} = 78.50161915521
x3=72.2151123545007x_{3} = 72.2151123545007
x4=−62.7841065943838x_{4} = -62.7841065943838
x5=−81.6446809310296x_{5} = -81.6446809310296
x6=91.0732583460488x_{6} = 91.0732583460488
x7=97.3585680793661x_{7} = 97.3585680793661
x8=−31.3204337466541x_{8} = -31.3204337466541
x9=40.7672484166364x_{9} = 40.7672484166364
x10=−25.0133755606323x_{10} = -25.0133755606323
x11=65.9279728888237x_{11} = 65.9279728888237
x12=21.8547311042253x_{12} = 21.8547311042253
x13=−87.9304896708771x_{13} = -87.9304896708771
x14=34.4707075119921x_{14} = 34.4707075119921
x15=28.1682308860662x_{15} = 28.1682308860662
x16=−94.2159486198017x_{16} = -94.2159486198017
x17=−37.6195344424891x_{17} = -37.6195344424891
x18=518.35700038984x_{18} = 518.35700038984
x19=47.0602278498565x_{19} = 47.0602278498565
x20=59.6400009696211x_{20} = 59.6400009696211
x21=53.3509027906022x_{21} = 53.3509027906022
x22=−18.6904032530853x_{22} = -18.6904032530853
x23=15.5169830019484x_{23} = 15.5169830019484
x24=−43.9140879217563x_{24} = -43.9140879217563
x25=−50.2057993706114x_{25} = -50.2057993706114
x26=9.10654133164946x_{26} = 9.10654133164946
x27=−12.327655521099x_{27} = -12.327655521099
x28=−75.3584349525985x_{28} = -75.3584349525985
x29=2.20452539445172x_{29} = 2.20452539445172
x30=84.7876338830228x_{30} = 84.7876338830228
x31=−5.80628149104622x_{31} = -5.80628149104622
x32=−56.4956161262601x_{32} = -56.4956161262601
x33=−69.0716324888295x_{33} = -69.0716324888295
Puntos máximos de la función:
x33=12.327655521099x_{33} = 12.327655521099
x33=−47.0602278498565x_{33} = -47.0602278498565
x33=75.3584349525985x_{33} = 75.3584349525985
x33=−84.7876338830228x_{33} = -84.7876338830228
x33=50.2057993706114x_{33} = 50.2057993706114
x33=37.6195344424891x_{33} = 37.6195344424891
x33=56.4956161262601x_{33} = 56.4956161262601
x33=94.2159486198017x_{33} = 94.2159486198017
x33=−380.124819103717x_{33} = -380.124819103717
x33=5.80628149104622x_{33} = 5.80628149104622
x33=100.50112336357x_{33} = 100.50112336357
x33=18.6904032530853x_{33} = 18.6904032530853
x33=−72.2151123545007x_{33} = -72.2151123545007
x33=−40.7672484166364x_{33} = -40.7672484166364
x33=31.3204337466541x_{33} = 31.3204337466541
x33=−34.4707075119921x_{33} = -34.4707075119921
x33=−65.9279728888237x_{33} = -65.9279728888237
x33=−91.0732583460488x_{33} = -91.0732583460488
x33=−59.6400009696211x_{33} = -59.6400009696211
x33=−9.10654133164946x_{33} = -9.10654133164946
x33=87.9304896708771x_{33} = 87.9304896708771
x33=69.0716324888295x_{33} = 69.0716324888295
x33=81.6446809310296x_{33} = 81.6446809310296
x33=−2.20452539445172x_{33} = -2.20452539445172
x33=−15.5169830019484x_{33} = -15.5169830019484
x33=−97.3585680793661x_{33} = -97.3585680793661
x33=43.9140879217563x_{33} = 43.9140879217563
x33=62.7841065943838x_{33} = 62.7841065943838
x33=−78.50161915521x_{33} = -78.50161915521
x33=−28.1682308860662x_{33} = -28.1682308860662
x33=−1083.84669757642x_{33} = -1083.84669757642
x33=−53.3509027906022x_{33} = -53.3509027906022
x33=−103.643620306534x_{33} = -103.643620306534
x33=25.0133755606323x_{33} = 25.0133755606323
x33=−21.8547311042253x_{33} = -21.8547311042253
Decrece en los intervalos
[518.35700038984,∞)\left[518.35700038984, \infty\right)
Crece en los intervalos
(−∞,−100.50112336357]\left(-\infty, -100.50112336357\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
−cos⁡(x)+6sin⁡(x)x+12cos⁡(x)x2x3=0\frac{- \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x} + \frac{12 \cos{\left(x \right)}}{x^{2}}}{x^{3}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−39.1165221766479x_{1} = -39.1165221766479
x2=−64.309350525737x_{2} = -64.309350525737
x3=51.7202705758154x_{3} = 51.7202705758154
x4=−1101.12277609958x_{4} = -1101.12277609958
x5=−10.4211159851982x_{5} = -10.4211159851982
x6=−26.4769383696331x_{6} = -26.4769383696331
x7=−20.122225770141x_{7} = -20.122225770141
x8=42.2695559651998x_{8} = 42.2695559651998
x9=45.4209968701311x_{9} = 45.4209968701311
x10=35.9614731475646x_{10} = 35.9614731475646
x11=86.3242926617524x_{11} = 86.3242926617524
x12=2.96199364864811x_{12} = 2.96199364864811
x13=23.3045087351796x_{13} = 23.3045087351796
x14=13.6995377525183x_{14} = 13.6995377525183
x15=10.4211159851982x_{15} = 10.4211159851982
x16=83.1800727023055x_{16} = 83.1800727023055
x17=−61.1629583560126x_{17} = -61.1629583560126
x18=73.7460671675927x_{18} = 73.7460671675927
x19=−98.8995009594538x_{19} = -98.8995009594538
x20=16.9243617828713x_{20} = 16.9243617828713
x21=7.00608718232099x_{21} = 7.00608718232099
x22=318.852836880997x_{22} = 318.852836880997
x23=−16.9243617828713x_{23} = -16.9243617828713
x24=61.1629583560126x_{24} = 61.1629583560126
x25=58.0160446870318x_{25} = 58.0160446870318
x26=−80.0356461224424x_{26} = -80.0356461224424
x27=−45.4209968701311x_{27} = -45.4209968701311
x28=70.6008499915982x_{28} = 70.6008499915982
x29=−58.0160446870318x_{29} = -58.0160446870318
x30=−89.4683278191374x_{30} = -89.4683278191374
x31=−70.6008499915982x_{31} = -70.6008499915982
x32=−67.4552943761651x_{32} = -67.4552943761651
x33=−35.9614731475646x_{33} = -35.9614731475646
x34=29.6427271594457x_{34} = 29.6427271594457
x35=−73.7460671675927x_{35} = -73.7460671675927
x36=−42.2695559651998x_{36} = -42.2695559651998
x37=−7.00608718232099x_{37} = -7.00608718232099
x38=−92.6121970232972x_{38} = -92.6121970232972
x39=−29.6427271594457x_{39} = -29.6427271594457
x40=−158.612600992057x_{40} = -158.612600992057
x41=−54.8685194624546x_{41} = -54.8685194624546
x42=−83.1800727023055x_{42} = -83.1800727023055
x43=95.7559166424368x_{43} = 95.7559166424368
x44=76.8909875249209x_{44} = 76.8909875249209
x45=−2.96199364864811x_{45} = -2.96199364864811
x46=20.122225770141x_{46} = 20.122225770141
x47=−13.6995377525183x_{47} = -13.6995377525183
x48=183.750517266523x_{48} = 183.750517266523
x49=−51.7202705758154x_{49} = -51.7202705758154
x50=89.4683278191374x_{50} = 89.4683278191374
x51=32.8038218584153x_{51} = 32.8038218584153
x52=64.309350525737x_{52} = 64.309350525737
x53=98.8995009594538x_{53} = 98.8995009594538
x54=48.5711566642438x_{54} = 48.5711566642438
x55=−23.3045087351796x_{55} = -23.3045087351796
x56=54.8685194624546x_{56} = 54.8685194624546
x57=−95.7559166424368x_{57} = -95.7559166424368
x58=92.6121970232972x_{58} = 92.6121970232972
x59=−32.8038218584153x_{59} = -32.8038218584153
x60=−48.5711566642438x_{60} = -48.5711566642438
x61=39.1165221766479x_{61} = 39.1165221766479
x62=80.0356461224424x_{62} = 80.0356461224424
x63=67.4552943761651x_{63} = 67.4552943761651
x64=−86.3242926617524x_{64} = -86.3242926617524
x65=−76.8909875249209x_{65} = -76.8909875249209
x66=26.4769383696331x_{66} = 26.4769383696331
x67=−180.608356528119x_{67} = -180.608356528119
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−(−cos⁡(x)+6sin⁡(x)x+12cos⁡(x)x2x3)=−∞\lim_{x \to 0^-}\left(\frac{- \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x} + \frac{12 \cos{\left(x \right)}}{x^{2}}}{x^{3}}\right) = -\infty
lim⁡x→0+(−cos⁡(x)+6sin⁡(x)x+12cos⁡(x)x2x3)=∞\lim_{x \to 0^+}\left(\frac{- \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x} + \frac{12 \cos{\left(x \right)}}{x^{2}}}{x^{3}}\right) = \infty
- los límites no son iguales, signo
x1=0x_{1} = 0
- es el punto de flexión

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
[183.750517266523,∞)\left[183.750517266523, \infty\right)
Convexa en los intervalos
(−∞,−1101.12277609958]\left(-\infty, -1101.12277609958\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→−∞(cos⁡(x)x3)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x^{3}}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(cos⁡(x)x3)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x^{3}}\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 cos(x)/x^3, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡(x)xx3)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x x^{3}}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(cos⁡(x)xx3)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x x^{3}}\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:
cos⁡(x)x3=−cos⁡(x)x3\frac{\cos{\left(x \right)}}{x^{3}} = - \frac{\cos{\left(x \right)}}{x^{3}}
- No
cos⁡(x)x3=cos⁡(x)x3\frac{\cos{\left(x \right)}}{x^{3}} = \frac{\cos{\left(x \right)}}{x^{3}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор