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y=x^2sin2x+x^3cos6x

  • ¿Cómo usar?

  • Gráfico de la función y =:
  • y=(x+1)^3 y=(x+1)^3
  • 2*x^2-6*x 2*x^2-6*x
  • y=2x y=2x
  • y=1/(x^2+1) y=1/(x^2+1)

  • Expresiones idénticas

  • y=x^2sin2x+x^3cos6x
  • y es igual a x al cuadrado seno de 2x más x al cubo coseno de 6x
  • y=x2sin2x+x3cos6x
  • y=x²sin2x+x³cos6x
  • y=x en el grado 2sin2x+x en el grado 3cos6x

  • Expresiones semejantes

  • y=x^2sin2x-x^3cos6x
Trazado el gráfico de la función/ y=x^2sin2x+x^3cos6x

Gráfico de la función y = y=x^2sin2x+x^3cos6x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        2             3         
f(x) = x *sin(2*x) + x *cos(6*x)
f(x)=x3cos⁡(6x)+x2sin⁡(2x)f{\left(x \right)} = x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)} 
f = x^3*cos(6*x) + x^2*sin(2*x)
Gráfico de la función
02468-8-6-4-2-1010-20002000
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:
x3cos⁡(6x)+x2sin⁡(2x)=0x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−28.0154788038127x_{1} = -28.0154788038127
x2=10.193808794838x_{2} = 10.193808794838
x3=−8.12641838476076x_{3} = -8.12641838476076
x4=74.0903559051904x_{4} = 74.0903559051904
x5=−9.69543911966972x_{5} = -9.69543911966972
x6=−55.7602805089514x_{6} = -55.7602805089514
x7=−67.8072756753362x_{7} = -67.8072756753362
x8=−52.0996865984972x_{8} = -52.0996865984972
x9=−75.6611286999348x_{9} = -75.6611286999348
x10=98.1730727230249x_{10} = 98.1730727230249
x11=40.0511446990708x_{11} = 40.0511446990708
x12=34.2981292537459x_{12} = 34.2981292537459
x13=−23.8272847528803x_{13} = -23.8272847528803
x14=30.1097241320694x_{14} = 30.1097241320694
x15=84.0356201663487x_{15} = 84.0356201663487
x16=−96.0812452601808x_{16} = -96.0812452601808
x17=−60.472902442502x_{17} = -60.472902442502
x18=−50.0053400111493x_{18} = -50.0053400111493
x19=−53.6704355966766x_{19} = -53.6704355966766
x20=42.1516650063277x_{20} = 42.1516650063277
x21=−21.7331335278959x_{21} = -21.7331335278959
x22=−25.9117062279096x_{22} = -25.9117062279096
x23=−62.0437685551729x_{23} = -62.0437685551729
x24=46.3348944531563x_{24} = 46.3348944531563
x25=86.1329628541732x_{25} = 86.1329628541732
x26=−31.6803806285001x_{26} = -31.6803806285001
x27=7.04487229385904x_{27} = 7.04487229385904
x28=62.0437685551729x_{28} = 62.0437685551729
x29=−89.7981210187881x_{29} = -89.7981210187881
x30=81.9442289324407x_{30} = 81.9442289324407
x31=59.9534565091502x_{31} = 59.9534565091502
x32=−79.8498531492477x_{32} = -79.8498531492477
x33=−99.743895786784x_{33} = -99.743895786784
x34=−35.8688209088003x_{34} = -35.8688209088003
x35=81.4206294854476x_{35} = 81.4206294854476
x36=68.3272009142264x_{36} = 68.3272009142264
x37=−47.9058087495602x_{37} = -47.9058087495602
x38=8.12641838476076x_{38} = 8.12641838476076
x39=−97.6520275520115x_{39} = -97.6520275520115
x40=88.2273413219038x_{40} = 88.2273413219038
x41=69.8980520630875x_{41} = 69.8980520630875
x42=22.2567415701179x_{42} = 22.2567415701179
x43=−7.60274672186039x_{43} = -7.60274672186039
x44=−71.9959845003571x_{44} = -71.9959845003571
x45=−84.0356201663487x_{45} = -84.0356201663487
x46=18.0549235162566x_{46} = 18.0549235162566
x47=15.9750757276842x_{47} = 15.9750757276842
x48=−91.8897713262871x_{48} = -91.8897713262871
x49=−93.986864156421x_{49} = -93.986864156421
x50=4.99193075669672x_{50} = 4.99193075669672
x51=−13.8812493456914x_{51} = -13.8812493456914
x52=12.3111861783929x_{52} = 12.3111861783929
x53=64.1421433963099x_{53} = 64.1421433963099
x54=91.3689012892751x_{54} = 91.3689012892751
x55=−18.0549235162566x_{55} = -18.0549235162566
x56=−69.8980520630875x_{56} = -69.8980520630875
x57=24.3404944805221x_{57} = 24.3404944805221
x58=−74.0903559051904x_{58} = -74.0903559051904
x59=54.1893975256372x_{59} = 54.1893975256372
x60=−65.7129089415496x_{60} = -65.7129089415496
x61=−43.7223912525467x_{61} = -43.7223912525467
x62=78.2790776123768x_{62} = 78.2790776123768
x63=−6.03457341378836x_{63} = -6.03457341378836
x64=56.2883413079972x_{64} = 56.2883413079972
x65=28.0154788038127x_{65} = 28.0154788038127
x66=25.9117062279096x_{66} = 25.9117062279096
x67=93.986864156421x_{67} = 93.986864156421
x68=6.03457341378836x_{68} = 6.03457341378836
x69=66.2365087463345x_{69} = 66.2365087463345
x70=−57.8590978455737x_{70} = -57.8590978455737
x71=2.2814790359167x_{71} = 2.2814790359167
x72=71.9959845003571x_{72} = 71.9959845003571
x73=−45.8167232631001x_{73} = -45.8167232631001
x74=3.88375402169664x_{74} = 3.88375402169664
x75=44.2459923439688x_{75} = 44.2459923439688
x76=−33.7671847865607x_{76} = -33.7671847865607
x77=47.9058087495602x_{77} = 47.9058087495602
x78=52.0996865984972x_{78} = 52.0996865984972
x79=0x_{79} = 0
x80=−77.7522745769354x_{80} = -77.7522745769354
x81=−1.8855169330842x_{81} = -1.8855169330842
x82=50.0053400111493x_{82} = 50.0053400111493
x83=76.181434048026x_{83} = 76.181434048026
x84=20.1626278461094x_{84} = 20.1626278461094
x85=37.9631232070365x_{85} = 37.9631232070365
x86=−15.9750757276842x_{86} = -15.9750757276842
x87=−76.7083029237545x_{87} = -76.7083029237545
x88=−59.9534565091502x_{88} = -59.9534565091502
x89=32.1961475414769x_{89} = 32.1961475414769
x90=−40.0511446990708x_{90} = -40.0511446990708
x91=96.0812452601808x_{91} = 96.0812452601808
x92=100.269994232962x_{92} = 100.269994232962
x93=−81.9442289324407x_{93} = -81.9442289324407
x94=−29.0539948445491x_{94} = -29.0539948445491
x95=90.3189434531672x_{95} = 90.3189434531672
x96=−87.7037419674016x_{96} = -87.7037419674016
x97=−37.9631232070365x_{97} = -37.9631232070365
x98=−3.88375402169664x_{98} = -3.88375402169664
x99=−11.7667969089396x_{99} = -11.7667969089396
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 x^2*sin(2*x) + x^3*cos(6*x).
02sin⁡(0⋅2)+03cos⁡(0⋅6)0^{2} \sin{\left(0 \cdot 2 \right)} + 0^{3} \cos{\left(0 \cdot 6 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(x3cos⁡(6x)+x2sin⁡(2x))y = \lim_{x \to -\infty}\left(x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(x3cos⁡(6x)+x2sin⁡(2x))y = \lim_{x \to \infty}\left(x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x^2*sin(2*x) + x^3*cos(6*x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(x3cos⁡(6x)+x2sin⁡(2x)x)y = x \lim_{x \to -\infty}\left(\frac{x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(x3cos⁡(6x)+x2sin⁡(2x)x)y = x \lim_{x \to \infty}\left(\frac{x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)}}{x}\right)
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:
x3cos⁡(6x)+x2sin⁡(2x)=−x3cos⁡(6x)−x2sin⁡(2x)x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)} = - x^{3} \cos{\left(6 x \right)} - x^{2} \sin{\left(2 x \right)}
- No
x3cos⁡(6x)+x2sin⁡(2x)=x3cos⁡(6x)+x2sin⁡(2x)x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)} = x^{3} \cos{\left(6 x \right)} + x^{2} \sin{\left(2 x \right)}
- Sí
es decir, función
es
impar
Gráfico
Gráfico de la función y = y=x^2sin2x+x^3cos6x
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