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- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
x^2*exp(-x)
-
1/(1-x^2)
-
-exp(x)-exp(-x)-exp(2*x)
-
-exp(5*x)
-
Expresiones idénticas
- (absolute(x- siete)*sin(x))/(x^ tres -x^ dos -42x)
- (absolute(x menos 7) multiplicar por seno de (x)) dividir por (x al cubo menos x al cuadrado menos 42x)
- (absolute(x menos siete) multiplicar por seno de (x)) dividir por (x en el grado tres menos x en el grado dos menos 42x)
- (absolute(x-7)*sin(x))/(x3-x2-42x)
- absolutex-7*sinx/x3-x2-42x
- (absolute(x-7)*sin(x))/(x³-x²-42x)
- (absolute(x-7)*sin(x))/(x en el grado 3-x en el grado 2-42x)
- (absolute(x-7)sin(x))/(x^3-x^2-42x)
- (absolute(x-7)sin(x))/(x3-x2-42x)
- absolutex-7sinx/x3-x2-42x
- absolutex-7sinx/x^3-x^2-42x
- (absolute(x-7)*sin(x)) dividir por (x^3-x^2-42x)
-
Expresiones semejantes
- (absolute(x-7)*sin(x))/(x^3+x^2-42x)
- (absolute(x-7)*sin(x))/(x^3-x^2+42x)
- (absolute(x+7)*sin(x))/(x^3-x^2-42x)
- (absolute(x-7)*sinx)/(x^3-x^2-42x)
-
Expresiones con funciones
- absolute
- absolute(sqrt(x)-4)
- absolute(x+2)+1/(x-1)^2
- absolute(x^2+x^3)
- absolute(3x+1)
- absolute(x)+cos(x)
- Seno sin
- sin(x)-x*cos(x)
- sin(2*x)/x
- sinx*cosx
- sin3x
- sin(x)^3
Gráfico de la función y = (absolute(x-7)*sin(x))/(x^3-x^2-42x)
Solución
Ha introducido
[src]
|x - 7|*sin(x)
f(x) = --------------
3 2
x - x - 42*x
$$f{\left(x \right)} = \frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)}$$
f = (sin(x)*|x - 7|)/(-42*x + x^3 - x^2)
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$x_{1} = -6$$
$$x_{2} = 0$$
$$x_{3} = 7$$
$$x_{1} = -6$$
$$x_{2} = 0$$
$$x_{3} = 7$$
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:
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = \pi$$
Solución numérica
$$x_{1} = 43.9822971502571$$
$$x_{2} = -97.3893722612836$$
$$x_{3} = -43.9822971502571$$
$$x_{4} = -72.2566310325652$$
$$x_{5} = -59.6902604182061$$
$$x_{6} = 81.6814089933346$$
$$x_{7} = -31.4159265358979$$
$$x_{8} = -78.5398163397448$$
$$x_{9} = 97.3893722612836$$
$$x_{10} = 9.42477796076938$$
$$x_{11} = -25.1327412287183$$
$$x_{12} = 84.8230016469244$$
$$x_{13} = 2214.8228207808$$
$$x_{14} = -21.9911485751286$$
$$x_{15} = -94.2477796076938$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = 3.14159265358979$$
$$x_{18} = -50.2654824574367$$
$$x_{19} = 28.2743338823081$$
$$x_{20} = -75.398223686155$$
$$x_{21} = -28.2743338823081$$
$$x_{22} = -56.5486677646163$$
$$x_{23} = -65.9734457253857$$
$$x_{24} = -40.8407044966673$$
$$x_{25} = 1316.32732185513$$
$$x_{26} = -91.106186954104$$
$$x_{27} = 50.2654824574367$$
$$x_{28} = -69.1150383789755$$
$$x_{29} = -100.530964914873$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = -62.8318530717959$$
$$x_{32} = -191.637151868977$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = 100.530964914873$$
$$x_{35} = -87.9645943005142$$
$$x_{36} = 18.8495559215388$$
$$x_{37} = 62.8318530717959$$
$$x_{38} = -53.4070751110265$$
$$x_{39} = 94.2477796076938$$
$$x_{40} = -3.14159265358979$$
$$x_{41} = 21.9911485751286$$
$$x_{42} = 12.5663706143592$$
$$x_{43} = -84.8230016469244$$
$$x_{44} = 34.5575191894877$$
$$x_{45} = 47.1238898038469$$
$$x_{46} = -15.707963267949$$
$$x_{47} = 53.4070751110265$$
$$x_{48} = 65.9734457253857$$
$$x_{49} = 87.9645943005142$$
$$x_{50} = 91.106186954104$$
$$x_{51} = 59.6902604182061$$
$$x_{52} = 69.1150383789755$$
$$x_{53} = 75.398223686155$$
$$x_{54} = -37.6991118430775$$
$$x_{55} = -12.5663706143592$$
$$x_{56} = -18.8495559215388$$
$$x_{57} = 31.4159265358979$$
$$x_{58} = -81.6814089933346$$
$$x_{59} = 78.5398163397448$$
$$x_{60} = 15.707963267949$$
$$x_{61} = 72.2566310325652$$
$$x_{62} = 37.6991118430775$$
$$x_{63} = 25.1327412287183$$
$$x_{64} = -47.1238898038469$$
$$x_{65} = -1671.32729170977$$
$$x_{66} = -9.42477796076938$$
$$x_{67} = -34.5575191894877$$
o sea hay que resolver la ecuación:
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = \pi$$
Solución numérica
$$x_{1} = 43.9822971502571$$
$$x_{2} = -97.3893722612836$$
$$x_{3} = -43.9822971502571$$
$$x_{4} = -72.2566310325652$$
$$x_{5} = -59.6902604182061$$
$$x_{6} = 81.6814089933346$$
$$x_{7} = -31.4159265358979$$
$$x_{8} = -78.5398163397448$$
$$x_{9} = 97.3893722612836$$
$$x_{10} = 9.42477796076938$$
$$x_{11} = -25.1327412287183$$
$$x_{12} = 84.8230016469244$$
$$x_{13} = 2214.8228207808$$
$$x_{14} = -21.9911485751286$$
$$x_{15} = -94.2477796076938$$
$$x_{16} = 6.28318530717959$$
$$x_{17} = 3.14159265358979$$
$$x_{18} = -50.2654824574367$$
$$x_{19} = 28.2743338823081$$
$$x_{20} = -75.398223686155$$
$$x_{21} = -28.2743338823081$$
$$x_{22} = -56.5486677646163$$
$$x_{23} = -65.9734457253857$$
$$x_{24} = -40.8407044966673$$
$$x_{25} = 1316.32732185513$$
$$x_{26} = -91.106186954104$$
$$x_{27} = 50.2654824574367$$
$$x_{28} = -69.1150383789755$$
$$x_{29} = -100.530964914873$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = -62.8318530717959$$
$$x_{32} = -191.637151868977$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = 100.530964914873$$
$$x_{35} = -87.9645943005142$$
$$x_{36} = 18.8495559215388$$
$$x_{37} = 62.8318530717959$$
$$x_{38} = -53.4070751110265$$
$$x_{39} = 94.2477796076938$$
$$x_{40} = -3.14159265358979$$
$$x_{41} = 21.9911485751286$$
$$x_{42} = 12.5663706143592$$
$$x_{43} = -84.8230016469244$$
$$x_{44} = 34.5575191894877$$
$$x_{45} = 47.1238898038469$$
$$x_{46} = -15.707963267949$$
$$x_{47} = 53.4070751110265$$
$$x_{48} = 65.9734457253857$$
$$x_{49} = 87.9645943005142$$
$$x_{50} = 91.106186954104$$
$$x_{51} = 59.6902604182061$$
$$x_{52} = 69.1150383789755$$
$$x_{53} = 75.398223686155$$
$$x_{54} = -37.6991118430775$$
$$x_{55} = -12.5663706143592$$
$$x_{56} = -18.8495559215388$$
$$x_{57} = 31.4159265358979$$
$$x_{58} = -81.6814089933346$$
$$x_{59} = 78.5398163397448$$
$$x_{60} = 15.707963267949$$
$$x_{61} = 72.2566310325652$$
$$x_{62} = 37.6991118430775$$
$$x_{63} = 25.1327412287183$$
$$x_{64} = -47.1238898038469$$
$$x_{65} = -1671.32729170977$$
$$x_{66} = -9.42477796076938$$
$$x_{67} = -34.5575191894877$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\frac{\sin{\left(x \right)} \operatorname{sign}{\left(x - 7 \right)} + \cos{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} + \frac{\left(- 3 x^{2} + 2 x + 42\right) \sin{\left(x \right)} \left|{x - 7}\right|}{\left(- 42 x + \left(x^{3} - x^{2}\right)\right)^{2}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 14.016453093047$$
$$x_{2} = 26.6354574736327$$
$$x_{3} = -42.3604359016656$$
$$x_{4} = -61.2266303830853$$
$$x_{5} = 54.9432759558649$$
$$x_{6} = -76.9419337897232$$
$$x_{7} = 83.2289873280938$$
$$x_{8} = 64.3729136691542$$
$$x_{9} = -64.369993732511$$
$$x_{10} = -13.9420438831868$$
$$x_{11} = 70.6586440153259$$
$$x_{12} = 29.7836865268305$$
$$x_{13} = 36.0768763247778$$
$$x_{14} = -32.919299828625$$
$$x_{15} = -51.7951587828659$$
$$x_{16} = 80.0865146143929$$
$$x_{17} = -95.7970043123775$$
$$x_{18} = -48.6507135445059$$
$$x_{19} = 42.3672514439482$$
$$x_{20} = 98.9405348240556$$
$$x_{21} = -26.6176780767465$$
$$x_{22} = -89.512248812553$$
$$x_{23} = -54.939255228509$$
$$x_{24} = -73.7991351656219$$
$$x_{25} = -67.5131834431642$$
$$x_{26} = 10.8451478646932$$
$$x_{27} = 17.1777448915114$$
$$x_{28} = 95.7983167647195$$
$$x_{29} = 23.485599433969$$
$$x_{30} = -17.1316249007671$$
$$x_{31} = -10.6983350907497$$
$$x_{32} = -39.2143570561418$$
$$x_{33} = 76.9439724516011$$
$$x_{34} = 149.212507171659$$
$$x_{35} = -58.0830633547885$$
$$x_{36} = 73.8013522673499$$
$$x_{37} = 48.6558568457253$$
$$x_{38} = -86.3697819811265$$
$$x_{39} = 89.5137528406582$$
$$x_{40} = 92.6560575082574$$
$$x_{41} = 146.07063730353$$
$$x_{42} = 7.65282388683543$$
$$x_{43} = -20.3017332658149$$
$$x_{44} = -92.6546541656147$$
$$x_{45} = -23.4623877903398$$
$$x_{46} = 67.5158358436257$$
$$x_{47} = 51.799688855665$$
$$x_{48} = 58.0866563372379$$
$$x_{49} = -98.9393046989388$$
$$x_{50} = -7.00360982839007$$
$$x_{51} = -80.0846336468534$$
$$x_{52} = 20.3334172344451$$
$$x_{53} = -70.6562239130531$$
$$x_{54} = 86.3713979521823$$
$$x_{55} = -45.5058407635821$$
$$x_{56} = -83.2272464103056$$
$$x_{57} = -36.0674064816266$$
$$x_{58} = 61.229860625401$$
$$x_{59} = 4.39955639048156$$
$$x_{60} = 39.2223354468251$$
$$x_{61} = -0.53859704600586$$
$$x_{62} = 45.5117316703557$$
$$x_{63} = -29.7696122729537$$
$$x_{64} = 32.9307280335231$$
Signos de extremos en los puntos:
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:
$$x_{1} = -42.3604359016656$$
$$x_{2} = -61.2266303830853$$
$$x_{3} = 54.9432759558649$$
$$x_{4} = 29.7836865268305$$
$$x_{5} = 36.0768763247778$$
$$x_{6} = 80.0865146143929$$
$$x_{7} = -48.6507135445059$$
$$x_{8} = 42.3672514439482$$
$$x_{9} = 98.9405348240556$$
$$x_{10} = -54.939255228509$$
$$x_{11} = -73.7991351656219$$
$$x_{12} = -67.5131834431642$$
$$x_{13} = 10.8451478646932$$
$$x_{14} = 17.1777448915114$$
$$x_{15} = 23.485599433969$$
$$x_{16} = -17.1316249007671$$
$$x_{17} = -10.6983350907497$$
$$x_{18} = 149.212507171659$$
$$x_{19} = 73.8013522673499$$
$$x_{20} = 48.6558568457253$$
$$x_{21} = -86.3697819811265$$
$$x_{22} = 92.6560575082574$$
$$x_{23} = -92.6546541656147$$
$$x_{24} = -23.4623877903398$$
$$x_{25} = 67.5158358436257$$
$$x_{26} = -98.9393046989388$$
$$x_{27} = -80.0846336468534$$
$$x_{28} = 86.3713979521823$$
$$x_{29} = -36.0674064816266$$
$$x_{30} = 61.229860625401$$
$$x_{31} = -0.53859704600586$$
$$x_{32} = -29.7696122729537$$
Puntos máximos de la función:
$$x_{32} = 14.016453093047$$
$$x_{32} = 26.6354574736327$$
$$x_{32} = -76.9419337897232$$
$$x_{32} = 83.2289873280938$$
$$x_{32} = 64.3729136691542$$
$$x_{32} = -64.369993732511$$
$$x_{32} = -13.9420438831868$$
$$x_{32} = 70.6586440153259$$
$$x_{32} = -32.919299828625$$
$$x_{32} = -51.7951587828659$$
$$x_{32} = -95.7970043123775$$
$$x_{32} = -26.6176780767465$$
$$x_{32} = -89.512248812553$$
$$x_{32} = 95.7983167647195$$
$$x_{32} = -39.2143570561418$$
$$x_{32} = 76.9439724516011$$
$$x_{32} = -58.0830633547885$$
$$x_{32} = 89.5137528406582$$
$$x_{32} = 146.07063730353$$
$$x_{32} = 7.65282388683543$$
$$x_{32} = -20.3017332658149$$
$$x_{32} = 51.799688855665$$
$$x_{32} = 58.0866563372379$$
$$x_{32} = -7.00360982839007$$
$$x_{32} = 20.3334172344451$$
$$x_{32} = -70.6562239130531$$
$$x_{32} = -45.5058407635821$$
$$x_{32} = -83.2272464103056$$
$$x_{32} = 4.39955639048156$$
$$x_{32} = 39.2223354468251$$
$$x_{32} = 45.5117316703557$$
$$x_{32} = 32.9307280335231$$
Decrece en los intervalos
$$\left[149.212507171659, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -98.9393046989388\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$\frac{\sin{\left(x \right)} \operatorname{sign}{\left(x - 7 \right)} + \cos{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} + \frac{\left(- 3 x^{2} + 2 x + 42\right) \sin{\left(x \right)} \left|{x - 7}\right|}{\left(- 42 x + \left(x^{3} - x^{2}\right)\right)^{2}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 14.016453093047$$
$$x_{2} = 26.6354574736327$$
$$x_{3} = -42.3604359016656$$
$$x_{4} = -61.2266303830853$$
$$x_{5} = 54.9432759558649$$
$$x_{6} = -76.9419337897232$$
$$x_{7} = 83.2289873280938$$
$$x_{8} = 64.3729136691542$$
$$x_{9} = -64.369993732511$$
$$x_{10} = -13.9420438831868$$
$$x_{11} = 70.6586440153259$$
$$x_{12} = 29.7836865268305$$
$$x_{13} = 36.0768763247778$$
$$x_{14} = -32.919299828625$$
$$x_{15} = -51.7951587828659$$
$$x_{16} = 80.0865146143929$$
$$x_{17} = -95.7970043123775$$
$$x_{18} = -48.6507135445059$$
$$x_{19} = 42.3672514439482$$
$$x_{20} = 98.9405348240556$$
$$x_{21} = -26.6176780767465$$
$$x_{22} = -89.512248812553$$
$$x_{23} = -54.939255228509$$
$$x_{24} = -73.7991351656219$$
$$x_{25} = -67.5131834431642$$
$$x_{26} = 10.8451478646932$$
$$x_{27} = 17.1777448915114$$
$$x_{28} = 95.7983167647195$$
$$x_{29} = 23.485599433969$$
$$x_{30} = -17.1316249007671$$
$$x_{31} = -10.6983350907497$$
$$x_{32} = -39.2143570561418$$
$$x_{33} = 76.9439724516011$$
$$x_{34} = 149.212507171659$$
$$x_{35} = -58.0830633547885$$
$$x_{36} = 73.8013522673499$$
$$x_{37} = 48.6558568457253$$
$$x_{38} = -86.3697819811265$$
$$x_{39} = 89.5137528406582$$
$$x_{40} = 92.6560575082574$$
$$x_{41} = 146.07063730353$$
$$x_{42} = 7.65282388683543$$
$$x_{43} = -20.3017332658149$$
$$x_{44} = -92.6546541656147$$
$$x_{45} = -23.4623877903398$$
$$x_{46} = 67.5158358436257$$
$$x_{47} = 51.799688855665$$
$$x_{48} = 58.0866563372379$$
$$x_{49} = -98.9393046989388$$
$$x_{50} = -7.00360982839007$$
$$x_{51} = -80.0846336468534$$
$$x_{52} = 20.3334172344451$$
$$x_{53} = -70.6562239130531$$
$$x_{54} = 86.3713979521823$$
$$x_{55} = -45.5058407635821$$
$$x_{56} = -83.2272464103056$$
$$x_{57} = -36.0674064816266$$
$$x_{58} = 61.229860625401$$
$$x_{59} = 4.39955639048156$$
$$x_{60} = 39.2223354468251$$
$$x_{61} = -0.53859704600586$$
$$x_{62} = 45.5117316703557$$
$$x_{63} = -29.7696122729537$$
$$x_{64} = 32.9307280335231$$
Signos de extremos en los puntos:
(14.016453093047046, 0.00353836638676052)
(26.635457473632727, 0.00114773837094551)
(-42.36043590166557, -0.000648401503723408)
(-61.2266303830853, -0.000295565464505356)
(54.943275955864934, -0.000298469329531356)
(-76.94193378972315, 0.000183136347207666)
(83.22898732809384, 0.000134617758893156)
(64.3729136691542, 0.000220647630392954)
(-64.369993732511, 0.00026600835720957)
(-13.942043883186841, 0.00885973686894448)
(70.65864401532592, 0.000184549555812555)
(29.783686526830525, -0.000936518043257309)
(36.07687632477782, -0.000657889201238731)
(-32.919299828625, 0.00112589471326007)
(-51.79515878286592, 0.000421234558721923)
(80.08651461439288, -0.000145003794971144)
(-95.79700431237748, 0.000116221150161414)
(-48.65071354450594, -0.000481464727267868)
(42.36725144394817, -0.000487520616923897)
(98.94053482405558, -9.62938965440315e-5)
(-26.61767807674652, 0.00181546269768391)
(-89.51224881255295, 0.000133736838158639)
(-54.939255228508955, -0.000371651579986343)
(-73.79913516562186, -0.000199779414092476)
(-67.51318344316424, -0.000240676511514366)
(10.845147864693171, -0.00541199541314581)
(17.17774489151138, -0.00249886693392249)
(95.79831676471952, 0.000102520896200968)
(23.485599433968986, -0.00143986404452334)
(-17.131624900767097, -0.00518710311846635)
(-10.698335090749685, -0.0190223979798966)
(-39.21435705614177, 0.000766581979435786)
(76.94397245160107, 0.000156640592186579)
(149.21250717165935, -4.31748206644313e-5)
(-58.08306335478854, 0.00033034381495904)
(73.80135226734993, -0.000169737488684419)
(48.655856845725324, -0.000375751471215424)
(-86.36978198112651, -0.000144019112679707)
(89.51375284065819, 0.000116934496654864)
(92.65605750825736, -0.000109372297110004)
(146.07063730352974, 4.50145170384153e-5)
(7.652823886835433, 0.00937797661890569)
(-20.3017332658149, 0.00341991769457062)
(-92.65465416561467, -0.000124518130309472)
(-23.46238779033976, -0.00242866893320253)
(67.51583584362565, -0.000201390142707435)
(51.799688855664975, 0.000333777119038759)
(58.08665633723788, 0.000268486368595447)
(-98.93930469893877, -0.000108726947503291)
(-7.003609828390072, 0.0938560163001481)
(-80.08463364685336, -0.000168490763387854)
(20.33341723444505, 0.00186054082102996)
(-70.65622391305313, 0.000218800755314414)
(86.37139795218235, -0.000125309376682272)
(-45.50584076358215, 0.000555631062996273)
(-83.22724641030557, 0.000155535180840878)
(-36.06740648162657, -0.00092041358758118)
(61.22986062540101, -0.000242808092240104)
(4.399556390481556, 0.0207955020018686)
(39.22233544682508, 0.000563147211410448)
(-0.5385970460058597, -0.174378019814268)
(45.511731670355665, 0.000426185714857683)
(-29.76961227295372, -0.00140917575807083)
(32.930728033523096, 0.000778798198554037)
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:
$$x_{1} = -42.3604359016656$$
$$x_{2} = -61.2266303830853$$
$$x_{3} = 54.9432759558649$$
$$x_{4} = 29.7836865268305$$
$$x_{5} = 36.0768763247778$$
$$x_{6} = 80.0865146143929$$
$$x_{7} = -48.6507135445059$$
$$x_{8} = 42.3672514439482$$
$$x_{9} = 98.9405348240556$$
$$x_{10} = -54.939255228509$$
$$x_{11} = -73.7991351656219$$
$$x_{12} = -67.5131834431642$$
$$x_{13} = 10.8451478646932$$
$$x_{14} = 17.1777448915114$$
$$x_{15} = 23.485599433969$$
$$x_{16} = -17.1316249007671$$
$$x_{17} = -10.6983350907497$$
$$x_{18} = 149.212507171659$$
$$x_{19} = 73.8013522673499$$
$$x_{20} = 48.6558568457253$$
$$x_{21} = -86.3697819811265$$
$$x_{22} = 92.6560575082574$$
$$x_{23} = -92.6546541656147$$
$$x_{24} = -23.4623877903398$$
$$x_{25} = 67.5158358436257$$
$$x_{26} = -98.9393046989388$$
$$x_{27} = -80.0846336468534$$
$$x_{28} = 86.3713979521823$$
$$x_{29} = -36.0674064816266$$
$$x_{30} = 61.229860625401$$
$$x_{31} = -0.53859704600586$$
$$x_{32} = -29.7696122729537$$
Puntos máximos de la función:
$$x_{32} = 14.016453093047$$
$$x_{32} = 26.6354574736327$$
$$x_{32} = -76.9419337897232$$
$$x_{32} = 83.2289873280938$$
$$x_{32} = 64.3729136691542$$
$$x_{32} = -64.369993732511$$
$$x_{32} = -13.9420438831868$$
$$x_{32} = 70.6586440153259$$
$$x_{32} = -32.919299828625$$
$$x_{32} = -51.7951587828659$$
$$x_{32} = -95.7970043123775$$
$$x_{32} = -26.6176780767465$$
$$x_{32} = -89.512248812553$$
$$x_{32} = 95.7983167647195$$
$$x_{32} = -39.2143570561418$$
$$x_{32} = 76.9439724516011$$
$$x_{32} = -58.0830633547885$$
$$x_{32} = 89.5137528406582$$
$$x_{32} = 146.07063730353$$
$$x_{32} = 7.65282388683543$$
$$x_{32} = -20.3017332658149$$
$$x_{32} = 51.799688855665$$
$$x_{32} = 58.0866563372379$$
$$x_{32} = -7.00360982839007$$
$$x_{32} = 20.3334172344451$$
$$x_{32} = -70.6562239130531$$
$$x_{32} = -45.5058407635821$$
$$x_{32} = -83.2272464103056$$
$$x_{32} = 4.39955639048156$$
$$x_{32} = 39.2223354468251$$
$$x_{32} = 45.5117316703557$$
$$x_{32} = 32.9307280335231$$
Decrece en los intervalos
$$\left[149.212507171659, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -98.9393046989388\right]$$
Asíntotas verticales
Hay:
$$x_{1} = -6$$
$$x_{2} = 0$$
$$x_{3} = 7$$
$$x_{1} = -6$$
$$x_{2} = 0$$
$$x_{3} = 7$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 0$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (|x - 7|*sin(x))/(x^3 - x^2 - 42*x), dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{x \left(- 42 x + \left(x^{3} - x^{2}\right)\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{x \left(- 42 x + \left(x^{3} - x^{2}\right)\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{x \left(- 42 x + \left(x^{3} - x^{2}\right)\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{x \left(- 42 x + \left(x^{3} - x^{2}\right)\right)}\right) = 0$$
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:
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = - \frac{\sin{\left(x \right)} \left|{x + 7}\right|}{- x^{3} - x^{2} + 42 x}$$
- No
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = \frac{\sin{\left(x \right)} \left|{x + 7}\right|}{- x^{3} - x^{2} + 42 x}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = - \frac{\sin{\left(x \right)} \left|{x + 7}\right|}{- x^{3} - x^{2} + 42 x}$$
- No
$$\frac{\sin{\left(x \right)} \left|{x - 7}\right|}{- 42 x + \left(x^{3} - x^{2}\right)} = \frac{\sin{\left(x \right)} \left|{x + 7}\right|}{- x^{3} - x^{2} + 42 x}$$
- No
es decir, función
no es
par ni impar