Sr Examen
Otras calculadoras
- 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^4-x^3
-
x*e^x
-
x^2-3*x+1
-
x^3/(x-1)^2
-
Expresiones idénticas
- abs(sin(x))+sin^ dos (x)+cos^ dos (x)- tres *tg^ cuatro (x)
- abs( seno de (x)) más seno de al cuadrado (x) más coseno de al cuadrado (x) menos 3 multiplicar por tg en el grado 4(x)
- abs( seno de (x)) más seno de en el grado dos (x) más coseno de en el grado dos (x) menos tres multiplicar por tg en el grado cuatro (x)
- abs(sin(x))+sin2(x)+cos2(x)-3*tg4(x)
- abssinx+sin2x+cos2x-3*tg4x
- abs(sin(x))+sin²(x)+cos²(x)-3*tg⁴(x)
- abs(sin(x))+sin en el grado 2(x)+cos en el grado 2(x)-3*tg en el grado 4(x)
- abs(sin(x))+sin^2(x)+cos^2(x)-3tg^4(x)
- abs(sin(x))+sin2(x)+cos2(x)-3tg4(x)
- abssinx+sin2x+cos2x-3tg4x
- abssinx+sin^2x+cos^2x-3tg^4x
-
Expresiones semejantes
- abs(sin(x))-sin^2(x)+cos^2(x)-3*tg^4(x)
- abs(sin(x))+sin^2(x)-cos^2(x)-3*tg^4(x)
- abs(sin(x))+sin^2(x)+cos^2(x)+3*tg^4(x)
- abs(sinx)+sin^2(x)+cos^2(x)-3*tg^4(x)
-
Expresiones con funciones
- abs
- abs(3-2*x^2)
- abs(arcsin(abs(arccos(x/(x+pi)))))
- abs(arccos(3abs(x-1)))
- absolute(x+2)+1/(x-1)^2
- absolute(3x+1)
- Seno sin
- sin(x/5)*exp(x/10)+5*exp(-x/2)
- sin(x)/(2*x+16)
- sin(2*x+3)^(2)
- sin(x^3)
- sin(10*x)
- Seno sin
- sin(x/5)*exp(x/10)+5*exp(-x/2)
- sin(x)/(2*x+16)
- sin(2*x+3)^(2)
- sin(x^3)
- sin(10*x)
- Coseno cos
- cos(x)/x
- cos(x)*cos(2x)
- cos(x)+1/2*sin(2x)
- cos(z)
- cos(x)*cos(x)
- tg
- tgx+3
- tg2x+sin2x
- tgx/x
- tgx+2
- tg(4x)
Gráfico de la función y = abs(sin(x))+sin^2(x)+cos^2(x)-3*tg^4(x)
Solución
Ha introducido
[src]
2 2 4 f(x) = |sin(x)| + sin (x) + cos (x) - 3*tan (x)
$$f{\left(x \right)} = \left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}$$
f = sin(x)^2 + Abs(sin(x)) + cos(x)^2 - 3*tan(x)^4
Gráfico de la función
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:
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -13.2775182235652$$
$$x_{2} = 3.8527402627958$$
$$x_{3} = -99.8198173056674$$
$$x_{4} = 10.1359255699754$$
$$x_{5} = 8.71363035156337$$
$$x_{6} = 55.8375201554103$$
$$x_{7} = -33.8463715802817$$
$$x_{8} = 32.1270741451039$$
$$x_{9} = 85.5341492561304$$
$$x_{10} = 616.463307712805$$
$$x_{11} = 60.4014080274121$$
$$x_{12} = -35.2686667986937$$
$$x_{13} = -11.8552230051532$$
$$x_{14} = 44.6934447594631$$
$$x_{15} = 62.1207054625899$$
$$x_{16} = -2.43044504438379$$
$$x_{17} = 58.9791128090001$$
$$x_{18} = 91.81733456331$$
$$x_{19} = -55.8375201554103$$
$$x_{20} = -24.4215936195123$$
$$x_{21} = 69.8261859881815$$
$$x_{22} = 41.5518521058733$$
$$x_{23} = -14989.2496978861$$
$$x_{24} = -18.1384083123328$$
$$x_{25} = 76.109371295361$$
$$x_{26} = 54.1182227202325$$
$$x_{27} = -84.1118540377184$$
$$x_{28} = 25.8438888379244$$
$$x_{29} = -41.5518521058733$$
$$x_{30} = -47.8350374130529$$
$$x_{31} = -74.687076076949$$
$$x_{32} = 30.7047789266919$$
$$x_{33} = -91.81733456331$$
$$x_{34} = -30.7047789266919$$
$$x_{35} = 40.1295568874613$$
$$x_{36} = -52.6959275018205$$
$$x_{37} = 96.6782246520776$$
$$x_{38} = -63.5430006810019$$
$$x_{39} = -79.2509639489508$$
$$x_{40} = 38.4102594522835$$
$$x_{41} = -8.71363035156337$$
$$x_{42} = -3.8527402627958$$
$$x_{43} = 49.5543348482307$$
$$x_{44} = -77.8286687305388$$
$$x_{45} = -71.5454834233592$$
$$x_{46} = -19.5607035307448$$
$$x_{47} = -96.6782246520776$$
$$x_{48} = -62.1207054625899$$
$$x_{49} = 63.5430006810019$$
$$x_{50} = 84.1118540377184$$
$$x_{51} = -203.492374874131$$
$$x_{52} = 74.687076076949$$
$$x_{53} = 68.4038907697694$$
$$x_{54} = -68.4038907697694$$
$$x_{55} = 80.9702613841286$$
$$x_{56} = 19.5607035307448$$
$$x_{57} = -25.8438888379244$$
$$x_{58} = -46.4127421946409$$
$$x_{59} = 18.1384083123328$$
$$x_{60} = 24.4215936195123$$
$$x_{61} = 128.094151187976$$
$$x_{62} = 47.8350374130529$$
$$x_{63} = -85.5341492561304$$
$$x_{64} = -69.8261859881815$$
$$x_{65} = 52.6959275018205$$
$$x_{66} = 82.3925566025406$$
$$x_{67} = -5465.66006963703$$
$$x_{68} = -16.419110877155$$
$$x_{69} = 90.395039344898$$
$$x_{70} = 13.2775182235652$$
$$x_{71} = 2.43044504438379$$
$$x_{72} = -90.395039344898$$
$$x_{73} = 79.2509639489508$$
$$x_{74} = -40.1295568874613$$
$$x_{75} = -57.2598153738223$$
$$x_{76} = 98.1005198704896$$
$$x_{77} = 46.4127421946409$$
o sea hay que resolver la ecuación:
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -13.2775182235652$$
$$x_{2} = 3.8527402627958$$
$$x_{3} = -99.8198173056674$$
$$x_{4} = 10.1359255699754$$
$$x_{5} = 8.71363035156337$$
$$x_{6} = 55.8375201554103$$
$$x_{7} = -33.8463715802817$$
$$x_{8} = 32.1270741451039$$
$$x_{9} = 85.5341492561304$$
$$x_{10} = 616.463307712805$$
$$x_{11} = 60.4014080274121$$
$$x_{12} = -35.2686667986937$$
$$x_{13} = -11.8552230051532$$
$$x_{14} = 44.6934447594631$$
$$x_{15} = 62.1207054625899$$
$$x_{16} = -2.43044504438379$$
$$x_{17} = 58.9791128090001$$
$$x_{18} = 91.81733456331$$
$$x_{19} = -55.8375201554103$$
$$x_{20} = -24.4215936195123$$
$$x_{21} = 69.8261859881815$$
$$x_{22} = 41.5518521058733$$
$$x_{23} = -14989.2496978861$$
$$x_{24} = -18.1384083123328$$
$$x_{25} = 76.109371295361$$
$$x_{26} = 54.1182227202325$$
$$x_{27} = -84.1118540377184$$
$$x_{28} = 25.8438888379244$$
$$x_{29} = -41.5518521058733$$
$$x_{30} = -47.8350374130529$$
$$x_{31} = -74.687076076949$$
$$x_{32} = 30.7047789266919$$
$$x_{33} = -91.81733456331$$
$$x_{34} = -30.7047789266919$$
$$x_{35} = 40.1295568874613$$
$$x_{36} = -52.6959275018205$$
$$x_{37} = 96.6782246520776$$
$$x_{38} = -63.5430006810019$$
$$x_{39} = -79.2509639489508$$
$$x_{40} = 38.4102594522835$$
$$x_{41} = -8.71363035156337$$
$$x_{42} = -3.8527402627958$$
$$x_{43} = 49.5543348482307$$
$$x_{44} = -77.8286687305388$$
$$x_{45} = -71.5454834233592$$
$$x_{46} = -19.5607035307448$$
$$x_{47} = -96.6782246520776$$
$$x_{48} = -62.1207054625899$$
$$x_{49} = 63.5430006810019$$
$$x_{50} = 84.1118540377184$$
$$x_{51} = -203.492374874131$$
$$x_{52} = 74.687076076949$$
$$x_{53} = 68.4038907697694$$
$$x_{54} = -68.4038907697694$$
$$x_{55} = 80.9702613841286$$
$$x_{56} = 19.5607035307448$$
$$x_{57} = -25.8438888379244$$
$$x_{58} = -46.4127421946409$$
$$x_{59} = 18.1384083123328$$
$$x_{60} = 24.4215936195123$$
$$x_{61} = 128.094151187976$$
$$x_{62} = 47.8350374130529$$
$$x_{63} = -85.5341492561304$$
$$x_{64} = -69.8261859881815$$
$$x_{65} = 52.6959275018205$$
$$x_{66} = 82.3925566025406$$
$$x_{67} = -5465.66006963703$$
$$x_{68} = -16.419110877155$$
$$x_{69} = 90.395039344898$$
$$x_{70} = 13.2775182235652$$
$$x_{71} = 2.43044504438379$$
$$x_{72} = -90.395039344898$$
$$x_{73} = 79.2509639489508$$
$$x_{74} = -40.1295568874613$$
$$x_{75} = -57.2598153738223$$
$$x_{76} = 98.1005198704896$$
$$x_{77} = 46.4127421946409$$
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
$$- 3 \left(4 \tan^{2}{\left(x \right)} + 4\right) \tan^{3}{\left(x \right)} + \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 81.2967143466105$$
$$x_{2} = 25.5174358754425$$
$$x_{3} = 53.0223804643024$$
$$x_{4} = 90.7214923073799$$
$$x_{5} = -56.9333624113404$$
$$x_{6} = -46.7391951571228$$
$$x_{7} = 38.0838064898016$$
$$x_{8} = 62.4471584250717$$
$$x_{9} = -40.4560098499432$$
$$x_{10} = -2.75689800686566$$
$$x_{11} = -93.8630849609697$$
$$x_{12} = -68.7303437322513$$
$$x_{13} = 24.7480465819942$$
$$x_{14} = -9.80947260749351$$
$$x_{15} = 60.0749550649302$$
$$x_{16} = -27.889639235584$$
$$x_{17} = -53.7917697577506$$
$$x_{18} = -34.1728245427636$$
$$x_{19} = -19.2342505682629$$
$$x_{20} = 91.4908816008281$$
$$x_{21} = 66.3581403721098$$
$$x_{22} = -71.8719363858411$$
$$x_{23} = -5.89849066045546$$
$$x_{24} = 88.3492889472383$$
$$x_{25} = -91.4908816008281$$
$$x_{26} = 75.7829183328792$$
$$x_{27} = 100.146270268149$$
$$x_{28} = -43.597602503533$$
$$x_{29} = 63.21654771852$$
$$x_{30} = -63.21654771852$$
$$x_{31} = 22.3758432218527$$
$$x_{32} = -31.8006211826221$$
$$x_{33} = 31.8006211826221$$
$$x_{34} = -100.146270268149$$
$$x_{35} = 19.2342505682629$$
$$x_{36} = 0$$
$$x_{37} = -62.4471584250717$$
$$x_{38} = -34.9422138362119$$
$$x_{39} = 68.7303437322513$$
$$x_{40} = 18.4648612748146$$
$$x_{41} = -82.0661036400588$$
$$x_{42} = -78.924510986469$$
$$x_{43} = 97.7740669080077$$
$$x_{44} = 12.181675967635$$
$$x_{45} = -25.5174358754425$$
$$x_{46} = -56.1639731178921$$
$$x_{47} = -3.52628730031392$$
$$x_{48} = -41.2253991433914$$
$$x_{49} = -49.8807878107126$$
$$x_{50} = 97.0046776145595$$
$$x_{51} = -69.4997330256996$$
$$x_{52} = 129.189993443906$$
$$x_{53} = 85.2076962936485$$
$$x_{54} = -84.4383070002003$$
$$x_{55} = 46.7391951571228$$
$$x_{56} = 44.3669917969812$$
$$x_{57} = -85.2076962936485$$
$$x_{58} = -38.0838064898016$$
$$x_{59} = -21.6064539284044$$
$$x_{60} = -53.0223804643024$$
$$x_{61} = 59.3055657714819$$
$$x_{62} = -12.9510652610833$$
$$x_{63} = 31.0312318891738$$
$$x_{64} = 3.52628730031392$$
$$x_{65} = 41.2253991433914$$
$$x_{66} = 40.4560098499432$$
$$x_{67} = 53.7917697577506$$
$$x_{68} = 2.75689800686566$$
$$x_{69} = -47.508584450571$$
$$x_{70} = -78.1551216930207$$
$$x_{71} = -12.181675967635$$
$$x_{72} = -16.0926579146731$$
$$x_{73} = 82.0661036400588$$
$$x_{74} = -97.0046776145595$$
$$x_{75} = -90.7214923073799$$
$$x_{76} = 69.4997330256996$$
$$x_{77} = 47.508584450571$$
$$x_{78} = 84.4383070002003$$
$$x_{79} = 37.3144171963534$$
$$x_{80} = 16.0926579146731$$
$$x_{81} = -75.7829183328792$$
$$x_{82} = -24.7480465819942$$
$$x_{83} = 75.0135290394309$$
$$x_{84} = 9.04008331404525$$
$$x_{85} = -75.0135290394309$$
$$x_{86} = 78.1551216930207$$
$$x_{87} = -97.7740669080077$$
$$x_{88} = 34.1728245427636$$
$$x_{89} = 9.80947260749351$$
$$x_{90} = -18.4648612748146$$
$$x_{91} = -31.0312318891738$$
$$x_{92} = -60.0749550649302$$
$$x_{93} = 56.1639731178921$$
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:
$$x_{1} = 0$$
Puntos máximos de la función:
$$x_{1} = 81.2967143466105$$
$$x_{1} = 25.5174358754425$$
$$x_{1} = 53.0223804643024$$
$$x_{1} = 90.7214923073799$$
$$x_{1} = -56.9333624113404$$
$$x_{1} = -46.7391951571228$$
$$x_{1} = 38.0838064898016$$
$$x_{1} = 62.4471584250717$$
$$x_{1} = -40.4560098499432$$
$$x_{1} = -2.75689800686566$$
$$x_{1} = -93.8630849609697$$
$$x_{1} = -68.7303437322513$$
$$x_{1} = 24.7480465819942$$
$$x_{1} = -9.80947260749351$$
$$x_{1} = 60.0749550649302$$
$$x_{1} = -27.889639235584$$
$$x_{1} = -53.7917697577506$$
$$x_{1} = -34.1728245427636$$
$$x_{1} = -19.2342505682629$$
$$x_{1} = 91.4908816008281$$
$$x_{1} = 66.3581403721098$$
$$x_{1} = -71.8719363858411$$
$$x_{1} = -5.89849066045546$$
$$x_{1} = 88.3492889472383$$
$$x_{1} = -91.4908816008281$$
$$x_{1} = 75.7829183328792$$
$$x_{1} = 100.146270268149$$
$$x_{1} = -43.597602503533$$
$$x_{1} = 63.21654771852$$
$$x_{1} = -63.21654771852$$
$$x_{1} = 22.3758432218527$$
$$x_{1} = -31.8006211826221$$
$$x_{1} = 31.8006211826221$$
$$x_{1} = -100.146270268149$$
$$x_{1} = 19.2342505682629$$
$$x_{1} = -62.4471584250717$$
$$x_{1} = -34.9422138362119$$
$$x_{1} = 68.7303437322513$$
$$x_{1} = 18.4648612748146$$
$$x_{1} = -82.0661036400588$$
$$x_{1} = -78.924510986469$$
$$x_{1} = 97.7740669080077$$
$$x_{1} = 12.181675967635$$
$$x_{1} = -25.5174358754425$$
$$x_{1} = -56.1639731178921$$
$$x_{1} = -3.52628730031392$$
$$x_{1} = -41.2253991433914$$
$$x_{1} = -49.8807878107126$$
$$x_{1} = 97.0046776145595$$
$$x_{1} = -69.4997330256996$$
$$x_{1} = 129.189993443906$$
$$x_{1} = 85.2076962936485$$
$$x_{1} = -84.4383070002003$$
$$x_{1} = 46.7391951571228$$
$$x_{1} = 44.3669917969812$$
$$x_{1} = -85.2076962936485$$
$$x_{1} = -38.0838064898016$$
$$x_{1} = -21.6064539284044$$
$$x_{1} = -53.0223804643024$$
$$x_{1} = 59.3055657714819$$
$$x_{1} = -12.9510652610833$$
$$x_{1} = 31.0312318891738$$
$$x_{1} = 3.52628730031392$$
$$x_{1} = 41.2253991433914$$
$$x_{1} = 40.4560098499432$$
$$x_{1} = 53.7917697577506$$
$$x_{1} = 2.75689800686566$$
$$x_{1} = -47.508584450571$$
$$x_{1} = -78.1551216930207$$
$$x_{1} = -12.181675967635$$
$$x_{1} = -16.0926579146731$$
$$x_{1} = 82.0661036400588$$
$$x_{1} = -97.0046776145595$$
$$x_{1} = -90.7214923073799$$
$$x_{1} = 69.4997330256996$$
$$x_{1} = 47.508584450571$$
$$x_{1} = 84.4383070002003$$
$$x_{1} = 37.3144171963534$$
$$x_{1} = 16.0926579146731$$
$$x_{1} = -75.7829183328792$$
$$x_{1} = -24.7480465819942$$
$$x_{1} = 75.0135290394309$$
$$x_{1} = 9.04008331404525$$
$$x_{1} = -75.0135290394309$$
$$x_{1} = 78.1551216930207$$
$$x_{1} = -97.7740669080077$$
$$x_{1} = 34.1728245427636$$
$$x_{1} = 9.80947260749351$$
$$x_{1} = -18.4648612748146$$
$$x_{1} = -31.0312318891738$$
$$x_{1} = -60.0749550649302$$
$$x_{1} = 56.1639731178921$$
Decrece en los intervalos
$$\left(-\infty, -100.146270268149\right] \cup \left[0, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, 0\right] \cup \left[129.189993443906, \infty\right)$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$- 3 \left(4 \tan^{2}{\left(x \right)} + 4\right) \tan^{3}{\left(x \right)} + \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 81.2967143466105$$
$$x_{2} = 25.5174358754425$$
$$x_{3} = 53.0223804643024$$
$$x_{4} = 90.7214923073799$$
$$x_{5} = -56.9333624113404$$
$$x_{6} = -46.7391951571228$$
$$x_{7} = 38.0838064898016$$
$$x_{8} = 62.4471584250717$$
$$x_{9} = -40.4560098499432$$
$$x_{10} = -2.75689800686566$$
$$x_{11} = -93.8630849609697$$
$$x_{12} = -68.7303437322513$$
$$x_{13} = 24.7480465819942$$
$$x_{14} = -9.80947260749351$$
$$x_{15} = 60.0749550649302$$
$$x_{16} = -27.889639235584$$
$$x_{17} = -53.7917697577506$$
$$x_{18} = -34.1728245427636$$
$$x_{19} = -19.2342505682629$$
$$x_{20} = 91.4908816008281$$
$$x_{21} = 66.3581403721098$$
$$x_{22} = -71.8719363858411$$
$$x_{23} = -5.89849066045546$$
$$x_{24} = 88.3492889472383$$
$$x_{25} = -91.4908816008281$$
$$x_{26} = 75.7829183328792$$
$$x_{27} = 100.146270268149$$
$$x_{28} = -43.597602503533$$
$$x_{29} = 63.21654771852$$
$$x_{30} = -63.21654771852$$
$$x_{31} = 22.3758432218527$$
$$x_{32} = -31.8006211826221$$
$$x_{33} = 31.8006211826221$$
$$x_{34} = -100.146270268149$$
$$x_{35} = 19.2342505682629$$
$$x_{36} = 0$$
$$x_{37} = -62.4471584250717$$
$$x_{38} = -34.9422138362119$$
$$x_{39} = 68.7303437322513$$
$$x_{40} = 18.4648612748146$$
$$x_{41} = -82.0661036400588$$
$$x_{42} = -78.924510986469$$
$$x_{43} = 97.7740669080077$$
$$x_{44} = 12.181675967635$$
$$x_{45} = -25.5174358754425$$
$$x_{46} = -56.1639731178921$$
$$x_{47} = -3.52628730031392$$
$$x_{48} = -41.2253991433914$$
$$x_{49} = -49.8807878107126$$
$$x_{50} = 97.0046776145595$$
$$x_{51} = -69.4997330256996$$
$$x_{52} = 129.189993443906$$
$$x_{53} = 85.2076962936485$$
$$x_{54} = -84.4383070002003$$
$$x_{55} = 46.7391951571228$$
$$x_{56} = 44.3669917969812$$
$$x_{57} = -85.2076962936485$$
$$x_{58} = -38.0838064898016$$
$$x_{59} = -21.6064539284044$$
$$x_{60} = -53.0223804643024$$
$$x_{61} = 59.3055657714819$$
$$x_{62} = -12.9510652610833$$
$$x_{63} = 31.0312318891738$$
$$x_{64} = 3.52628730031392$$
$$x_{65} = 41.2253991433914$$
$$x_{66} = 40.4560098499432$$
$$x_{67} = 53.7917697577506$$
$$x_{68} = 2.75689800686566$$
$$x_{69} = -47.508584450571$$
$$x_{70} = -78.1551216930207$$
$$x_{71} = -12.181675967635$$
$$x_{72} = -16.0926579146731$$
$$x_{73} = 82.0661036400588$$
$$x_{74} = -97.0046776145595$$
$$x_{75} = -90.7214923073799$$
$$x_{76} = 69.4997330256996$$
$$x_{77} = 47.508584450571$$
$$x_{78} = 84.4383070002003$$
$$x_{79} = 37.3144171963534$$
$$x_{80} = 16.0926579146731$$
$$x_{81} = -75.7829183328792$$
$$x_{82} = -24.7480465819942$$
$$x_{83} = 75.0135290394309$$
$$x_{84} = 9.04008331404525$$
$$x_{85} = -75.0135290394309$$
$$x_{86} = 78.1551216930207$$
$$x_{87} = -97.7740669080077$$
$$x_{88} = 34.1728245427636$$
$$x_{89} = 9.80947260749351$$
$$x_{90} = -18.4648612748146$$
$$x_{91} = -31.0312318891738$$
$$x_{92} = -60.0749550649302$$
$$x_{93} = 56.1639731178921$$
Signos de extremos en los puntos:
(81.2967143466105, 1.29466982577999)
(25.517435875442473, 1.29466982577999)
(53.02238046430236, 1.29466982577999)
(90.72149230737988, 1.29466982577999)
(-56.933362411340404, 1.29466982577999)
(-46.73919515712277, 1.29466982577999)
(38.083806489801646, 1.29466982577999)
(62.447158425071734, 1.29466982577999)
(-40.456009849943186, 1.29466982577999)
(-2.756898006865665, 1.29466982577999)
(-93.86308496096967, 1.29466982577999)
(-68.73034373225133, 1.29466982577999)
(24.748046581994217, 1.29466982577999)
(-9.809472607493507, 1.29466982577999)
(60.0749550649302, 1.29466982577999)
(-27.88963923558401, 1.29466982577999)
(-53.791769757750615, 1.29466982577999)
(-34.1728245427636, 1.29466982577999)
(-19.234250568262887, 1.29466982577998)
(91.49088160082813, 1.29466982577999)
(66.35814037210979, 1.29466982577999)
(-71.87193638584111, 1.29466982577999)
(-5.898490660455458, 1.29466982577999)
(88.34928894723834, 1.29466982577999)
(-91.49088160082813, 1.29466982577999)
(75.78291833287916, 1.29466982577999)
(100.14627026814925, 1.29466982577999)
(-43.597602503532976, 1.29466982577999)
(63.21654771851999, 1.29466982577999)
(-63.21654771851999, 1.29466982577999)
(22.37584322185268, 1.29466982577999)
(-31.80062118262206, 1.29466982577999)
(31.80062118262206, 1.29466982577999)
(-100.14627026814925, 1.29466982577999)
(19.234250568262887, 1.29466982577998)
(0, 1)
(-62.447158425071734, 1.29466982577999)
(-34.942213836211856, 1.29466982577998)
(68.73034373225133, 1.29466982577999)
(18.46486127481463, 1.29466982577999)
(-82.06610364005876, 1.29466982577999)
(-78.92451098646896, 1.29466982577999)
(97.77406690800773, 1.29466982577999)
(12.181675967635044, 1.29466982577999)
(-25.517435875442473, 1.29466982577999)
(-56.16397311789215, 1.29466982577998)
(-3.5262873003139217, 1.29466982577999)
(-41.22539914339144, 1.29466982577999)
(-49.88078781071256, 1.29466982577999)
(97.00467761455947, 1.29466982577999)
(-69.49973302569958, 1.29466982577999)
(129.18999344390565, 1.29466982577999)
(85.20769629364854, 1.29466982577999)
(-84.43830700020028, 1.29466982577999)
(46.73919515712277, 1.29466982577999)
(44.36699179698123, 1.29466982577999)
(-85.20769629364854, 1.29466982577999)
(-38.083806489801646, 1.29466982577999)
(-21.606453928404424, 1.29466982577999)
(-53.02238046430236, 1.29466982577999)
(59.305565771481945, 1.29466982577999)
(-12.9510652610833, 1.29466982577999)
(31.031231889173803, 1.29466982577999)
(3.5262873003139217, 1.29466982577999)
(41.22539914339144, 1.29466982577999)
(40.456009849943186, 1.29466982577999)
(53.791769757750615, 1.29466982577999)
(2.756898006865665, 1.29466982577999)
(-47.50858445057103, 1.29466982577999)
(-78.1551216930207, 1.29466982577999)
(-12.181675967635044, 1.29466982577999)
(-16.092657914673094, 1.29466982577999)
(82.06610364005876, 1.29466982577999)
(-97.00467761455947, 1.29466982577999)
(-90.72149230737988, 1.29466982577999)
(69.49973302569958, 1.29466982577999)
(47.50858445057103, 1.29466982577999)
(84.43830700020028, 1.29466982577999)
(37.31441719635339, 1.29466982577999)
(16.092657914673094, 1.29466982577999)
(-75.78291833287916, 1.29466982577999)
(-24.748046581994217, 1.29466982577999)
(75.0135290394309, 1.29466982577999)
(9.040083314045251, 1.29466982577999)
(-75.0135290394309, 1.29466982577999)
(78.1551216930207, 1.29466982577999)
(-97.77406690800773, 1.29466982577999)
(34.1728245427636, 1.29466982577999)
(9.809472607493507, 1.29466982577999)
(-18.46486127481463, 1.29466982577999)
(-31.031231889173803, 1.29466982577999)
(-60.0749550649302, 1.29466982577999)
(56.16397311789215, 1.29466982577998)
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:
$$x_{1} = 0$$
Puntos máximos de la función:
$$x_{1} = 81.2967143466105$$
$$x_{1} = 25.5174358754425$$
$$x_{1} = 53.0223804643024$$
$$x_{1} = 90.7214923073799$$
$$x_{1} = -56.9333624113404$$
$$x_{1} = -46.7391951571228$$
$$x_{1} = 38.0838064898016$$
$$x_{1} = 62.4471584250717$$
$$x_{1} = -40.4560098499432$$
$$x_{1} = -2.75689800686566$$
$$x_{1} = -93.8630849609697$$
$$x_{1} = -68.7303437322513$$
$$x_{1} = 24.7480465819942$$
$$x_{1} = -9.80947260749351$$
$$x_{1} = 60.0749550649302$$
$$x_{1} = -27.889639235584$$
$$x_{1} = -53.7917697577506$$
$$x_{1} = -34.1728245427636$$
$$x_{1} = -19.2342505682629$$
$$x_{1} = 91.4908816008281$$
$$x_{1} = 66.3581403721098$$
$$x_{1} = -71.8719363858411$$
$$x_{1} = -5.89849066045546$$
$$x_{1} = 88.3492889472383$$
$$x_{1} = -91.4908816008281$$
$$x_{1} = 75.7829183328792$$
$$x_{1} = 100.146270268149$$
$$x_{1} = -43.597602503533$$
$$x_{1} = 63.21654771852$$
$$x_{1} = -63.21654771852$$
$$x_{1} = 22.3758432218527$$
$$x_{1} = -31.8006211826221$$
$$x_{1} = 31.8006211826221$$
$$x_{1} = -100.146270268149$$
$$x_{1} = 19.2342505682629$$
$$x_{1} = -62.4471584250717$$
$$x_{1} = -34.9422138362119$$
$$x_{1} = 68.7303437322513$$
$$x_{1} = 18.4648612748146$$
$$x_{1} = -82.0661036400588$$
$$x_{1} = -78.924510986469$$
$$x_{1} = 97.7740669080077$$
$$x_{1} = 12.181675967635$$
$$x_{1} = -25.5174358754425$$
$$x_{1} = -56.1639731178921$$
$$x_{1} = -3.52628730031392$$
$$x_{1} = -41.2253991433914$$
$$x_{1} = -49.8807878107126$$
$$x_{1} = 97.0046776145595$$
$$x_{1} = -69.4997330256996$$
$$x_{1} = 129.189993443906$$
$$x_{1} = 85.2076962936485$$
$$x_{1} = -84.4383070002003$$
$$x_{1} = 46.7391951571228$$
$$x_{1} = 44.3669917969812$$
$$x_{1} = -85.2076962936485$$
$$x_{1} = -38.0838064898016$$
$$x_{1} = -21.6064539284044$$
$$x_{1} = -53.0223804643024$$
$$x_{1} = 59.3055657714819$$
$$x_{1} = -12.9510652610833$$
$$x_{1} = 31.0312318891738$$
$$x_{1} = 3.52628730031392$$
$$x_{1} = 41.2253991433914$$
$$x_{1} = 40.4560098499432$$
$$x_{1} = 53.7917697577506$$
$$x_{1} = 2.75689800686566$$
$$x_{1} = -47.508584450571$$
$$x_{1} = -78.1551216930207$$
$$x_{1} = -12.181675967635$$
$$x_{1} = -16.0926579146731$$
$$x_{1} = 82.0661036400588$$
$$x_{1} = -97.0046776145595$$
$$x_{1} = -90.7214923073799$$
$$x_{1} = 69.4997330256996$$
$$x_{1} = 47.508584450571$$
$$x_{1} = 84.4383070002003$$
$$x_{1} = 37.3144171963534$$
$$x_{1} = 16.0926579146731$$
$$x_{1} = -75.7829183328792$$
$$x_{1} = -24.7480465819942$$
$$x_{1} = 75.0135290394309$$
$$x_{1} = 9.04008331404525$$
$$x_{1} = -75.0135290394309$$
$$x_{1} = 78.1551216930207$$
$$x_{1} = -97.7740669080077$$
$$x_{1} = 34.1728245427636$$
$$x_{1} = 9.80947260749351$$
$$x_{1} = -18.4648612748146$$
$$x_{1} = -31.0312318891738$$
$$x_{1} = -60.0749550649302$$
$$x_{1} = 56.1639731178921$$
Decrece en los intervalos
$$\left(-\infty, -100.146270268149\right] \cup \left[0, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, 0\right] \cup \left[129.189993443906, \infty\right)$$
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$- 36 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)} - 24 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)} - \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + 2 \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$- 36 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)} - 24 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{4}{\left(x \right)} - \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)} + 2 \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right) = 0$$
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(sin(x)) + sin(x)^2 + cos(x)^2 - 3*tan(x)^4, dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}}{x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}}{x}\right)$$
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:
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = \left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}$$
- Sí
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = \left(\left(- \sin^{2}{\left(x \right)} - \left|{\sin{\left(x \right)}}\right|\right) - \cos^{2}{\left(x \right)}\right) + 3 \tan^{4}{\left(x \right)}$$
- No
es decir, función
es
par
Pues, comprobamos:
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = \left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)}$$
- Sí
$$\left(\left(\sin^{2}{\left(x \right)} + \left|{\sin{\left(x \right)}}\right|\right) + \cos^{2}{\left(x \right)}\right) - 3 \tan^{4}{\left(x \right)} = \left(\left(- \sin^{2}{\left(x \right)} - \left|{\sin{\left(x \right)}}\right|\right) - \cos^{2}{\left(x \right)}\right) + 3 \tan^{4}{\left(x \right)}$$
- No
es decir, función
es
par
Gráfico