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 =:
-
y=(x+1)^3
-
y=2x
-
2*x^3-3*x
-
3-x^2
-
Expresiones idénticas
- (sin(nueve *x)*tan(tres *x))/(sqrt(dos -sin(cuatro *x)^ dos)-sqrt(dos +sin(cuatro *x)^ dos))
- ( seno de (9 multiplicar por x) multiplicar por tangente de (3 multiplicar por x)) dividir por ( raíz cuadrada de (2 menos seno de (4 multiplicar por x) al cuadrado ) menos raíz cuadrada de (2 más seno de (4 multiplicar por x) al cuadrado ))
- ( seno de (nueve multiplicar por x) multiplicar por tangente de (tres multiplicar por x)) dividir por ( raíz cuadrada de (dos menos seno de (cuatro multiplicar por x) en el grado dos) menos raíz cuadrada de (dos más seno de (cuatro multiplicar por x) en el grado dos))
- (sin(9*x)*tan(3*x))/(√(2-sin(4*x)^2)-√(2+sin(4*x)^2))
- (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x)2)-sqrt(2+sin(4*x)2))
- sin9*x*tan3*x/sqrt2-sin4*x2-sqrt2+sin4*x2
- (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x)²)-sqrt(2+sin(4*x)²))
- (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x) en el grado 2)-sqrt(2+sin(4*x) en el grado 2))
- (sin(9x)tan(3x))/(sqrt(2-sin(4x)^2)-sqrt(2+sin(4x)^2))
- (sin(9x)tan(3x))/(sqrt(2-sin(4x)2)-sqrt(2+sin(4x)2))
- sin9xtan3x/sqrt2-sin4x2-sqrt2+sin4x2
- sin9xtan3x/sqrt2-sin4x^2-sqrt2+sin4x^2
- (sin(9*x)*tan(3*x)) dividir por (sqrt(2-sin(4*x)^2)-sqrt(2+sin(4*x)^2))
-
Expresiones semejantes
- (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x)^2)-sqrt(2-sin(4*x)^2))
- (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x)^2)+sqrt(2+sin(4*x)^2))
- (sin(9*x)*tan(3*x))/(sqrt(2+sin(4*x)^2)-sqrt(2+sin(4*x)^2))
-
Expresiones con funciones
- Seno sin
- sin(0,5x+pi/4)+0,5
- sin(x×4)
- sin(x^4-3*x^2+1)
- sin(x)+cos(x)+sin(x)/x!
- sin(2*x+x-1)
- Tangente tan
- tan(x+e^x)
- tan(x)^6*tan(3*x-3)
- tan(13*x/10)
- tan(x+5*pi/4)
- tan(9*x)*4
- Raíz cuadrada sqrt
- sqrt(x^2+4*x+4)
- sqrt(x^2+1)-sqrt(x^2-1)
- sqrt(x^2-6*x+11)
- sqrt[x^2+10x+26]-2
- sqrt(9*x)^2+5
- Seno sin
- sin(0,5x+pi/4)+0,5
- sin(x×4)
- sin(x^4-3*x^2+1)
- sin(x)+cos(x)+sin(x)/x!
- sin(2*x+x-1)
- Raíz cuadrada sqrt
- sqrt(x^2+4*x+4)
- sqrt(x^2+1)-sqrt(x^2-1)
- sqrt(x^2-6*x+11)
- sqrt[x^2+10x+26]-2
- sqrt(9*x)^2+5
- Seno sin
- sin(0,5x+pi/4)+0,5
- sin(x×4)
- sin(x^4-3*x^2+1)
- sin(x)+cos(x)+sin(x)/x!
- sin(2*x+x-1)
Gráfico de la función y = (sin(9*x)*tan(3*x))/(sqrt(2-sin(4*x)^2)-sqrt(2+sin(4*x)^2))
Solución
Ha introducido
[src]
sin(9*x)*tan(3*x)
f(x) = ---------------------------------------
_______________ _______________
/ 2 / 2
\/ 2 - sin (4*x) - \/ 2 + sin (4*x)
$$f{\left(x \right)} = \frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}$$
f = (sin(9*x)*tan(3*x))/(sqrt(2 - sin(4*x)^2) - sqrt(sin(4*x)^2 + 2))
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$x_{1} = 0$$
$$x_{2} = 0.785398163397448$$
$$x_{1} = 0$$
$$x_{2} = 0.785398163397448$$
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:
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -79.587013957071$$
$$x_{2} = 58.2939970166106$$
$$x_{3} = -91.8043186549017$$
$$x_{4} = -8.02851455917392$$
$$x_{5} = 41.8879019551629$$
$$x_{6} = 66.3225115757845$$
$$x_{7} = -31.7649923862968$$
$$x_{8} = 98.4365698456188$$
$$x_{9} = 32.1140582366957$$
$$x_{10} = 60.0393262686049$$
$$x_{11} = -9.77384381116824$$
$$x_{12} = -16.0570291183478$$
$$x_{13} = 16.0570291183478$$
$$x_{14} = -93.8987137572949$$
$$x_{15} = 76.0963553869528$$
$$x_{16} = -83.7758040786232$$
$$x_{17} = 12.2173047639603$$
$$x_{18} = 70.1622359788179$$
$$x_{19} = -71.9075651821664$$
$$x_{20} = 92.1533845581785$$
$$x_{21} = 18.151424220741$$
$$x_{22} = 62.1337213709981$$
$$x_{23} = -97.7384381116825$$
$$x_{24} = -60.0393262686049$$
$$x_{25} = 94.5968454580927$$
$$x_{26} = -38.0481776934764$$
$$x_{27} = -74.0019602845596$$
$$x_{28} = 82.0304748437335$$
$$x_{29} = 72.6056968829641$$
$$x_{30} = -13.613568229432$$
$$x_{31} = -55.8505360638185$$
$$x_{32} = 80.2851455917392$$
$$x_{33} = -5.93411945678072$$
$$x_{34} = 63.8790507190579$$
$$x_{35} = -99.8328332140756$$
$$x_{36} = 84.1248699461267$$
$$x_{37} = -17.8023583387693$$
$$x_{38} = 90.0589893442465$$
$$x_{39} = -69.8131700797732$$
$$x_{40} = -77.8416846389471$$
$$x_{41} = 38.0481776934764$$
$$x_{42} = 28.623399732707$$
$$x_{43} = -19.8967535778114$$
$$x_{44} = -33.85938748869$$
$$x_{45} = 2.09439500680622$$
$$x_{46} = 48.1710873994927$$
$$x_{47} = -65.6243798749868$$
$$x_{48} = -27.9252680319093$$
$$x_{49} = -95.9931088596881$$
$$x_{50} = 44.331363000656$$
$$x_{51} = 8.3775803464205$$
$$x_{52} = 78.190750489346$$
$$x_{53} = 68.0678407607945$$
$$x_{54} = 26.1799388201561$$
$$x_{55} = 85.8701993037672$$
$$x_{56} = 4.18879024075387$$
$$x_{57} = -87.6155284501153$$
$$x_{58} = -68.0678408119881$$
$$x_{59} = 74.3510260903306$$
$$x_{60} = -46.0766922667605$$
$$x_{61} = -24.4346095279206$$
$$x_{62} = 52.3598774972308$$
$$x_{63} = -39.7935069184688$$
$$x_{64} = -41.8879021208032$$
$$x_{65} = 100.181899064475$$
$$x_{66} = -35.6047168053919$$
$$x_{67} = 36.3028484414821$$
$$x_{68} = -53.7561409614254$$
$$x_{69} = 22.3402144255274$$
$$x_{70} = -47.8220215046446$$
$$x_{71} = -90.0589893805018$$
$$x_{72} = -82.0304748437335$$
$$x_{73} = 54.1052068118242$$
$$x_{74} = -43.6332312998582$$
$$x_{75} = 10.1229096615671$$
$$x_{76} = -57.5958653813132$$
$$x_{77} = -11.8682389135614$$
$$x_{78} = 34.2084533390889$$
$$x_{79} = 24.0855435922613$$
$$x_{80} = -3.83972435438753$$
$$x_{81} = 30.3687289219779$$
$$x_{82} = -49.9164166070378$$
$$x_{83} = -148.003920569119$$
$$x_{84} = 56.1996019142174$$
$$x_{85} = -52.010811709431$$
$$x_{86} = 20.2458193231342$$
$$x_{87} = 14.3116998663535$$
$$x_{88} = 88.3136601509131$$
$$x_{89} = 46.0766921768866$$
$$x_{90} = -75.7472895365539$$
$$x_{91} = -61.7846554984007$$
$$x_{92} = 40.1425727958696$$
$$x_{93} = -30.0196631343025$$
$$x_{94} = -25.8308729295161$$
o sea hay que resolver la ecuación:
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -79.587013957071$$
$$x_{2} = 58.2939970166106$$
$$x_{3} = -91.8043186549017$$
$$x_{4} = -8.02851455917392$$
$$x_{5} = 41.8879019551629$$
$$x_{6} = 66.3225115757845$$
$$x_{7} = -31.7649923862968$$
$$x_{8} = 98.4365698456188$$
$$x_{9} = 32.1140582366957$$
$$x_{10} = 60.0393262686049$$
$$x_{11} = -9.77384381116824$$
$$x_{12} = -16.0570291183478$$
$$x_{13} = 16.0570291183478$$
$$x_{14} = -93.8987137572949$$
$$x_{15} = 76.0963553869528$$
$$x_{16} = -83.7758040786232$$
$$x_{17} = 12.2173047639603$$
$$x_{18} = 70.1622359788179$$
$$x_{19} = -71.9075651821664$$
$$x_{20} = 92.1533845581785$$
$$x_{21} = 18.151424220741$$
$$x_{22} = 62.1337213709981$$
$$x_{23} = -97.7384381116825$$
$$x_{24} = -60.0393262686049$$
$$x_{25} = 94.5968454580927$$
$$x_{26} = -38.0481776934764$$
$$x_{27} = -74.0019602845596$$
$$x_{28} = 82.0304748437335$$
$$x_{29} = 72.6056968829641$$
$$x_{30} = -13.613568229432$$
$$x_{31} = -55.8505360638185$$
$$x_{32} = 80.2851455917392$$
$$x_{33} = -5.93411945678072$$
$$x_{34} = 63.8790507190579$$
$$x_{35} = -99.8328332140756$$
$$x_{36} = 84.1248699461267$$
$$x_{37} = -17.8023583387693$$
$$x_{38} = 90.0589893442465$$
$$x_{39} = -69.8131700797732$$
$$x_{40} = -77.8416846389471$$
$$x_{41} = 38.0481776934764$$
$$x_{42} = 28.623399732707$$
$$x_{43} = -19.8967535778114$$
$$x_{44} = -33.85938748869$$
$$x_{45} = 2.09439500680622$$
$$x_{46} = 48.1710873994927$$
$$x_{47} = -65.6243798749868$$
$$x_{48} = -27.9252680319093$$
$$x_{49} = -95.9931088596881$$
$$x_{50} = 44.331363000656$$
$$x_{51} = 8.3775803464205$$
$$x_{52} = 78.190750489346$$
$$x_{53} = 68.0678407607945$$
$$x_{54} = 26.1799388201561$$
$$x_{55} = 85.8701993037672$$
$$x_{56} = 4.18879024075387$$
$$x_{57} = -87.6155284501153$$
$$x_{58} = -68.0678408119881$$
$$x_{59} = 74.3510260903306$$
$$x_{60} = -46.0766922667605$$
$$x_{61} = -24.4346095279206$$
$$x_{62} = 52.3598774972308$$
$$x_{63} = -39.7935069184688$$
$$x_{64} = -41.8879021208032$$
$$x_{65} = 100.181899064475$$
$$x_{66} = -35.6047168053919$$
$$x_{67} = 36.3028484414821$$
$$x_{68} = -53.7561409614254$$
$$x_{69} = 22.3402144255274$$
$$x_{70} = -47.8220215046446$$
$$x_{71} = -90.0589893805018$$
$$x_{72} = -82.0304748437335$$
$$x_{73} = 54.1052068118242$$
$$x_{74} = -43.6332312998582$$
$$x_{75} = 10.1229096615671$$
$$x_{76} = -57.5958653813132$$
$$x_{77} = -11.8682389135614$$
$$x_{78} = 34.2084533390889$$
$$x_{79} = 24.0855435922613$$
$$x_{80} = -3.83972435438753$$
$$x_{81} = 30.3687289219779$$
$$x_{82} = -49.9164166070378$$
$$x_{83} = -148.003920569119$$
$$x_{84} = 56.1996019142174$$
$$x_{85} = -52.010811709431$$
$$x_{86} = 20.2458193231342$$
$$x_{87} = 14.3116998663535$$
$$x_{88} = 88.3136601509131$$
$$x_{89} = 46.0766921768866$$
$$x_{90} = -75.7472895365539$$
$$x_{91} = -61.7846554984007$$
$$x_{92} = 40.1425727958696$$
$$x_{93} = -30.0196631343025$$
$$x_{94} = -25.8308729295161$$
Asíntotas verticales
Hay:
$$x_{1} = 0$$
$$x_{2} = 0.785398163397448$$
$$x_{1} = 0$$
$$x_{2} = 0.785398163397448$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
No se ha logrado calcular el límite a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}\right)$$
No se ha logrado calcular el límite a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}\right)$$
No se ha logrado calcular el límite a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}\right)$$
No se ha logrado calcular el límite a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (sin(9*x)*tan(3*x))/(sqrt(2 - sin(4*x)^2) - sqrt(2 + sin(4*x)^2)), dividida por x con x->+oo y x ->-oo
No se ha logrado calcular el límite a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{x \left(\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}\right)}\right)$$
No se ha logrado calcular el límite a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{x \left(\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}\right)}\right)$$
No se ha logrado calcular el límite a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{x \left(\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}\right)}\right)$$
No se ha logrado calcular el límite a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{x \left(\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}\right)}\right)$$
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:
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = \frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}$$
- Sí
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = - \frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}$$
- No
es decir, función
es
par
Pues, comprobamos:
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = \frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}$$
- Sí
$$\frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}} = - \frac{\sin{\left(9 x \right)} \tan{\left(3 x \right)}}{\sqrt{2 - \sin^{2}{\left(4 x \right)}} - \sqrt{\sin^{2}{\left(4 x \right)} + 2}}$$
- No
es decir, función
es
par