Sr Examen
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- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
x+27/x^3
-
(x^2-8)/(x-3)
-
x-2+4/(x-2)
-
x^2-9*x+14
-
Expresiones idénticas
- cos(dos . cinco *x)*sin(x)^ dos
- coseno de (2.5 multiplicar por x) multiplicar por seno de (x) al cuadrado
- coseno de (dos . cinco multiplicar por x) multiplicar por seno de (x) en el grado dos
- cos(2.5*x)*sin(x)2
- cos2.5*x*sinx2
- cos(2.5*x)*sin(x)²
- cos(2.5*x)*sin(x) en el grado 2
- cos(2.5x)sin(x)^2
- cos(2.5x)sin(x)2
- cos2.5xsinx2
- cos2.5xsinx^2
-
Expresiones semejantes
- cos(2.5*x)*sinx^2
-
Expresiones con funciones
- Coseno cos
- cos(x-pi)-2
- cos(x)/(2*sqrt(x))-sin(x)*sqrt(x)
- cos(x)/18+cos(x*sqrt(19))+sin(x*sqrt(19))
- cos(x^2)+2
- cos(x)*x^3+9
- Seno sin
- sin(x-pi/4)*(-2)
- sin(pi*x)/asin(x)
- sin(x)*e^((1/2)*cot(x)^(2))
- sin(697*t)+sin(1209*t)
- sin(3x-29)
Gráfico de la función y = cos(2.5*x)*sin(x)^2
Solución
Ha introducido
[src]
/5*x\ 2
f(x) = cos|---|*sin (x)
\ 2 /
$$f{\left(x \right)} = \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}$$
f = sin(x)^2*cos(5*x/2)
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:
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = - \frac{\pi}{5}$$
$$x_{3} = \frac{\pi}{5}$$
Solución numérica
$$x_{1} = -69.1150383991702$$
$$x_{2} = -86.0796387083603$$
$$x_{3} = -59.6902756893242$$
$$x_{4} = -19.4778744522567$$
$$x_{5} = -65.9734546902005$$
$$x_{6} = 28.2743275406062$$
$$x_{7} = -78.5397480779278$$
$$x_{8} = -15.7079741298643$$
$$x_{9} = -69.7433569096934$$
$$x_{10} = -11.9380520836412$$
$$x_{11} = -9.42473471504747$$
$$x_{12} = -47.1238560999113$$
$$x_{13} = 38.3274303737955$$
$$x_{14} = 42.0973415581032$$
$$x_{15} = 6.28318528490966$$
$$x_{16} = -25.1327414194977$$
$$x_{17} = 14.451326206513$$
$$x_{18} = 25.7610597594363$$
$$x_{19} = 58.4336233567702$$
$$x_{20} = -50.2654823548004$$
$$x_{21} = 96.1327351998477$$
$$x_{22} = -96.1327351998477$$
$$x_{23} = 68.4867198482575$$
$$x_{24} = 84.8229456515933$$
$$x_{25} = 78.53975568656$$
$$x_{26} = 52.1504380495906$$
$$x_{27} = -47.1238898720042$$
$$x_{28} = 18.2212373908208$$
$$x_{29} = -53.4071426455963$$
$$x_{30} = 72.2566292958362$$
$$x_{31} = 1.88495559215388$$
$$x_{32} = 48.3805268652828$$
$$x_{33} = 87.9645943335107$$
$$x_{34} = 69.7433569096934$$
$$x_{35} = -73.5132680940012$$
$$x_{36} = 0$$
$$x_{37} = 4.39822971502571$$
$$x_{38} = -83.5663645854885$$
$$x_{39} = -34.5574563255819$$
$$x_{40} = -32.0442450666159$$
$$x_{41} = -72.2565686777662$$
$$x_{42} = -91.1061490237928$$
$$x_{43} = 21.9911516412945$$
$$x_{44} = -81.6814090344349$$
$$x_{45} = 50.2654824464708$$
$$x_{46} = 92.3628240155399$$
$$x_{47} = -94.2477796441908$$
$$x_{48} = 97.3893965718329$$
$$x_{49} = -35.8141562509236$$
$$x_{50} = 15.7080305239798$$
$$x_{51} = -21.9911516399334$$
$$x_{52} = 94.2477797091428$$
$$x_{53} = -43.9822971751701$$
$$x_{54} = -62.2035345410779$$
$$x_{55} = 82.3097275240526$$
$$x_{56} = -3.14161975923629$$
$$x_{57} = -63.4601716025138$$
$$x_{58} = 35.8141562509236$$
$$x_{59} = -8.16814089933346$$
$$x_{60} = -28.2742689759286$$
$$x_{61} = -29.5309709437441$$
$$x_{62} = 32.0442450666159$$
$$x_{63} = -76.026542216873$$
$$x_{64} = 9.42483284931873$$
$$x_{65} = 24.5044226980004$$
$$x_{66} = -25.7610597594363$$
$$x_{67} = 89.8495498926681$$
$$x_{68} = 40.8406598530557$$
$$x_{69} = -89.8495498926681$$
$$x_{70} = 53.4071179646183$$
$$x_{71} = 43.9822971688583$$
$$x_{72} = -39.5840674352314$$
$$x_{73} = -45.867252742411$$
$$x_{74} = 8.16814089933346$$
$$x_{75} = 59.6903298169878$$
$$x_{76} = -87.9645943610618$$
$$x_{77} = -18.2212373908208$$
$$x_{78} = -9.42484338601178$$
$$x_{79} = -1.88495559215388$$
$$x_{80} = -55.9203492338983$$
$$x_{81} = 76.026542216873$$
$$x_{82} = 34.5574560620254$$
$$x_{83} = -99.9026463841554$$
$$x_{84} = 62.2035345410779$$
$$x_{85} = 79.7964534011807$$
$$x_{86} = 65.9734548006501$$
$$x_{87} = -97.3894417021481$$
$$x_{88} = 45.867252742411$$
$$x_{89} = -79.7964534011807$$
$$x_{90} = 94.2477796093546$$
$$x_{91} = -37.6991118753961$$
$$x_{92} = 86.0796387083603$$
$$x_{93} = -42.0973415581032$$
o sea hay que resolver la ecuación:
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = 0$$
$$x_{2} = - \frac{\pi}{5}$$
$$x_{3} = \frac{\pi}{5}$$
Solución numérica
$$x_{1} = -69.1150383991702$$
$$x_{2} = -86.0796387083603$$
$$x_{3} = -59.6902756893242$$
$$x_{4} = -19.4778744522567$$
$$x_{5} = -65.9734546902005$$
$$x_{6} = 28.2743275406062$$
$$x_{7} = -78.5397480779278$$
$$x_{8} = -15.7079741298643$$
$$x_{9} = -69.7433569096934$$
$$x_{10} = -11.9380520836412$$
$$x_{11} = -9.42473471504747$$
$$x_{12} = -47.1238560999113$$
$$x_{13} = 38.3274303737955$$
$$x_{14} = 42.0973415581032$$
$$x_{15} = 6.28318528490966$$
$$x_{16} = -25.1327414194977$$
$$x_{17} = 14.451326206513$$
$$x_{18} = 25.7610597594363$$
$$x_{19} = 58.4336233567702$$
$$x_{20} = -50.2654823548004$$
$$x_{21} = 96.1327351998477$$
$$x_{22} = -96.1327351998477$$
$$x_{23} = 68.4867198482575$$
$$x_{24} = 84.8229456515933$$
$$x_{25} = 78.53975568656$$
$$x_{26} = 52.1504380495906$$
$$x_{27} = -47.1238898720042$$
$$x_{28} = 18.2212373908208$$
$$x_{29} = -53.4071426455963$$
$$x_{30} = 72.2566292958362$$
$$x_{31} = 1.88495559215388$$
$$x_{32} = 48.3805268652828$$
$$x_{33} = 87.9645943335107$$
$$x_{34} = 69.7433569096934$$
$$x_{35} = -73.5132680940012$$
$$x_{36} = 0$$
$$x_{37} = 4.39822971502571$$
$$x_{38} = -83.5663645854885$$
$$x_{39} = -34.5574563255819$$
$$x_{40} = -32.0442450666159$$
$$x_{41} = -72.2565686777662$$
$$x_{42} = -91.1061490237928$$
$$x_{43} = 21.9911516412945$$
$$x_{44} = -81.6814090344349$$
$$x_{45} = 50.2654824464708$$
$$x_{46} = 92.3628240155399$$
$$x_{47} = -94.2477796441908$$
$$x_{48} = 97.3893965718329$$
$$x_{49} = -35.8141562509236$$
$$x_{50} = 15.7080305239798$$
$$x_{51} = -21.9911516399334$$
$$x_{52} = 94.2477797091428$$
$$x_{53} = -43.9822971751701$$
$$x_{54} = -62.2035345410779$$
$$x_{55} = 82.3097275240526$$
$$x_{56} = -3.14161975923629$$
$$x_{57} = -63.4601716025138$$
$$x_{58} = 35.8141562509236$$
$$x_{59} = -8.16814089933346$$
$$x_{60} = -28.2742689759286$$
$$x_{61} = -29.5309709437441$$
$$x_{62} = 32.0442450666159$$
$$x_{63} = -76.026542216873$$
$$x_{64} = 9.42483284931873$$
$$x_{65} = 24.5044226980004$$
$$x_{66} = -25.7610597594363$$
$$x_{67} = 89.8495498926681$$
$$x_{68} = 40.8406598530557$$
$$x_{69} = -89.8495498926681$$
$$x_{70} = 53.4071179646183$$
$$x_{71} = 43.9822971688583$$
$$x_{72} = -39.5840674352314$$
$$x_{73} = -45.867252742411$$
$$x_{74} = 8.16814089933346$$
$$x_{75} = 59.6903298169878$$
$$x_{76} = -87.9645943610618$$
$$x_{77} = -18.2212373908208$$
$$x_{78} = -9.42484338601178$$
$$x_{79} = -1.88495559215388$$
$$x_{80} = -55.9203492338983$$
$$x_{81} = 76.026542216873$$
$$x_{82} = 34.5574560620254$$
$$x_{83} = -99.9026463841554$$
$$x_{84} = 62.2035345410779$$
$$x_{85} = 79.7964534011807$$
$$x_{86} = 65.9734548006501$$
$$x_{87} = -97.3894417021481$$
$$x_{88} = 45.867252742411$$
$$x_{89} = -79.7964534011807$$
$$x_{90} = 94.2477796093546$$
$$x_{91} = -37.6991118753961$$
$$x_{92} = 86.0796387083603$$
$$x_{93} = -42.0973415581032$$
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
$$- (2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(\frac{5 x}{2} \right)} + \frac{25 \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{4} + 10 \sin{\left(x \right)} \sin{\left(\frac{5 x}{2} \right)} \cos{\left(x \right)}) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 16.2621653968953$$
$$x_{2} = -49.3217297290289$$
$$x_{3} = 0.231570987287359$$
$$x_{4} = 19.7933086499466$$
$$x_{5} = -17.9058031931309$$
$$x_{6} = 70.0587911073833$$
$$x_{7} = -55.6049150362085$$
$$x_{8} = -43.0385444218493$$
$$x_{9} = 58.3307728980475$$
$$x_{10} = -45.7644022836883$$
$$x_{11} = -21.9911485751286$$
$$x_{12} = -71.7024289036189$$
$$x_{13} = -43.7507261629697$$
$$x_{14} = -87.7330233132269$$
$$x_{15} = 26.0764939571262$$
$$x_{16} = -9.9789800897157$$
$$x_{17} = -12.7979416016465$$
$$x_{18} = 98.7488597814422$$
$$x_{19} = -37.9306828303649$$
$$x_{20} = 35.9170067096463$$
$$x_{21} = -75.6297946734424$$
$$x_{22} = 84.2687995179781$$
$$x_{23} = -59.6902604182061$$
$$x_{24} = -94.0162086204064$$
$$x_{25} = 79.8993038599034$$
$$x_{26} = -44.9260498786649$$
$$x_{27} = -77.9856142107985$$
$$x_{28} = -31.6474975231853$$
$$x_{29} = 12.3347996270718$$
$$x_{30} = -68.1712856505676$$
$$x_{31} = -27.7201317533618$$
$$x_{32} = 17.9058031931309$$
$$x_{33} = 14.3484757477904$$
$$x_{34} = -61.888100343388$$
$$x_{35} = -98.7488597814422$$
$$x_{36} = 97.9435743902299$$
$$x_{37} = -15.707963267949$$
$$x_{38} = 44.2138681375445$$
$$x_{39} = 34.0033170605414$$
$$x_{40} = 76.3419764145629$$
$$x_{41} = -70.0587911073833$$
$$x_{42} = 50.0339114701493$$
$$x_{43} = -65.9734457253857$$
$$x_{44} = -56.3170967773289$$
$$x_{45} = 77.9856142107985$$
$$x_{46} = -85.3772037758707$$
$$x_{47} = -26.0764939571262$$
$$x_{48} = 61.888100343388$$
$$x_{49} = -29.6338214024668$$
$$x_{50} = 30.4721738074901$$
$$x_{51} = 88.1961652878016$$
$$x_{52} = 53.9612772399728$$
$$x_{53} = 68.1712856505676$$
$$x_{54} = 24.1889885003105$$
$$x_{55} = 86.182489167083$$
$$x_{56} = 52.0475875908679$$
$$x_{57} = -34.0033170605414$$
$$x_{58} = 28.2743338823081$$
$$x_{59} = -97.9435743902299$$
$$x_{60} = 65.9734457253857$$
$$x_{61} = 95.1915323361016$$
$$x_{62} = -3.69579478253611$$
$$x_{63} = -81.912979980622$$
$$x_{64} = 9.9789800897157$$
$$x_{65} = -50.0339114701493$$
$$x_{66} = 100.299393927586$$
$$x_{67} = -0.943752728407827$$
$$x_{68} = 37.9306828303649$$
$$x_{69} = -6.05161431989223$$
$$x_{70} = -89.7466994339454$$
$$x_{71} = -86.182489167083$$
$$x_{72} = -91.6603890830503$$
$$x_{73} = -52.0475875908679$$
$$x_{74} = -11.6226178859513$$
$$x_{75} = -53.9612772399728$$
$$x_{76} = -8.06529044061076$$
$$x_{77} = 42.2001920168259$$
$$x_{78} = 63.7756058002037$$
$$x_{79} = -35.9170067096463$$
$$x_{80} = 72.2566310325652$$
$$x_{81} = -19.7933086499466$$
$$x_{82} = -24.1889885003105$$
$$x_{83} = -79.8993038599034$$
$$x_{84} = 94.0162086204064$$
$$x_{85} = -63.7756058002037$$
$$x_{86} = 50.4970534447241$$
$$x_{87} = 81.912979980622$$
$$x_{88} = 21.9911485751286$$
$$x_{89} = -96.029884741125$$
$$x_{90} = 8.06529044061076$$
$$x_{91} = 96.029884741125$$
$$x_{92} = -1.78210513343118$$
$$x_{93} = 32.3596792643058$$
$$x_{94} = 6.05161431989223$$
$$x_{95} = -73.6161185527239$$
$$x_{96} = -47.6780919327932$$
$$x_{97} = 74.4544709577472$$
$$x_{98} = 60.2444625471524$$
$$x_{99} = 56.3170967773289$$
$$x_{100} = 40.286502367721$$
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
$$\left[100.299393927586, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -97.9435743902299\right]$$
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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
$$- (2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(\frac{5 x}{2} \right)} + \frac{25 \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{4} + 10 \sin{\left(x \right)} \sin{\left(\frac{5 x}{2} \right)} \cos{\left(x \right)}) = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 16.2621653968953$$
$$x_{2} = -49.3217297290289$$
$$x_{3} = 0.231570987287359$$
$$x_{4} = 19.7933086499466$$
$$x_{5} = -17.9058031931309$$
$$x_{6} = 70.0587911073833$$
$$x_{7} = -55.6049150362085$$
$$x_{8} = -43.0385444218493$$
$$x_{9} = 58.3307728980475$$
$$x_{10} = -45.7644022836883$$
$$x_{11} = -21.9911485751286$$
$$x_{12} = -71.7024289036189$$
$$x_{13} = -43.7507261629697$$
$$x_{14} = -87.7330233132269$$
$$x_{15} = 26.0764939571262$$
$$x_{16} = -9.9789800897157$$
$$x_{17} = -12.7979416016465$$
$$x_{18} = 98.7488597814422$$
$$x_{19} = -37.9306828303649$$
$$x_{20} = 35.9170067096463$$
$$x_{21} = -75.6297946734424$$
$$x_{22} = 84.2687995179781$$
$$x_{23} = -59.6902604182061$$
$$x_{24} = -94.0162086204064$$
$$x_{25} = 79.8993038599034$$
$$x_{26} = -44.9260498786649$$
$$x_{27} = -77.9856142107985$$
$$x_{28} = -31.6474975231853$$
$$x_{29} = 12.3347996270718$$
$$x_{30} = -68.1712856505676$$
$$x_{31} = -27.7201317533618$$
$$x_{32} = 17.9058031931309$$
$$x_{33} = 14.3484757477904$$
$$x_{34} = -61.888100343388$$
$$x_{35} = -98.7488597814422$$
$$x_{36} = 97.9435743902299$$
$$x_{37} = -15.707963267949$$
$$x_{38} = 44.2138681375445$$
$$x_{39} = 34.0033170605414$$
$$x_{40} = 76.3419764145629$$
$$x_{41} = -70.0587911073833$$
$$x_{42} = 50.0339114701493$$
$$x_{43} = -65.9734457253857$$
$$x_{44} = -56.3170967773289$$
$$x_{45} = 77.9856142107985$$
$$x_{46} = -85.3772037758707$$
$$x_{47} = -26.0764939571262$$
$$x_{48} = 61.888100343388$$
$$x_{49} = -29.6338214024668$$
$$x_{50} = 30.4721738074901$$
$$x_{51} = 88.1961652878016$$
$$x_{52} = 53.9612772399728$$
$$x_{53} = 68.1712856505676$$
$$x_{54} = 24.1889885003105$$
$$x_{55} = 86.182489167083$$
$$x_{56} = 52.0475875908679$$
$$x_{57} = -34.0033170605414$$
$$x_{58} = 28.2743338823081$$
$$x_{59} = -97.9435743902299$$
$$x_{60} = 65.9734457253857$$
$$x_{61} = 95.1915323361016$$
$$x_{62} = -3.69579478253611$$
$$x_{63} = -81.912979980622$$
$$x_{64} = 9.9789800897157$$
$$x_{65} = -50.0339114701493$$
$$x_{66} = 100.299393927586$$
$$x_{67} = -0.943752728407827$$
$$x_{68} = 37.9306828303649$$
$$x_{69} = -6.05161431989223$$
$$x_{70} = -89.7466994339454$$
$$x_{71} = -86.182489167083$$
$$x_{72} = -91.6603890830503$$
$$x_{73} = -52.0475875908679$$
$$x_{74} = -11.6226178859513$$
$$x_{75} = -53.9612772399728$$
$$x_{76} = -8.06529044061076$$
$$x_{77} = 42.2001920168259$$
$$x_{78} = 63.7756058002037$$
$$x_{79} = -35.9170067096463$$
$$x_{80} = 72.2566310325652$$
$$x_{81} = -19.7933086499466$$
$$x_{82} = -24.1889885003105$$
$$x_{83} = -79.8993038599034$$
$$x_{84} = 94.0162086204064$$
$$x_{85} = -63.7756058002037$$
$$x_{86} = 50.4970534447241$$
$$x_{87} = 81.912979980622$$
$$x_{88} = 21.9911485751286$$
$$x_{89} = -96.029884741125$$
$$x_{90} = 8.06529044061076$$
$$x_{91} = 96.029884741125$$
$$x_{92} = -1.78210513343118$$
$$x_{93} = 32.3596792643058$$
$$x_{94} = 6.05161431989223$$
$$x_{95} = -73.6161185527239$$
$$x_{96} = -47.6780919327932$$
$$x_{97} = 74.4544709577472$$
$$x_{98} = 60.2444625471524$$
$$x_{99} = 56.3170967773289$$
$$x_{100} = 40.286502367721$$
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
$$\left[100.299393927586, \infty\right)$$
Convexa en los intervalos
$$\left(-\infty, -97.9435743902299\right]$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
$$\lim_{x \to -\infty}\left(\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}\right) = \left\langle -1, 1\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty}\left(\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}\right) = \left\langle -1, 1\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to -\infty}\left(\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}\right) = \left\langle -1, 1\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to \infty}\left(\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}\right) = \left\langle -1, 1\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -1, 1\right\rangle$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(5*x/2)*sin(x)^2, dividida por x con x->+oo y x ->-oo
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}}{x}\right) = 0$$
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:
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}$$
- Sí
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = - \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}$$
- No
es decir, función
es
par
Pues, comprobamos:
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}$$
- Sí
$$\sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)} = - \sin^{2}{\left(x \right)} \cos{\left(\frac{5 x}{2} \right)}$$
- No
es decir, función
es
par