Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ 5*sin^2(x+0.6*sin^2(x))

Gráfico de la función y = 5*sin^2(x+0.6*sin^2(x))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
             /         2   \
            2|    3*sin (x)|
f(x) = 5*sin |x + ---------|
             \        5    /
f(x)=5sin⁡2(x+3sin⁡2(x)5)f{\left(x \right)} = 5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)} 
f = 5*sin(x + 3*sin(x)^2/5)^2
Gráfico de la función
-3.0-2.5-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5010
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:
5sin⁡2(x+3sin⁡2(x)5)=05 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−56.5486679786238x_{1} = -56.5486679786238
x2=−97.3893723544936x_{2} = -97.3893723544936
x3=−6.28318555164612x_{3} = -6.28318555164612
x4=15.707963023601x_{4} = 15.707963023601
x5=97.3893720660128x_{5} = 97.3893720660128
x6=−37.6991118739071x_{6} = -37.6991118739071
x7=87.9645940650334x_{7} = 87.9645940650334
x8=94.2477796093603x_{8} = 94.2477796093603
x9=81.6814092495825x_{9} = 81.6814092495825
x10=−81.6814090324637x_{10} = -81.6814090324637
x11=−53.4070752038331x_{11} = -53.4070752038331
x12=37.6991120885621x_{12} = 37.6991120885621
x13=34.5575190982584x_{13} = 34.5575190982584
x14=−87.9645942980512x_{14} = -87.9645942980512
x15=−72.256630816129x_{15} = -72.256630816129
x16=−87.964594351572x_{16} = -87.964594351572
x17=−3.14159274924226x_{17} = -3.14159274924226
x18=81.6814085935423x_{18} = 81.6814085935423
x19=−75.3982237791927x_{19} = -75.3982237791927
x20=25.1327410823708x_{20} = 25.1327410823708
x21=28.2743338660279x_{21} = 28.2743338660279
x22=−91.106187054105x_{22} = -91.106187054105
x23=−72.2566312772204x_{23} = -72.2566312772204
x24=21.9911483619786x_{24} = 21.9911483619786
x25=53.4070749102453x_{25} = 53.4070749102453
x26=−28.2743336539162x_{26} = -28.2743336539162
x27=−100.530964593916x_{27} = -100.530964593916
x28=−65.9734458178566x_{28} = -65.9734458178566
x29=−6.28318507297213x_{29} = -6.28318507297213
x30=−56.5486674465296x_{30} = -56.5486674465296
x31=65.9734457546774x_{31} = 65.9734457546774
x32=31.4159268419459x_{32} = 31.4159268419459
x33=−62.8318533151223x_{33} = -62.8318533151223
x34=65.9734454948399x_{34} = 65.9734454948399
x35=6.28318528573057x_{35} = 6.28318528573057
x36=9.42477827070862x_{36} = 9.42477827070862
x37=9.42477775454435x_{37} = 9.42477775454435
x38=15.707963507856x_{38} = 15.707963507856
x39=−94.2477798523536x_{39} = -94.2477798523536
x40=0x_{40} = 0
x41=18.849555826706x_{41} = 18.849555826706
x42=87.9645943386963x_{42} = 87.9645943386963
x43=59.6902606691398x_{43} = 59.6902606691398
x44=62.8318529782904x_{44} = 62.8318529782904
x45=47.123889658753x_{45} = 47.123889658753
x46=81.681408749507x_{46} = 81.681408749507
x47=−12.5663703011446x_{47} = -12.5663703011446
x48=75.3982234881286x_{48} = 75.3982234881286
x49=−40.840704646463x_{49} = -40.840704646463
x50=−50.2654827020575x_{50} = -50.2654827020575
x51=56.5486676739601x_{51} = 56.5486676739601
x52=78.5398162497392x_{52} = 78.5398162497392
x53=3.14159250604555x_{53} = 3.14159250604555
x54=−31.4159266284114x_{54} = -31.4159266284114
x55=−34.5575188735702x_{55} = -34.5575188735702
x56=43.9822969268829x_{56} = 43.9822969268829
x57=−28.2743341268658x_{57} = -28.2743341268658
x58=75.3982239823686x_{58} = 75.3982239823686
x59=−12.5663708232433x_{59} = -12.5663708232433
x60=−9.42477805292438x_{60} = -9.42477805292438
x61=100.530964825598x_{61} = 100.530964825598
x62=72.2566310277859x_{62} = 72.2566310277859
x63=50.2654824466962x_{63} = 50.2654824466962
x64=−15.7079632942366x_{64} = -15.7079632942366
x65=12.5663705226312x_{65} = 12.5663705226312
x66=−84.8230017988415x_{66} = -84.8230017988415
x67=−50.2654822349703x_{67} = -50.2654822349703
x68=−40.8407047520115x_{68} = -40.8407047520115
x69=−18.8495560702297x_{69} = -18.8495560702297
x70=−84.8230018986011x_{70} = -84.8230018986011
x71=−47.12388990146x_{71} = -47.12388990146
x72=21.9911485854309x_{72} = 21.9911485854309
x73=−25.1327413252974x_{73} = -25.1327413252974
x74=37.6991115988752x_{74} = 37.6991115988752
x75=−34.5575194009703x_{75} = -34.5575194009703
x76=40.8407044025493x_{76} = 40.8407044025493
x77=59.6902601741769x_{77} = 59.6902601741769
x78=−21.9911487525914x_{78} = -21.9911487525914
x79=−65.9734457615965x_{79} = -65.9734457615965
x80=−59.6902604533084x_{80} = -59.6902604533084
x81=69.1150382351973x_{81} = 69.1150382351973
x82=53.4070754125178x_{82} = 53.4070754125178
x83=−43.9822972955314x_{83} = -43.9822972955314
x84=31.4159263323788x_{84} = 31.4159263323788
x85=91.1061868117081x_{85} = 91.1061868117081
x86=97.3893725514347x_{86} = 97.3893725514347
x87=−43.9822971732639x_{87} = -43.9822971732639
x88=−69.1150384777298x_{88} = -69.1150384777298
x89=−62.8318532226635x_{89} = -62.8318532226635
x90=−18.8495562683072x_{90} = -18.8495562683072
x91=84.8230015539332x_{91} = 84.8230015539332
x92=−21.9911485861619x_{92} = -21.9911485861619
x93=−78.5398165561923x_{93} = -78.5398165561923
x94=43.9822971702849x_{94} = 43.9822971702849
x95=−78.5398160199884x_{95} = -78.5398160199884
x96=−94.2477793973868x_{96} = -94.2477793973868
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 5*sin(x + 3*sin(x)^2/5)^2.
5sin⁡2(3sin⁡2(0)5)5 \sin^{2}{\left(\frac{3 \sin^{2}{\left(0 \right)}}{5} \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
lim⁡x→−∞(5sin⁡2(x+3sin⁡2(x)5))=⟨0,5⟩\lim_{x \to -\infty}\left(5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)}\right) = \left\langle 0, 5\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨0,5⟩y = \left\langle 0, 5\right\rangle
lim⁡x→∞(5sin⁡2(x+3sin⁡2(x)5))=⟨0,5⟩\lim_{x \to \infty}\left(5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)}\right) = \left\langle 0, 5\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨0,5⟩y = \left\langle 0, 5\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función 5*sin(x + 3*sin(x)^2/5)^2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(5sin⁡2(x+3sin⁡2(x)5)x)=0\lim_{x \to -\infty}\left(\frac{5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(5sin⁡2(x+3sin⁡2(x)5)x)=0\lim_{x \to \infty}\left(\frac{5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \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:
5sin⁡2(x+3sin⁡2(x)5)=5sin⁡2(x−3sin⁡2(x)5)5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)} = 5 \sin^{2}{\left(x - \frac{3 \sin^{2}{\left(x \right)}}{5} \right)}
- No
5sin⁡2(x+3sin⁡2(x)5)=−5sin⁡2(x−3sin⁡2(x)5)5 \sin^{2}{\left(x + \frac{3 \sin^{2}{\left(x \right)}}{5} \right)} = - 5 \sin^{2}{\left(x - \frac{3 \sin^{2}{\left(x \right)}}{5} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор