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Trazado el gráfico de la función/ sin(6*x)*cos(5*x)

Gráfico de la función y = sin(6*x)*cos(5*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = sin(6*x)*cos(5*x)
f(x)=sin⁡(6x)cos⁡(5x)f{\left(x \right)} = \sin{\left(6 x \right)} \cos{\left(5 x \right)} 
f = sin(6*x)*cos(5*x)
Gráfico de la función
02468-8-6-4-2-10102-2
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⁡(6x)cos⁡(5x)=0\sin{\left(6 x \right)} \cos{\left(5 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π10x_{2} = - \frac{\pi}{10}
x3=π10x_{3} = \frac{\pi}{10}
Solución numérica
x1=−34.0339204138894x_{1} = -34.0339204138894
x2=−95.8185758726953x_{2} = -95.8185758726953
x3=−5.75958653158129x_{3} = -5.75958653158129
x4=2.82743338823081x_{4} = 2.82743338823081
x5=−31.7300858012569x_{5} = -31.7300858012569
x6=−21.9911485751286x_{6} = -21.9911485751286
x7=24.60914245312x_{7} = 24.60914245312
x8=−63.7743308678728x_{8} = -63.7743308678728
x9=−38.0132711084365x_{9} = -38.0132711084365
x10=48.0663675999238x_{10} = 48.0663675999238
x11=−49.7418836818384x_{11} = -49.7418836818384
x12=31.4159265358979x_{12} = 31.4159265358979
x13=−16.0221225333079x_{13} = -16.0221225333079
x14=−8.37758040957278x_{14} = -8.37758040957278
x15=−53.7212343763855x_{15} = -53.7212343763855
x16=78.8539756051038x_{16} = 78.8539756051038
x17=−56.025068989018x_{17} = -56.025068989018
x18=−43.9822971502571x_{18} = -43.9822971502571
x19=−7.85398143185297x_{19} = -7.85398143185297
x20=−31.4159265358979x_{20} = -31.4159265358979
x21=−46.18141200777x_{21} = -46.18141200777
x22=23.0383461263252x_{22} = 23.0383461263252
x23=66.497044500984x_{23} = 66.497044500984
x24=43.9822971502571x_{24} = 43.9822971502571
x25=−39.7935069454707x_{25} = -39.7935069454707
x26=98.9601685219405x_{26} = 98.9601685219405
x27=9.42477796076938x_{27} = 9.42477796076938
x28=−41.7831822927443x_{28} = -41.7831822927443
x29=74.8746249105567x_{29} = 74.8746249105567
x30=0x_{30} = 0
x31=−65.9734457253857x_{31} = -65.9734457253857
x32=93.3053018116169x_{32} = 93.3053018116169
x33=−12.0427718387609x_{33} = -12.0427718387609
x34=88.4881930761125x_{34} = 88.4881930761125
x35=84.5088423815654x_{35} = 84.5088423815654
x36=−81.9955682586936x_{36} = -81.9955682586936
x37=−80.1106127548258x_{37} = -80.1106127548258
x38=12.2522113490002x_{38} = 12.2522113490002
x39=21.4675497995303x_{39} = 21.4675497995303
x40=−90.0589894029074x_{40} = -90.0589894029074
x41=57.5958653158129x_{41} = 57.5958653158129
x42=65.9734457253857x_{42} = 65.9734457253857
x43=40.8407044966673x_{43} = 40.8407044966673
x44=203.889363217978x_{44} = 203.889363217978
x45=−85.7654794430014x_{45} = -85.7654794430014
x46=53.0929158456675x_{46} = 53.0929158456675
x47=−97.7035315266426x_{47} = -97.7035315266426
x48=−87.9645943005142x_{48} = -87.9645943005142
x49=−51.8362787159186x_{49} = -51.8362787159186
x50=−78.0162175641465x_{50} = -78.0162175641465
x51=52.3598775598299x_{51} = 52.3598775598299
x52=−25.4469004940773x_{52} = -25.4469004940773
x53=27.3318560862312x_{53} = 27.3318560862312
x54=79.4822941358218x_{54} = 79.4822941358218
x55=66.9159235214626x_{55} = 66.9159235214626
x56=−70.162235930172x_{56} = -70.162235930172
x57=94.2477796076938x_{57} = 94.2477796076938
x58=36.6519142918809x_{58} = 36.6519142918809
x59=72.2566310325652x_{59} = 72.2566310325652
x60=−60.2138591938044x_{60} = -60.2138591938044
x61=−83.7758040957278x_{61} = -83.7758040957278
x62=56.5486677646163x_{62} = 56.5486677646163
x63=95.8185758249797x_{63} = 95.8185758249797
x64=−9.73893722612836x_{64} = -9.73893722612836
x65=−17.8023583703422x_{65} = -17.8023583703422
x66=−75.712382951514x_{66} = -75.712382951514
x67=−19.7920337176157x_{67} = -19.7920337176157
x68=−48.6946862156121x_{68} = -48.6946862156121
x69=−100.007366139275x_{69} = -100.007366139275
x70=21.9911485751286x_{70} = 21.9911485751286
x71=14.13716703905x_{71} = 14.13716703905
x72=14.6607657167524x_{72} = 14.6607657167524
x73=−36.6519142918809x_{73} = -36.6519142918809
x74=−72.2566310325652x_{74} = -72.2566310325652
x75=37.6991118430775x_{75} = 37.6991118430775
x76=21.6769893097696x_{76} = 21.6769893097696
x77=50.2654824574367x_{77} = 50.2654824574367
x78=−92.0486647501809x_{78} = -92.0486647501809
x79=2.19911485751286x_{79} = 2.19911485751286
x80=34.2433599241287x_{80} = 34.2433599241287
x81=12.8805298797182x_{81} = 12.8805298797182
x82=−29.8451301634312x_{82} = -29.8451301634312
x83=60.632738214283x_{83} = 60.632738214283
x84=92.1533845053006x_{84} = 92.1533845053006
x85=3.66519142918809x_{85} = 3.66519142918809
x86=89.5353905699159x_{86} = 89.5353905699159
x87=−71.733032256967x_{87} = -71.733032256967
x88=−27.7507351067098x_{88} = -27.7507351067098
x89=−73.8274272914878x_{89} = -73.8274272914878
x90=−60.0044196835651x_{90} = -60.0044196835651
x91=81.9955682586936x_{91} = 81.9955682586936
x92=−93.7241808320955x_{92} = -93.7241808320955
x93=−68.1725605828985x_{93} = -68.1725605828985
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 sin(6*x)*cos(5*x).
sin⁡(0⋅6)cos⁡(0⋅5)\sin{\left(0 \cdot 6 \right)} \cos{\left(0 \cdot 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→−∞(sin⁡(6x)cos⁡(5x))=⟨−1,1⟩\lim_{x \to -\infty}\left(\sin{\left(6 x \right)} \cos{\left(5 x \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞(sin⁡(6x)cos⁡(5x))=⟨−1,1⟩\lim_{x \to \infty}\left(\sin{\left(6 x \right)} \cos{\left(5 x \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(6*x)*cos(5*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(6x)cos⁡(5x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(6 x \right)} \cos{\left(5 x \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(6x)cos⁡(5x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(6 x \right)} \cos{\left(5 x \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⁡(6x)cos⁡(5x)=−sin⁡(6x)cos⁡(5x)\sin{\left(6 x \right)} \cos{\left(5 x \right)} = - \sin{\left(6 x \right)} \cos{\left(5 x \right)}
- No
sin⁡(6x)cos⁡(5x)=sin⁡(6x)cos⁡(5x)\sin{\left(6 x \right)} \cos{\left(5 x \right)} = \sin{\left(6 x \right)} \cos{\left(5 x \right)}
- No
es decir, función
no es
par ni impar
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