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y=sin(x+3)/(x^5*ctg(x^3)*cos(x^3))
Trazado el gráfico de la función/ y=sin(x+3)/(x^5*ctg(x^3)*cos(x^3))

Gráfico de la función y = y=sin(x+3)/(x^5*ctg(x^3)*cos(x^3))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
           sin(x + 3)    
f(x) = ------------------
        5    / 3\    / 3\
       x *cot\x /*cos\x /
f(x)=sin⁡(x+3)x5cot⁡(x3)cos⁡(x3)f{\left(x \right)} = \frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}} 
f = sin(x + 3)/(((x^5*cot(x^3))*cos(x^3)))
Gráfico de la función
468201012141618-25002500
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
x2=1.16244735150963x_{2} = 1.16244735150963
x3=1.67653919321974x_{3} = 1.67653919321974
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⁡(x+3)x5cot⁡(x3)cos⁡(x3)=0\frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−3x_{1} = -3
x2=−3+πx_{2} = -3 + \pi
Solución numérica
x1=−95.8242118727143x_{1} = -95.8242118727143
x2=−94.0165774861814x_{2} = -94.0165774861814
x3=94.3940553180249x_{3} = 94.3940553180249
x4=84.2499915828561x_{4} = 84.2499915828561
x5=−86.0188396280711x_{5} = -86.0188396280711
x6=7.98402023694881x_{6} = 7.98402023694881
x7=−83.7510368333762x_{7} = -83.7510368333762
x8=88.1061232029598x_{8} = 88.1061232029598
x9=−29.7969066259943x_{9} = -29.7969066259943
x10=57.991880743649x_{10} = 57.991880743649
x11=−87.8300602769334x_{11} = -87.8300602769334
x12=−11.7091020461491x_{12} = -11.7091020461491
x13=−59.6839063038101x_{13} = -59.6839063038101
x14=−15.8896228830588x_{14} = -15.8896228830588
x15=43.9962623639006x_{15} = 43.9962623639006
x16=−73.8716880719569x_{16} = -73.8716880719569
x17=36.007217388419x_{17} = 36.007217388419
x18=−77.7132929560174x_{18} = -77.7132929560174
x19=22.0940106342634x_{19} = 22.0940106342634
x20=28.240311600252x_{20} = 28.240311600252
x21=−49.7521645172534x_{21} = -49.7521645172534
x22=−65.8793810571914x_{22} = -65.8793810571914
x23=73.9992722863653x_{23} = 73.9992722863653
x24=6.23084382613116x_{24} = 6.23084382613116
x25=−31.7574556994989x_{25} = -31.7574556994989
x26=32.1583620829028x_{26} = 32.1583620829028
x27=−37.743507680763x_{27} = -37.743507680763
x28=−35.6959941414773x_{28} = -35.6959941414773
x29=34.7619865475744x_{29} = 34.7619865475744
x30=−27.7513073852549x_{30} = -27.7513073852549
x31=−9.74968601332573x_{31} = -9.74968601332573
x32=99.1306322333143x_{32} = 99.1306322333143
x33=14.2496162144817x_{33} = 14.2496162144817
x34=2.32489470301925x_{34} = 2.32489470301925
x35=−67.7392826024758x_{35} = -67.7392826024758
x36=−90.0002705862446x_{36} = -90.0002705862446
x37=−34.0091905995315x_{37} = -34.0091905995315
x38=38.0584341722139x_{38} = 38.0584341722139
x39=−99.997812756108x_{39} = -99.997812756108
x40=3.90811940747395x_{40} = 3.90811940747395
x41=62.0054048132249x_{41} = 62.0054048132249
x42=91.9550553686763x_{42} = 91.9550553686763
x43=78.2478276854666x_{43} = 78.2478276854666
x44=−62.7729542603862x_{44} = -62.7729542603862
x45=−25.750350237363x_{45} = -25.750350237363
x46=86.031858206354x_{46} = 86.031858206354
x47=54.1645687836743x_{47} = 54.1645687836743
x48=−47.7562696674737x_{48} = -47.7562696674737
x49=40.1370838297797x_{49} = 40.1370838297797
x50=24.2513121604348x_{50} = 24.2513121604348
x51=−45.9588814972479x_{51} = -45.9588814972479
x52=10.6545930701833x_{52} = 10.6545930701833
x53=72.2479097034996x_{53} = 72.2479097034996
x54=63.6317684657264x_{54} = 63.6317684657264
x55=72.3390775154369x_{55} = 72.3390775154369
x56=−21.7497227712982x_{56} = -21.7497227712982
x57=45.9777134506256x_{57} = 45.9777134506256
x58=−19.7495306722652x_{58} = -19.7495306722652
x59=52.0182279848261x_{59} = 52.0182279848261
x60=−75.7629529060725x_{60} = -75.7629529060725
x61=−43.9420957298392x_{61} = -43.9420957298392
x62=98.0399222184108x_{62} = 98.0399222184108
x63=−39.9745678805764x_{63} = -39.9745678805764
x64=20.2495640883152x_{64} = 20.2495640883152
x65=48.1926090522382x_{65} = 48.1926090522382
x66=57.0136103979535x_{66} = 57.0136103979535
x67=11.8747833238121x_{67} = 11.8747833238121
x68=−71.7627657817972x_{68} = -71.7627657817972
x69=−91.7502558421128x_{69} = -91.7502558421128
x70=64.0094512996448x_{70} = 64.0094512996448
x71=−6.00712018694079x_{71} = -6.00712018694079
x72=−41.9167581396038x_{72} = -41.9167581396038
x73=−97.7431194829307x_{73} = -97.7431194829307
x74=−13.9493682181155x_{74} = -13.9493682181155
x75=−55.7500062668987x_{75} = -55.7500062668987
x76=42.2584586090697x_{76} = 42.2584586090697
x77=60.2419335987566x_{77} = 60.2419335987566
x78=26.0392654802548x_{78} = 26.0392654802548
x79=−3.69054029728806x_{79} = -3.69054029728806
x80=−57.9909465810375x_{80} = -57.9909465810375
x81=18.2757085861653x_{81} = 18.2757085861653
x82=−51.9899612016088x_{82} = -51.9899612016088
x83=16.250504839295x_{83} = 16.250504839295
x84=106.369723352868x_{84} = 106.369723352868
x85=−7.71200986014021x_{85} = -7.71200986014021
x86=30.2499753188897x_{86} = 30.2499753188897
x87=49.9707720656106x_{87} = 49.9707720656106
x88=90.2624673490639x_{88} = 90.2624673490639
x89=82.6699745128054x_{89} = 82.6699745128054
x90=−23.8916724949998x_{90} = -23.8916724949998
x91=−17.7629424025955x_{91} = -17.7629424025955
x92=−54.0812731955784x_{92} = -54.0812731955784
x93=76.2507456826782x_{93} = 76.2507456826782
x94=80.9079725392532x_{94} = 80.9079725392532
x95=−71.1052471837948x_{95} = -71.1052471837948
x96=−63.751032328341x_{96} = -63.751032328341
x97=−1.84527014864403x_{97} = -1.84527014864403
x98=−82.0018866992414x_{98} = -82.0018866992414
x99=−79.9854901274451x_{99} = -79.9854901274451
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(x + 3)/(((x^5*cot(x^3))*cos(x^3))).
sin⁡(3)05cot⁡(03)cos⁡(03)\frac{\sin{\left(3 \right)}}{0^{5} \cot{\left(0^{3} \right)} \cos{\left(0^{3} \right)}}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
Asíntotas verticales
Hay:
x1=0x_{1} = 0
x2=1.16244735150963x_{2} = 1.16244735150963
x3=1.67653919321974x_{3} = 1.67653919321974
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(sin⁡(x+3)x5cot⁡(x3)cos⁡(x3))y = \lim_{x \to -\infty}\left(\frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(sin⁡(x+3)x5cot⁡(x3)cos⁡(x3))y = \lim_{x \to \infty}\left(\frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x + 3)/(((x^5*cot(x^3))*cos(x^3))), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(1x5cos⁡(x3)cot⁡(x3)sin⁡(x+3)x)y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{x^{5} \cos{\left(x^{3} \right)} \cot{\left(x^{3} \right)}} \sin{\left(x + 3 \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(1x5cos⁡(x3)cot⁡(x3)sin⁡(x+3)x)y = x \lim_{x \to \infty}\left(\frac{\frac{1}{x^{5} \cos{\left(x^{3} \right)} \cot{\left(x^{3} \right)}} \sin{\left(x + 3 \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:
sin⁡(x+3)x5cot⁡(x3)cos⁡(x3)=−1x5cos⁡(x3)cot⁡(x3)sin⁡(x−3)\frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}} = - \frac{1}{x^{5} \cos{\left(x^{3} \right)} \cot{\left(x^{3} \right)}} \sin{\left(x - 3 \right)}
- No
sin⁡(x+3)x5cot⁡(x3)cos⁡(x3)=1x5cos⁡(x3)cot⁡(x3)sin⁡(x−3)\frac{\sin{\left(x + 3 \right)}}{x^{5} \cot{\left(x^{3} \right)} \cos{\left(x^{3} \right)}} = \frac{1}{x^{5} \cos{\left(x^{3} \right)} \cot{\left(x^{3} \right)}} \sin{\left(x - 3 \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = y=sin(x+3)/(x^5*ctg(x^3)*cos(x^3))
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