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tan(x)^sin(x)
Trazado el gráfico de la función/ tan(x)^sin(x)

Gráfico de la función y = tan(x)^sin(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          sin(x)   
f(x) = tan      (x)
f(x)=tan⁡sin⁡(x)(x)f{\left(x \right)} = \tan^{\sin{\left(x \right)}}{\left(x \right)} 
f = tan(x)^sin(x)
Gráfico de la función
02468-8-6-4-2-10100100
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:
tan⁡sin⁡(x)(x)=0\tan^{\sin{\left(x \right)}}{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−64.4026493985908x_{1} = -64.4026493985908
x2=67.5442420521806x_{2} = 67.5442420521806
x3=4.71238898038469x_{3} = 4.71238898038469
x4=−7.85398163397448x_{4} = -7.85398163397448
x5=−89.5353906273091x_{5} = -89.5353906273091
x6=−58.1194640914112x_{6} = -58.1194640914112
x7=92.6769832808989x_{7} = 92.6769832808989
x8=42.4115008234622x_{8} = 42.4115008234622
x9=80.1106126665397x_{9} = 80.1106126665397
x10=−1.5707963267949x_{10} = -1.5707963267949
x11=−51.8362787842316x_{11} = -51.8362787842316
x12=10.9955742875643x_{12} = 10.9955742875643
x13=−95.8185759344887x_{13} = -95.8185759344887
x14=73.8274273593601x_{14} = 73.8274273593601
x15=−70.6858347057704x_{15} = -70.6858347057704
x16=−20.4203522483337x_{16} = -20.4203522483337
x17=−32.9867228626927x_{17} = -32.9867228626927
x18=36.1283155162826x_{18} = 36.1283155162826
x19=54.9778714378214x_{19} = 54.9778714378214
x20=86.3937979737193x_{20} = 86.3937979737193
x21=−76.9690200129499x_{21} = -76.9690200129499
x22=23.5619449019235x_{22} = 23.5619449019235
x23=−45.553093477052x_{23} = -45.553093477052
x24=48.6946861306418x_{24} = 48.6946861306418
x25=−83.2522053201295x_{25} = -83.2522053201295
x26=−39.2699081698724x_{26} = -39.2699081698724
x27=−14.1371669411541x_{27} = -14.1371669411541
x28=29.845130209103x_{28} = 29.845130209103
x29=98.9601685880785x_{29} = 98.9601685880785
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 tan(x)^sin(x).
tan⁡sin⁡(0)(0)\tan^{\sin{\left(0 \right)}}{\left(0 \right)}
Resultado:
f(0)=1f{\left(0 \right)} = 1
Punto:
(0, 1)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
((tan⁡2(x)+1)sin⁡(x)tan⁡(x)+log⁡(tan⁡(x))cos⁡(x))tan⁡sin⁡(x)(x)=0\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=3.46028220939344x_{1} = 3.46028220939344
x2=−93.9290900518902x_{2} = -93.9290900518902
x3=12.8850601701628x_{3} = 12.8850601701628
x4=53.7257646668301x_{4} = 53.7257646668301
x5=63.1505426275995x_{5} = 63.1505426275995
x6=97.7080618170872x_{6} = 97.7080618170872
x7=88.2832838563179x_{7} = 88.2832838563179
x8=72.5753205883689x_{8} = 72.5753205883689
x9=−71.9379414767616x_{9} = -71.9379414767616
x10=82.0000985491383x_{10} = 82.0000985491383
x11=41.159394052471x_{11} = 41.159394052471
x12=−31.0972369800943x_{12} = -31.0972369800943
x13=−46.8052002480433x_{13} = -46.8052002480433
x14=−87.6459047447106x_{14} = -87.6459047447106
x15=−18.5308663657351x_{15} = -18.5308663657351
x16=−37.3804222872739x_{16} = -37.3804222872739
x17=−43.6636075944535x_{17} = -43.6636075944535
x18=−9.10608840496574x_{18} = -9.10608840496574
x19=47.4425793596505x_{19} = 47.4425793596505
x20=−78.2211267839412x_{20} = -78.2211267839412
x21=−53.0883855552228x_{21} = -53.0883855552228
x22=−15.3892737121453x_{22} = -15.3892737121453
x23=−100.21227535907x_{23} = -100.21227535907
x24=16.0266528237526x_{24} = 16.0266528237526
x25=66.2921352811893x_{25} = 66.2921352811893
x26=−34.2388296336841x_{26} = -34.2388296336841
x27=−40.5220149408637x_{27} = -40.5220149408637
x28=22.3098381309322x_{28} = 22.3098381309322
x29=−5.96449575137594x_{29} = -5.96449575137594
x30=19.1682454773424x_{30} = 19.1682454773424
x31=−49.946792901633x_{31} = -49.946792901633
x32=44.3009867060607x_{32} = 44.3009867060607
x33=−56.2299782088126x_{33} = -56.2299782088126
x34=69.4337279347791x_{34} = 69.4337279347791
x35=−24.8140516729147x_{35} = -24.8140516729147
x36=−27.9556443265045x_{36} = -27.9556443265045
x37=−59.3715708624024x_{37} = -59.3715708624024
x38=9.74346751657302x_{38} = 9.74346751657302
x39=60.0089499740097x_{39} = 60.0089499740097
x40=25.451430784522x_{40} = 25.451430784522
x41=−97.07068270548x_{41} = -97.07068270548
x42=−62.5131635159922x_{42} = -62.5131635159922
x43=−75.0795341303514x_{43} = -75.0795341303514
x44=−12.2476810585555x_{44} = -12.2476810585555
x45=−65.654756169582x_{45} = -65.654756169582
x46=38.0178013988812x_{46} = 38.0178013988812
x47=85.1416912027281x_{47} = 85.1416912027281
x48=−84.5043120911208x_{48} = -84.5043120911208
x49=−90.7874973983004x_{49} = -90.7874973983004
x50=91.4248765099076x_{50} = 91.4248765099076
x51=75.7169132419587x_{51} = 75.7169132419587
x52=−68.7963488231718x_{52} = -68.7963488231718
x53=34.8762087452914x_{53} = 34.8762087452914
x54=−21.6724590193249x_{54} = -21.6724590193249
x55=31.7346160917016x_{55} = 31.7346160917016
x56=−2.82290309778615x_{56} = -2.82290309778615
Signos de extremos en los puntos:
(3.4602822093934367, 1.41542505382344)

(-93.92909005189016, 0.706501553931617)

(12.885060170162816, 0.706501553931617)

(53.72576466683013, 1.41542505382344)

(63.150542627599506, 0.706501553931617)

(97.70806181708723, 1.41542505382344)

(88.28328385631785, 0.706501553931617)

(72.57532058836888, 1.41542505382344)

(-71.9379414767616, 1.41542505382344)

(82.00009854913827, 0.706501553931617)

(41.15939405247096, 1.41542505382344)

(-31.097236980094287, 0.706501553931617)

(-46.805200248043256, 1.41542505382344)

(-87.64590474471056, 0.706501553931617)

(-18.530866365735115, 0.706501553931617)

(-37.38042228727387, 0.706501553931617)

(-43.66360759445346, 0.706501553931617)

(-9.106088404965735, 1.41542505382344)

(47.442579359650544, 1.41542505382344)

(-78.22112678394119, 1.41542505382344)

(-53.08838555522284, 1.41542505382344)

(-15.389273712145323, 1.41542505382344)

(-100.21227535906974, 0.706501553931617)

(16.02665282375261, 1.41542505382344)

(66.2921352811893, 1.41542505382344)

(-34.238829633684084, 1.41542505382344)

(-40.52201494086367, 1.41542505382344)

(22.309838130932196, 1.41542505382344)

(-5.964495751375943, 0.706501553931617)

(19.168245477342403, 0.706501553931617)

(-49.946792901633046, 0.706501553931617)

(44.30098670606075, 0.706501553931617)

(-56.22997820881263, 0.706501553931617)

(69.4337279347791, 0.706501553931617)

(-24.8140516729147, 0.706501553931617)

(-27.955644326504494, 1.41542505382344)

(-59.37157086240243, 1.41542505382344)

(9.743467516573023, 1.41542505382344)

(60.00894997400972, 1.41542505382344)

(25.45143078452199, 0.706501553931617)

(-97.07068270547995, 1.41542505382344)

(-62.51316351599222, 0.706501553931617)

(-75.07953413035139, 0.706501553931617)

(-12.24768105855553, 0.706501553931617)

(-65.65475616958201, 1.41542505382344)

(38.01780139888116, 0.706501553931617)

(85.14169120272805, 1.41542505382344)

(-84.50431209112078, 1.41542505382344)

(-90.78749739830036, 1.41542505382344)

(91.42487650990765, 1.41542505382344)

(75.71691324195868, 0.706501553931617)

(-68.79634882317181, 0.706501553931617)

(34.87620874529137, 1.41542505382344)

(-21.672459019324908, 1.41542505382344)

(31.734616091701575, 0.706501553931617)

(-2.8229030977861496, 1.41542505382344)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=−93.9290900518902x_{1} = -93.9290900518902
x2=12.8850601701628x_{2} = 12.8850601701628
x3=63.1505426275995x_{3} = 63.1505426275995
x4=88.2832838563179x_{4} = 88.2832838563179
x5=82.0000985491383x_{5} = 82.0000985491383
x6=−31.0972369800943x_{6} = -31.0972369800943
x7=−87.6459047447106x_{7} = -87.6459047447106
x8=−18.5308663657351x_{8} = -18.5308663657351
x9=−37.3804222872739x_{9} = -37.3804222872739
x10=−43.6636075944535x_{10} = -43.6636075944535
x11=−100.21227535907x_{11} = -100.21227535907
x12=−5.96449575137594x_{12} = -5.96449575137594
x13=19.1682454773424x_{13} = 19.1682454773424
x14=−49.946792901633x_{14} = -49.946792901633
x15=44.3009867060607x_{15} = 44.3009867060607
x16=−56.2299782088126x_{16} = -56.2299782088126
x17=69.4337279347791x_{17} = 69.4337279347791
x18=−24.8140516729147x_{18} = -24.8140516729147
x19=25.451430784522x_{19} = 25.451430784522
x20=−62.5131635159922x_{20} = -62.5131635159922
x21=−75.0795341303514x_{21} = -75.0795341303514
x22=−12.2476810585555x_{22} = -12.2476810585555
x23=38.0178013988812x_{23} = 38.0178013988812
x24=75.7169132419587x_{24} = 75.7169132419587
x25=−68.7963488231718x_{25} = -68.7963488231718
x26=31.7346160917016x_{26} = 31.7346160917016
Puntos máximos de la función:
x26=3.46028220939344x_{26} = 3.46028220939344
x26=53.7257646668301x_{26} = 53.7257646668301
x26=97.7080618170872x_{26} = 97.7080618170872
x26=72.5753205883689x_{26} = 72.5753205883689
x26=−71.9379414767616x_{26} = -71.9379414767616
x26=41.159394052471x_{26} = 41.159394052471
x26=−46.8052002480433x_{26} = -46.8052002480433
x26=−9.10608840496574x_{26} = -9.10608840496574
x26=47.4425793596505x_{26} = 47.4425793596505
x26=−78.2211267839412x_{26} = -78.2211267839412
x26=−53.0883855552228x_{26} = -53.0883855552228
x26=−15.3892737121453x_{26} = -15.3892737121453
x26=16.0266528237526x_{26} = 16.0266528237526
x26=66.2921352811893x_{26} = 66.2921352811893
x26=−34.2388296336841x_{26} = -34.2388296336841
x26=−40.5220149408637x_{26} = -40.5220149408637
x26=22.3098381309322x_{26} = 22.3098381309322
x26=−27.9556443265045x_{26} = -27.9556443265045
x26=−59.3715708624024x_{26} = -59.3715708624024
x26=9.74346751657302x_{26} = 9.74346751657302
x26=60.0089499740097x_{26} = 60.0089499740097
x26=−97.07068270548x_{26} = -97.07068270548
x26=−65.654756169582x_{26} = -65.654756169582
x26=85.1416912027281x_{26} = 85.1416912027281
x26=−84.5043120911208x_{26} = -84.5043120911208
x26=−90.7874973983004x_{26} = -90.7874973983004
x26=91.4248765099076x_{26} = 91.4248765099076
x26=34.8762087452914x_{26} = 34.8762087452914
x26=−21.6724590193249x_{26} = -21.6724590193249
x26=−2.82290309778615x_{26} = -2.82290309778615
Decrece en los intervalos
[88.2832838563179,∞)\left[88.2832838563179, \infty\right)
Crece en los intervalos
(−∞,−100.21227535907]\left(-\infty, -100.21227535907\right]
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→−∞tan⁡sin⁡(x)(x)y = \lim_{x \to -\infty} \tan^{\sin{\left(x \right)}}{\left(x \right)}
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞tan⁡sin⁡(x)(x)y = \lim_{x \to \infty} \tan^{\sin{\left(x \right)}}{\left(x \right)}
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x)^sin(x), 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→−∞(tan⁡sin⁡(x)(x)x)y = x \lim_{x \to -\infty}\left(\frac{\tan^{\sin{\left(x \right)}}{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(tan⁡sin⁡(x)(x)x)y = x \lim_{x \to \infty}\left(\frac{\tan^{\sin{\left(x \right)}}{\left(x \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:
tan⁡sin⁡(x)(x)=(−tan⁡(x))−sin⁡(x)\tan^{\sin{\left(x \right)}}{\left(x \right)} = \left(- \tan{\left(x \right)}\right)^{- \sin{\left(x \right)}}
- No
tan⁡sin⁡(x)(x)=−(−tan⁡(x))−sin⁡(x)\tan^{\sin{\left(x \right)}}{\left(x \right)} = - \left(- \tan{\left(x \right)}\right)^{- \sin{\left(x \right)}}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = tan(x)^sin(x)
    © Sr Examen – Калькулятор