Sr Examen

Otras calculadoras

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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
          cos(x)   
f(x) = tan      (x)
f(x)=tan⁡cos⁡(x)(x)f{\left(x \right)} = \tan^{\cos{\left(x \right)}}{\left(x \right)} 
f = tan(x)^cos(x)
Gráfico de la función
02468-8-6-4-2-1010050
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⁡cos⁡(x)(x)=0\tan^{\cos{\left(x \right)}}{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
Solución numérica
x1=87.9645943005142x_{1} = 87.9645943005142
x2=31.4159265358979x_{2} = 31.4159265358979
x3=−56.5486677646163x_{3} = -56.5486677646163
x4=69.1150383789755x_{4} = 69.1150383789755
x5=−31.4159265358979x_{5} = -31.4159265358979
x6=−87.9645943005142x_{6} = -87.9645943005142
x7=−81.6814089933346x_{7} = -81.6814089933346
x8=−43.9822971502571x_{8} = -43.9822971502571
x9=12.5663706143592x_{9} = 12.5663706143592
x10=−12.5663706143592x_{10} = -12.5663706143592
x11=−18.8495559215388x_{11} = -18.8495559215388
x12=−100.530964914873x_{12} = -100.530964914873
x13=−37.6991118430775x_{13} = -37.6991118430775
x14=50.2654824574367x_{14} = 50.2654824574367
x15=25.1327412287183x_{15} = 25.1327412287183
x16=−94.2477796076938x_{16} = -94.2477796076938
x17=56.5486677646163x_{17} = 56.5486677646163
x18=0x_{18} = 0
x19=−25.1327412287183x_{19} = -25.1327412287183
x20=−50.2654824574367x_{20} = -50.2654824574367
x21=18.8495559215388x_{21} = 18.8495559215388
x22=6.28318530717959x_{22} = 6.28318530717959
x23=37.6991118430775x_{23} = 37.6991118430775
x24=−6.28318530717959x_{24} = -6.28318530717959
x25=43.9822971502571x_{25} = 43.9822971502571
x26=−62.8318530717959x_{26} = -62.8318530717959
x27=75.398223686155x_{27} = 75.398223686155
x28=100.530964914873x_{28} = 100.530964914873
x29=81.6814089933346x_{29} = 81.6814089933346
x30=−69.1150383789755x_{30} = -69.1150383789755
x31=−75.398223686155x_{31} = -75.398223686155
x32=62.8318530717959x_{32} = 62.8318530717959
x33=94.2477796076938x_{33} = 94.2477796076938
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)^cos(x).
tan⁡cos⁡(0)(0)\tan^{\cos{\left(0 \right)}}{\left(0 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
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)cos⁡(x)tan⁡(x)−log⁡(tan⁡(x))sin⁡(x))tan⁡cos⁡(x)(x)=0\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} - \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) \tan^{\cos{\left(x \right)}}{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−99.2788581438821x_{1} = -99.2788581438821
x2=−45.8717830328556x_{2} = -45.8717830328556
x3=−86.712487529523x_{3} = -86.712487529523
x4=−77.2877095687536x_{4} = -77.2877095687536
x5=−17.5974491505475x_{5} = -17.5974491505475
x6=−96.1372654902923x_{6} = -96.1372654902923
x7=10.6768847317606x_{7} = 10.6768847317606
x8=1.25210677099125x_{8} = 1.25210677099125
x9=−74.1461169151638x_{9} = -74.1461169151638
x10=23.2432553461198x_{10} = 23.2432553461198
x11=−11.3142638433679x_{11} = -11.3142638433679
x12=32.6680333068892x_{12} = 32.6680333068892
x13=76.6503304571463x_{13} = 76.6503304571463
x14=−61.5797463008046x_{14} = -61.5797463008046
x15=−20.7390418041373x_{15} = -20.7390418041373
x16=26.3848479997096x_{16} = 26.3848479997096
x17=−36.4470050720863x_{17} = -36.4470050720863
x18=45.2344039212484x_{18} = 45.2344039212484
x19=4.39369942458105x_{19} = 4.39369942458105
x20=−23.8806344577271x_{20} = -23.8806344577271
x21=13.8184773853504x_{21} = 13.8184773853504
x22=−1.88948588259854x_{22} = -1.88948588259854
x23=−30.1638197649067x_{23} = -30.1638197649067
x24=16.9600700389402x_{24} = 16.9600700389402
x25=54.6591818820177x_{25} = 54.6591818820177
x26=−55.296560993625x_{26} = -55.296560993625
x27=95.499886378685x_{27} = 95.499886378685
x28=42.0928112676586x_{28} = 42.0928112676586
x29=−52.1549683400352x_{29} = -52.1549683400352
x30=−89.8540801831128x_{30} = -89.8540801831128
x31=−80.4293022223434x_{31} = -80.4293022223434
x32=51.5175892284279x_{32} = 51.5175892284279
x33=64.0839598427871x_{33} = 64.0839598427871
x34=89.2167010715055x_{34} = 89.2167010715055
x35=82.9335157643259x_{35} = 82.9335157643259
x36=57.8007745356075x_{36} = 57.8007745356075
x37=35.809625960479x_{37} = 35.809625960479
x38=−67.8629316079842x_{38} = -67.8629316079842
x39=60.9423671891973x_{39} = 60.9423671891973
x40=−42.7301903792658x_{40} = -42.7301903792658
x41=48.3759965748382x_{41} = 48.3759965748382
x42=86.0751084179157x_{42} = 86.0751084179157
x43=−49.0133756864454x_{43} = -49.0133756864454
x44=−33.3054124184965x_{44} = -33.3054124184965
x45=−39.5885977256761x_{45} = -39.5885977256761
x46=38.9512186140688x_{46} = 38.9512186140688
x47=−5.03107853618833x_{47} = -5.03107853618833
x48=20.10166269253x_{48} = 20.10166269253
x49=−71.004524261574x_{49} = -71.004524261574
x50=98.6414790322748x_{50} = 98.6414790322748
x51=−64.7213389543944x_{51} = -64.7213389543944
x52=7.53529207817084x_{52} = 7.53529207817084
x53=70.3671451499667x_{53} = 70.3671451499667
x54=79.7919231107361x_{54} = 79.7919231107361
x55=67.2255524963769x_{55} = 67.2255524963769
x56=92.3582937250953x_{56} = 92.3582937250953
x57=−27.0222271113169x_{57} = -27.0222271113169
x58=−83.5708948759332x_{58} = -83.5708948759332
x59=−8.17267118977813x_{59} = -8.17267118977813
Signos de extremos en los puntos:
(-99.27885814388213, 1.41542505382344)

(-45.871783032855646, 0.706501553931617)

(-86.71248752952296, 1.41542505382344)

(-77.28770956875358, 0.706501553931617)

(-17.597449150547508, 1.41542505382344)

(-96.13726549029234, 0.706501553931617)

(10.676884731760632, 0.706501553931617)

(1.252106770991253, 1.41542505382344)

(-74.14611691516379, 1.41542505382344)

(23.243255346119806, 0.706501553931617)

(-11.31426384336792, 1.41542505382344)

(32.668033306889185, 1.41542505382344)

(76.6503304571463, 1.41542505382344)

(-61.579746300804615, 1.41542505382344)

(-20.7390418041373, 0.706501553931617)

(26.3848479997096, 1.41542505382344)

(-36.44700507208626, 1.41542505382344)

(45.23440392124836, 1.41542505382344)

(4.393699424581047, 0.706501553931617)

(-23.880634457727094, 1.41542505382344)

(13.818477385350427, 1.41542505382344)

(-1.8894858825985401, 0.706501553931617)

(-30.16381976490668, 1.41542505382344)

(16.96007003894022, 0.706501553931617)

(54.65918188201774, 0.706501553931617)

(-55.29656099362502, 1.41542505382344)

(95.49988637868505, 1.41542505382344)

(42.09281126765857, 0.706501553931617)

(-52.15496834003523, 0.706501553931617)

(-89.85408018311276, 0.706501553931617)

(-80.42930222234337, 1.41542505382344)

(51.517589228427944, 1.41542505382344)

(64.08395984278712, 1.41542505382344)

(89.21670107150547, 1.41542505382344)

(82.93351576432588, 1.41542505382344)

(57.80077453560753, 1.41542505382344)

(35.80962596047898, 0.706501553931617)

(-67.8629316079842, 1.41542505382344)

(60.94236718919733, 0.706501553931617)

(-42.73019037926585, 1.41542505382344)

(48.375996574838155, 0.706501553931617)

(86.07510841791567, 0.706501553931617)

(-49.013375686445436, 1.41542505382344)

(-33.30541241849647, 0.706501553931617)

(-39.58859772567606, 0.706501553931617)

(38.95121861406877, 1.41542505382344)

(-5.031078536188334, 1.41542505382344)

(20.101662692530013, 1.41542505382344)

(-71.00452426157399, 0.706501553931617)

(98.64147903227484, 0.706501553931617)

(-64.72133895439441, 0.706501553931617)

(7.53529207817084, 1.41542505382344)

(70.3671451499667, 1.41542505382344)

(79.79192311073608, 0.706501553931617)

(67.2255524963769, 0.706501553931617)

(92.35829372509525, 0.706501553931617)

(-27.022227111316887, 0.706501553931617)

(-83.57089487593316, 0.706501553931617)

(-8.172671189778127, 0.706501553931617)


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=−45.8717830328556x_{1} = -45.8717830328556
x2=−77.2877095687536x_{2} = -77.2877095687536
x3=−96.1372654902923x_{3} = -96.1372654902923
x4=10.6768847317606x_{4} = 10.6768847317606
x5=23.2432553461198x_{5} = 23.2432553461198
x6=−20.7390418041373x_{6} = -20.7390418041373
x7=4.39369942458105x_{7} = 4.39369942458105
x8=−1.88948588259854x_{8} = -1.88948588259854
x9=16.9600700389402x_{9} = 16.9600700389402
x10=54.6591818820177x_{10} = 54.6591818820177
x11=42.0928112676586x_{11} = 42.0928112676586
x12=−52.1549683400352x_{12} = -52.1549683400352
x13=−89.8540801831128x_{13} = -89.8540801831128
x14=35.809625960479x_{14} = 35.809625960479
x15=60.9423671891973x_{15} = 60.9423671891973
x16=48.3759965748382x_{16} = 48.3759965748382
x17=86.0751084179157x_{17} = 86.0751084179157
x18=−33.3054124184965x_{18} = -33.3054124184965
x19=−39.5885977256761x_{19} = -39.5885977256761
x20=−71.004524261574x_{20} = -71.004524261574
x21=98.6414790322748x_{21} = 98.6414790322748
x22=−64.7213389543944x_{22} = -64.7213389543944
x23=79.7919231107361x_{23} = 79.7919231107361
x24=67.2255524963769x_{24} = 67.2255524963769
x25=92.3582937250953x_{25} = 92.3582937250953
x26=−27.0222271113169x_{26} = -27.0222271113169
x27=−83.5708948759332x_{27} = -83.5708948759332
x28=−8.17267118977813x_{28} = -8.17267118977813
Puntos máximos de la función:
x28=−99.2788581438821x_{28} = -99.2788581438821
x28=−86.712487529523x_{28} = -86.712487529523
x28=−17.5974491505475x_{28} = -17.5974491505475
x28=1.25210677099125x_{28} = 1.25210677099125
x28=−74.1461169151638x_{28} = -74.1461169151638
x28=−11.3142638433679x_{28} = -11.3142638433679
x28=32.6680333068892x_{28} = 32.6680333068892
x28=76.6503304571463x_{28} = 76.6503304571463
x28=−61.5797463008046x_{28} = -61.5797463008046
x28=26.3848479997096x_{28} = 26.3848479997096
x28=−36.4470050720863x_{28} = -36.4470050720863
x28=45.2344039212484x_{28} = 45.2344039212484
x28=−23.8806344577271x_{28} = -23.8806344577271
x28=13.8184773853504x_{28} = 13.8184773853504
x28=−30.1638197649067x_{28} = -30.1638197649067
x28=−55.296560993625x_{28} = -55.296560993625
x28=95.499886378685x_{28} = 95.499886378685
x28=−80.4293022223434x_{28} = -80.4293022223434
x28=51.5175892284279x_{28} = 51.5175892284279
x28=64.0839598427871x_{28} = 64.0839598427871
x28=89.2167010715055x_{28} = 89.2167010715055
x28=82.9335157643259x_{28} = 82.9335157643259
x28=57.8007745356075x_{28} = 57.8007745356075
x28=−67.8629316079842x_{28} = -67.8629316079842
x28=−42.7301903792658x_{28} = -42.7301903792658
x28=−49.0133756864454x_{28} = -49.0133756864454
x28=38.9512186140688x_{28} = 38.9512186140688
x28=−5.03107853618833x_{28} = -5.03107853618833
x28=20.10166269253x_{28} = 20.10166269253
x28=7.53529207817084x_{28} = 7.53529207817084
x28=70.3671451499667x_{28} = 70.3671451499667
Decrece en los intervalos
[98.6414790322748,∞)\left[98.6414790322748, \infty\right)
Crece en los intervalos
(−∞,−96.1372654902923]\left(-\infty, -96.1372654902923\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⁡cos⁡(x)(x)y = \lim_{x \to -\infty} \tan^{\cos{\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⁡cos⁡(x)(x)y = \lim_{x \to \infty} \tan^{\cos{\left(x \right)}}{\left(x \right)}
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x)^cos(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⁡cos⁡(x)(x)x)y = x \lim_{x \to -\infty}\left(\frac{\tan^{\cos{\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⁡cos⁡(x)(x)x)y = x \lim_{x \to \infty}\left(\frac{\tan^{\cos{\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⁡cos⁡(x)(x)=(−tan⁡(x))cos⁡(x)\tan^{\cos{\left(x \right)}}{\left(x \right)} = \left(- \tan{\left(x \right)}\right)^{\cos{\left(x \right)}}
- No
tan⁡cos⁡(x)(x)=−(−tan⁡(x))cos⁡(x)\tan^{\cos{\left(x \right)}}{\left(x \right)} = - \left(- \tan{\left(x \right)}\right)^{\cos{\left(x \right)}}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = tan(x)^cos(x)
    © Sr Examen – Калькулятор