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  • Gráfico de la función y =:
  • x^3-x x^3-x
  • 1/(x^2+4) 1/(x^2+4)
  • y^2 y^2
  • -cos(x)-sin(x) -cos(x)-sin(x)

  • Expresiones idénticas

  • tanh(x)^ dos *sqrt(x)*acot(tres *x)^ dos
  • tangente de gente hiperbólica de (x) al cuadrado multiplicar por raíz cuadrada de (x) multiplicar por arcoco tangente de gente de (3 multiplicar por x) al cuadrado
  • tangente de gente hiperbólica de (x) en el grado dos multiplicar por raíz cuadrada de (x) multiplicar por arcoco tangente de gente de (tres multiplicar por x) en el grado dos
  • tanh(x)^2*√(x)*acot(3*x)^2
  • tanh(x)2*sqrt(x)*acot(3*x)2
  • tanhx2*sqrtx*acot3*x2
  • tanh(x)²*sqrt(x)*acot(3*x)²
  • tanh(x) en el grado 2*sqrt(x)*acot(3*x) en el grado 2
  • tanh(x)^2sqrt(x)acot(3x)^2
  • tanh(x)2sqrt(x)acot(3x)2
  • tanhx2sqrtxacot3x2
  • tanhx^2sqrtxacot3x^2

  • Expresiones semejantes

  • tanh(x)^2*sqrt(x)*arccot(3*x)^2

  • Expresiones con funciones

  • Tangente hiperbólica tanh
  • tanh(x+3)
  • tanh^-1(x+2)
  • Raíz cuadrada sqrt
  • sqrt(y)
  • sqrt(x)*(x-1)
  • sqrt(x^2-8*x+17)-2
  • sqrt(x^2+3*x)-x
  • sqrt(25x^2)
  • Arcocotangente arccot
  • acot(1/x)
  • acot(x)/(1+x^2)
  • acot(2*x/5+1)
  • acotx/(x-3)
  • acot(1/(x-5))
Trazado el gráfico de la función/ tanh(x)^2*sqrt(x)*acot(3*x)^2

Gráfico de la función y = tanh(x)^2*sqrt(x)*acot(3*x)^2

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
           2      ___     2     
f(x) = tanh (x)*\/ x *acot (3*x)
f(x)=xtanh⁡2(x)acot⁡2(3x)f{\left(x \right)} = \sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)} 
f = (sqrt(x)*tanh(x)^2)*acot(3*x)^2
Gráfico de la función
02468-8-6-4-2-10100.000.10
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:
xtanh⁡2(x)acot⁡2(3x)=0\sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
Solución numérica
x1=0x_{1} = 0
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 (tanh(x)^2*sqrt(x))*acot(3*x)^2.
0tanh⁡2(0)acot⁡2(0⋅3)\sqrt{0} \tanh^{2}{\left(0 \right)} \operatorname{acot}^{2}{\left(0 \cdot 3 \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
−6xtanh⁡2(x)acot⁡(3x)9x2+1+(x(2−2tanh⁡2(x))tanh⁡(x)+tanh⁡2(x)2x)acot⁡2(3x)=0- \frac{6 \sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}{\left(3 x \right)}}{9 x^{2} + 1} + \left(\sqrt{x} \left(2 - 2 \tanh^{2}{\left(x \right)}\right) \tanh{\left(x \right)} + \frac{\tanh^{2}{\left(x \right)}}{2 \sqrt{x}}\right) \operatorname{acot}^{2}{\left(3 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−35313.9547446642x_{1} = -35313.9547446642
x2=−108665.095446708x_{2} = -108665.095446708
x3=97200.3230699824x_{3} = 97200.3230699824
x4=−54242.6728820705x_{4} = -54242.6728820705
x5=−44778.1854046872x_{5} = -44778.1854046872
x6=−75538.2086602841x_{6} = -75538.2086602841
x7=−63707.302711128x_{7} = -63707.302711128
x8=113763.830381841x_{8} = 113763.830381841
x9=45144.4655947252x_{9} = 45144.4655947252
x10=−115763.750986489x_{10} = -115763.750986489
x11=56975.1082427518x_{11} = 56975.1082427518
x12=75904.5031947823x_{12} = 75904.5031947823
x13=80636.8914127834x_{13} = 80636.8914127834
x14=111397.611698726x_{14} = 111397.611698726
x15=99566.5346489819x_{15} = 99566.5346489819
x16=−77904.4008662005x_{16} = -77904.4008662005
x17=94834.1129910077x_{17} = 94834.1129910077
x18=−101566.449604102x_{18} = -101566.449604102
x19=61707.4260257409x_{19} = 61707.4260257409
x20=−92101.6074405722x_{20} = -92101.6074405722
x21=101932.747623541x_{21} = 101932.747623541
x22=109031.394011951x_{22} = 109031.394011951
x23=33314.2246847333x_{23} = 33314.2246847333
x24=−49510.4062468157x_{24} = -49510.4062468157
x25=118496.270498335x_{25} = 118496.270498335
x26=−56608.8197830767x_{26} = -56608.8197830767
x27=116130.05000039x_{27} = 116130.05000039
x28=−30582.0102415896x_{28} = -30582.0102415896
x29=−32947.9631455023x_{29} = -32947.9631455023
x30=−82636.7937706248x_{30} = -82636.7937706248
x31=90101.6978058649x_{31} = 90101.6978058649
x32=35680.2215432929x_{32} = 35680.2215432929
x33=59341.2638346033x_{33} = 59341.2638346033
x34=64073.5940850034x_{34} = 64073.5940850034
x35=47510.5715898323x_{35} = 47510.5715898323
x36=83003.0895866811x_{36} = 83003.0895866811
x37=78270.6958668897x_{37} = 78270.6958668897
x38=−111031.312974353x_{38} = -111031.312974353
x39=38046.2488519593x_{39} = 38046.2488519593
x40=−68439.6525512153x_{40} = -68439.6525512153
x41=−58974.9742863202x_{41} = -58974.9742863202
x42=−89735.4009996172x_{42} = -89735.4009996172
x43=73538.3136738788x_{43} = 73538.3136738788
x44=−96834.0254828412x_{44} = -96834.0254828412
x45=42778.3746065434x_{45} = 42778.3746065434
x46=30948.265261576x_{46} = 30948.265261576
x47=−113397.53150818x_{47} = -113397.53150818
x48=−99200.2368379737x_{48} = -99200.2368379737
x49=−85002.9939963141x_{49} = -85002.9939963141
x50=−94467.8156447326x_{50} = -94467.8156447326
x51=71172.1276184902x_{51} = 71172.1276184902
x52=−73172.0196514105x_{52} = -73172.0196514105
x53=28582.3525725723x_{53} = 28582.3525725723
x54=−87369.1964651273x_{54} = -87369.1964651273
x55=106665.177387825x_{55} = 106665.177387825
x56=68805.9453861661x_{56} = 68805.9453861661
x57=−118129.971352523x_{57} = -118129.971352523
x58=−70805.8341601038x_{58} = -70805.8341601038
x59=−61341.1355120264x_{59} = -61341.1355120264
x60=−106298.878992437x_{60} = -106298.878992437
x61=104298.961898674x_{61} = 104298.961898674
x62=−28216.1057687048x_{62} = -28216.1057687048
x63=40412.3012615648x_{63} = 40412.3012615648
x64=−66073.4752418611x_{64} = -66073.4752418611
x65=49876.6904558884x_{65} = 49876.6904558884
x66=87735.4929679377x_{66} = 87735.4929679377
x67=66439.7673853935x_{67} = 66439.7673853935
x68=−80270.5959864298x_{68} = -80270.5959864298
x69=92467.9045272165x_{69} = 92467.9045272165
x70=85369.2901700512x_{70} = 85369.2901700512
x71=52242.8204439142x_{71} = 52242.8204439142
x72=−40046.0265910906x_{72} = -40046.0265910906
x73=−42412.0969465425x_{73} = -42412.0969465425
x74=−103932.663684853x_{74} = -103932.663684853
x75=−37679.9777488965x_{75} = -37679.9777488965
x76=−51876.5346235941x_{76} = -51876.5346235941
x77=−47144.2892396889x_{77} = -47144.2892396889
x78=54608.9601080797x_{78} = 54608.9601080797
Signos de extremos en los puntos:
(-35313.95474466418, 1.67431803909311e-8*I)

(-108665.09544670767, 3.10186142467102e-9*I)

(97200.32306998238, 3.66653578425491e-9)

(-54242.67288207048, 8.79520300058616e-9*I)

(-44778.18540468717, 1.17262123680939e-8*I)

(-75538.20866028406, 5.3518935683966e-9*I)

(-63707.302711127995, 6.9099302505218e-9*I)

(113763.83038184051, 2.89568409921101e-9)

(45144.46559472521, 1.15837910753813e-8)

(-115763.75098648857, 2.82097089227423e-9*I)

(56975.10824275183, 8.17014477208121e-9)

(75904.50319478233, 5.31320016439687e-9)

(80636.89141278336, 4.8524025779054e-9)

(111397.61169872602, 2.98843401288235e-9)

(99566.53464898195, 3.53661188845978e-9)

(-77904.4008662005, 5.10992472669512e-9*I)

(94834.11299100767, 3.80461408032056e-9)

(-101566.4496041019, 3.43267022945952e-9*I)

(61707.42602574095, 7.24855341608485e-9)

(-92101.60744057223, 3.97517887323945e-9*I)

(101932.74762354096, 3.414183775632e-9)

(109031.39401195123, 3.08624318132831e-9)

(33314.22468473332, 1.82731291963931e-8)

(-49510.406246815655, 1.00858558258929e-8*I)

(118496.27049833543, 2.72395838197377e-9)

(-56608.81978307667, 8.24957052714269e-9*I)

(116130.0500003902, 2.80763450431894e-9)

(-30582.010241589636, 2.07758330340204e-8*I)

(-32947.96314550232, 1.85786705354849e-8*I)

(-82636.7937706248, 4.67732236218596e-9*I)

(90101.69780586493, 4.10826101848509e-9)

(35680.22154329286, 1.64860334647916e-8)

(59341.26383460335, 7.6863879970305e-9)

(64073.59408500344, 6.85076171709716e-9)

(47510.57158983226, 1.07293177585663e-8)

(83003.0895866811, 4.64639474194329e-9)

(78270.69586688966, 5.07409621607454e-9)

(-111031.3129743532, 3.0032347282563e-9*I)

(38046.24885195933, 1.49723414991928e-8)

(-68439.65255121535, 6.20577172651711e-9*I)

(-58974.974286320234, 7.75810852099888e-9*I)

(-89735.40099961721, 4.13344134045678e-9*I)

(73538.31367387876, 5.5716905836758e-9)

(-96834.02548284116, 3.68735975340016e-9*I)

(42778.374606543366, 1.25580171462192e-8)

(30948.265261575994, 2.04081211920561e-8)

(-113397.53150818005, 2.90972596473321e-9*I)

(-99200.23683797367, 3.55621841916662e-9*I)

(-85002.99399631414, 4.48338625810876e-9*I)

(-94467.81564473256, 3.82676400663795e-9*I)

(71172.12761849022, 5.85184167248094e-9)

(-73172.0196514105, 5.61358013982987e-9*I)

(28582.352572572272, 2.299378850275e-8)

(-87369.19646512732, 4.30249107663149e-9*I)

(106665.17738782511, 3.18950656677908e-9)

(68805.94538616607, 6.1562825058839e-9)

(-118129.97135252264, 2.73663793361535e-9*I)

(-70805.83416010381, 5.89730955969872e-9*I)

(-61341.13551202637, 7.31357591703849e-9*I)

(-106298.87899243688, 3.20600698123204e-9*I)

(104298.9618986742, 3.29865967786017e-9)

(-28216.105768704794, 2.34429293424775e-8*I)

(40412.30126156482, 1.36768825595649e-8)

(-66073.47524186112, 6.54209378630908e-9*I)

(49876.69045588843, 9.97495736294332e-9)

(87735.49296793774, 4.27557480886179e-9)

(66439.76738539347, 6.48806714390046e-9)

(-80270.59598642979, 4.88565458646478e-9*I)

(92467.9045272165, 3.95158171047675e-9)

(85369.29017005119, 4.45456176468658e-9)

(52242.82044391421, 9.30502550102191e-9)

(-40046.0265910906, 1.38649511390944e-8*I)

(-42412.09694654248, 1.27210474441791e-8*I)

(-103932.66368485343, 3.31611362979895e-9*I)

(-37679.97774889652, 1.51911808512933e-8*I)

(-51876.534623594074, 9.40374956168266e-9*I)

(-47144.28923968889, 1.08546006914101e-8*I)

(54608.96010807971, 8.70686139018676e-9)


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:
La función no tiene puntos mínimos
La función no tiene puntos máximos
No cambia el valor en todo el eje numérico
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xtanh⁡2(x)acot⁡2(3x))=0\lim_{x \to -\infty}\left(\sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(xtanh⁡2(x)acot⁡2(3x))=0\lim_{x \to \infty}\left(\sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (tanh(x)^2*sqrt(x))*acot(3*x)^2, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(tanh⁡2(x)acot⁡2(3x)x)=0\lim_{x \to -\infty}\left(\frac{\tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}}{\sqrt{x}}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(tanh⁡2(x)acot⁡2(3x)x)=0\lim_{x \to \infty}\left(\frac{\tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}}{\sqrt{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:
xtanh⁡2(x)acot⁡2(3x)=−xtanh⁡2(x)acot⁡2(3x)\sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)} = \sqrt{- x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}
- No
xtanh⁡2(x)acot⁡2(3x)=−−xtanh⁡2(x)acot⁡2(3x)\sqrt{x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)} = - \sqrt{- x} \tanh^{2}{\left(x \right)} \operatorname{acot}^{2}{\left(3 x \right)}
- No
es decir, función
no es
par ni impar
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