Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ tan(x)/(-1+e^(2*x))

Gráfico de la función y = tan(x)/(-1+e^(2*x))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
         tan(x) 
f(x) = ---------
             2*x
       -1 + E
f(x)=tan⁡(x)e2x−1f{\left(x \right)} = \frac{\tan{\left(x \right)}}{e^{2 x} - 1} 
f = tan(x)/(E^(2*x) - 1)
Gráfico de la función
02468-8-6-4-2-1010-100100
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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⁡(x)e2x−1=0\frac{\tan{\left(x \right)}}{e^{2 x} - 1} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−18.8495559215388x_{1} = -18.8495559215388
x2=−53.4070751110265x_{2} = -53.4070751110265
x3=−37.6991118430775x_{3} = -37.6991118430775
x4=−59.6902604182061x_{4} = -59.6902604182061
x5=−15.707963267949x_{5} = -15.707963267949
x6=−56.5486677646163x_{6} = -56.5486677646163
x7=12.5663706143592x_{7} = 12.5663706143592
x8=3.14159265358979x_{8} = 3.14159265358979
x9=−31.4159265358979x_{9} = -31.4159265358979
x10=84.8230016469244x_{10} = 84.8230016469244
x11=−81.6814089933346x_{11} = -81.6814089933346
x12=82.3021803875655x_{12} = 82.3021803875655
x13=94.2477796076938x_{13} = 94.2477796076938
x14=21.9911485751286x_{14} = 21.9911485751286
x15=20.318502058709x_{15} = 20.318502058709
x16=16.1830740058675x_{16} = 16.1830740058675
x17=−87.9645943005142x_{17} = -87.9645943005142
x18=60.2286259262238x_{18} = 60.2286259262238
x19=43.9822971502571x_{19} = 43.9822971502571
x20=81.6814089933346x_{20} = 81.6814089933346
x21=−78.5398163397448x_{21} = -78.5398163397448
x22=62.8318530717959x_{22} = 62.8318530717959
x23=100.530964914873x_{23} = 100.530964914873
x24=−21.9911485751286x_{24} = -21.9911485751286
x25=47.1238898038469x_{25} = 47.1238898038469
x26=91.106186954104x_{26} = 91.106186954104
x27=−75.398223686155x_{27} = -75.398223686155
x28=40.8407044966673x_{28} = 40.8407044966673
x29=32.25x_{29} = 32.25
x30=75.398223686155x_{30} = 75.398223686155
x31=28.2743338823081x_{31} = 28.2743338823081
x32=34.5575191894877x_{32} = 34.5575191894877
x33=6.28318530717959x_{33} = 6.28318530717959
x34=78.5398163397448x_{34} = 78.5398163397448
x35=72.2566310325652x_{35} = 72.2566310325652
x36=−6.28318530717959x_{36} = -6.28318530717959
x37=15.707963267949x_{37} = 15.707963267949
x38=26.0791295424636x_{38} = 26.0791295424636
x39=31.4159265358979x_{39} = 31.4159265358979
x40=54.25x_{40} = 54.25
x41=−47.1238898038469x_{41} = -47.1238898038469
x42=25.1327412287183x_{42} = 25.1327412287183
x43=18.8495559215388x_{43} = 18.8495559215388
x44=−94.2477796076938x_{44} = -94.2477796076938
x45=−3.14159265358979x_{45} = -3.14159265358979
x46=−40.8407044966673x_{46} = -40.8407044966673
x47=56.5486677646163x_{47} = 56.5486677646163
x48=−25.1327412287183x_{48} = -25.1327412287183
x49=53.4070751110265x_{49} = 53.4070751110265
x50=−28.2743338823081x_{50} = -28.2743338823081
x51=−9.42477796076938x_{51} = -9.42477796076938
x52=87.9645943005142x_{52} = 87.9645943005142
x53=−50.2654824574367x_{53} = -50.2654824574367
x54=−100.530964914873x_{54} = -100.530964914873
x55=−43.9822971502571x_{55} = -43.9822971502571
x56=50.2654824574367x_{56} = 50.2654824574367
x57=−97.3893722612836x_{57} = -97.3893722612836
x58=69.1150383789755x_{58} = 69.1150383789755
x59=59.6902604182061x_{59} = 59.6902604182061
x60=97.3893722612836x_{60} = 97.3893722612836
x61=−62.8318530717959x_{61} = -62.8318530717959
x62=−72.2566310325652x_{62} = -72.2566310325652
x63=−91.106186954104x_{63} = -91.106186954104
x64=−12.5663706143592x_{64} = -12.5663706143592
x65=−69.1150383789755x_{65} = -69.1150383789755
x66=98.25x_{66} = 98.25
x67=37.6991118430775x_{67} = 37.6991118430775
x68=9.42477796076938x_{68} = 9.42477796076938
x69=38.2648301745772x_{69} = 38.2648301745772
x70=65.9734457253857x_{70} = 65.9734457253857
x71=−65.9734457253857x_{71} = -65.9734457253857
x72=−84.8230016469244x_{72} = -84.8230016469244
x73=−34.5575191894877x_{73} = -34.5575191894877
x74=48.1947877693911x_{74} = 48.1947877693911
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)/(-1 + E^(2*x)).
tan⁡(0)−1+e0⋅2\frac{\tan{\left(0 \right)}}{-1 + e^{0 \cdot 2}}
Resultado:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- no hay soluciones de la ecuación
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)+1e2x−1−2e2xtan⁡(x)(e2x−1)2=0\frac{\tan^{2}{\left(x \right)} + 1}{e^{2 x} - 1} - \frac{2 e^{2 x} \tan{\left(x \right)}}{\left(e^{2 x} - 1\right)^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=7.06943096389999x_{1} = 7.06943096389999
x2=29.0552751468191x_{2} = 29.0552751468191
x3=82.4667771569824x_{3} = 82.4667771569824
x4=66.7588434775171x_{4} = 66.7588434775171
x5=25.9179268232698x_{5} = 25.9179268232698
x6=3650219.43631002x_{6} = 3650219.43631002
x7=13.3517665954103x_{7} = 13.3517665954103
x8=22.7765463052278x_{8} = 22.7765463052278
x9=21.908394444317x_{9} = 21.908394444317
x10=303.648946954791x_{10} = 303.648946954791
x11=98.1747705021718x_{11} = 98.1747705021718
x12=14413.475701446x_{12} = 14413.475701446
x13=1903.60146135975x_{13} = 1903.60146135975
x14=60.475655841018x_{14} = 60.475655841018
x15=98.174741869371x_{15} = 98.174741869371
x16=504.902241247893x_{16} = 504.902241247893
x17=1.03841563726656x_{17} = 1.03841563726656
x18=25.918129436993x_{18} = 25.918129436993
x19=32.2013247418039x_{19} = 32.2013247418039
x20=50.3680730377739x_{20} = 50.3680730377739
x21=39.0902727499673x_{21} = 39.0902727499673
x22=7.06798102285062x_{22} = 7.06798102285062
x23=54195.9007622273x_{23} = 54195.9007622273
x24=91.8915760192588x_{24} = 91.8915760192588
x25=88.7499920633502x_{25} = 88.7499920633502
x26=10.2101354071304x_{26} = 10.2101354071304
x27=3.94073313569291x_{27} = 3.94073313569291
x28=47.9092783089831x_{28} = 47.9092783089831
x29=13.3517699020769x_{29} = 13.3517699020769
x30=31.4142468707456x_{30} = 31.4142468707456
x31=60.4756584331219x_{31} = 60.4756584331219
x32=44.7676948914779x_{32} = 44.7676948914779
x33=7.06798104991329x_{33} = 7.06798104991329
x34=69.9004366341518x_{34} = 69.9004366341518
x35=73.006938040758x_{35} = 73.006938040758
x36=103.308122851043x_{36} = 103.308122851043
x37=47.9092880515278x_{37} = 47.9092880515278
x38=61.7702424093541x_{38} = 61.7702424093541
x39=116.45721053301x_{39} = 116.45721053301
x40=25.9172713828843x_{40} = 25.9172713828843
x41=35.342915423867x_{41} = 35.342915423867
x42=63.6172518113096x_{42} = 63.6172518113096
x43=1192.06973386492x_{43} = 1192.06973386492
x44=57.3340640422361x_{44} = 57.3340640422361
x45=82.466807014469x_{45} = 82.466807014469
x46=63.6172472513623x_{46} = 63.6172472513623
x47=91.8915852168499x_{47} = 91.8915852168499
x48=1093.45039666415x_{48} = 1093.45039666415
x49=29.0597311101121x_{49} = 29.0597311101121
x50=54.1924419909645x_{50} = 54.1924419909645
x51=2174.21619762905x_{51} = 2174.21619762905
x52=73.0420283023126x_{52} = 73.0420283023126
x53=1276.23125428615x_{53} = 1276.23125428615
x54=3.91286004365428x_{54} = 3.91286004365428
x55=69.9004271695477x_{55} = 69.9004271695477
x56=101.316361275969x_{56} = 101.316361275969
x57=41.6260985772562x_{57} = 41.6260985772562
x58=215.963337872594x_{58} = 215.963337872594
x59=178.626504570686x_{59} = 178.626504570686
x60=68.6812469957114x_{60} = 68.6812469957114
x61=16.4931135506018x_{61} = 16.4931135506018
x62=51.0508797064333x_{62} = 51.0508797064333
x63=353.555550942936x_{63} = 353.555550942936
x64=85.9041250054655x_{64} = 85.9041250054655
x65=130.553050526301x_{65} = 130.553050526301
x66=19.6349545976546x_{66} = 19.6349545976546
x67=10.2102021407676x_{67} = 10.2102021407676
x68=76.1835919739591x_{68} = 76.1835919739591
x69=25.9181394689439x_{69} = 25.9181394689439
x70=375.949617452605x_{70} = 375.949617452605
x71=104.948291699965x_{71} = 104.948291699965
x72=111.988968300685x_{72} = 111.988968300685
x73=415.723398319174x_{73} = 415.723398319174
x74=54.1924733270196x_{74} = 54.1924733270196
x75=101.568116241867x_{75} = 101.568116241867
x76=38.4844973672652x_{76} = 38.4844973672652
x77=16.4933563010577x_{77} = 16.4933563010577
x78=85.6084004219006x_{78} = 85.6084004219006
x79=1705.32420908187x_{79} = 1705.32420908187
x80=119.839356170111x_{80} = 119.839356170111
x81=32.2012919127297x_{81} = 32.2012919127297
x82=1910.23456138949x_{82} = 1910.23456138949
x83=79.325212659594x_{83} = 79.325212659594
x84=95.0331768977606x_{84} = 95.0331768977606
x85=41.6261032033073x_{85} = 41.6261032033073
x86=19.6349499002663x_{86} = 19.6349499002663
x87=16.4933612653207x_{87} = 16.4933612653207
x88=38.4845098516913x_{88} = 38.4845098516913
x89=135.56426144606x_{89} = 135.56426144606
x90=85.6083959226871x_{90} = 85.6083959226871
x91=197.682638343258x_{91} = 197.682638343258
x92=76.1836219136185x_{92} = 76.1836219136185
Signos de extremos en los puntos:
(7.069430963899989, 7.24947776846024e-7)

(29.055275146819106, 5.74165908857836e-26)

(82.46677715698245, 2.34553232900158e-72)

(66.75884347751709, 1.03277320490739e-58)

(25.917926823269752, 3.0746108937031e-23)

(3650219.436310024, -1.02265341922139e-3170541)

(13.351766595410286, 2.52813925652416e-12)

(22.776546305227832, 1.64642847758464e-20)

(21.90839444431696, -7.75162982196271e-21)

(303.64894695479086, -3.40259362340927e-264)

(98.17477050217181, 5.32694097818438e-86)

(14413.475701445954, -6.2736158879614e-12521)

(1903.6014613597451, -7.37575963085113e-1655)

(60.47565584101803, 2.96149072679543e-53)

(98.17474186937098, 5.32694097818421e-86)

(504.90224124789313, -3.48917640026392e-439)

(1.0384156372665563, 0.243217265781763)

(25.918129436992963, 3.07461089374247e-23)

(32.20132474180388, 1.07222207986097e-28)

(50.368073037773875, 1.83435123034787e-45)

(39.09027274996735, 6.13086324789531e-34)

(7.067981022850621, 7.24947777569955e-7)

(54195.900762227284, 3.21354698691675e-47075)

(91.89157601925884, 1.52750732049582e-80)

(88.74999206335016, 8.17967423878503e-78)

(10.210135407130412, 1.35379747770265e-9)

(3.940733135692915, 0.000388351219548046)

(47.90927830898309, 2.43512471105294e-42)

(13.351769902076903, 2.52813925652416e-12)

(31.414246870745593, -8.69270581765751e-31)

(60.475658433121914, 2.96149072679543e-53)

(44.76769489147791, 1.303988962931e-39)

(7.067981049913294, 7.24947777569955e-7)

(69.9004366341518, 1.92864481500706e-61)

(73.00693804075802, 3.60142598563987e-64)

(103.30812285104271, -7.06594072409094e-91)

(47.90928805152782, 2.43512471105294e-42)

(61.77024240935412, -3.9828068371911e-54)

(116.45721053301014, 1.55792361781381e-102)

(25.917271382884298, 3.07461089106145e-23)

(35.34291542386698, 2.0023133298132e-31)

(63.61725181130964, 5.53041433277473e-56)

(1192.0697338649243, 2.29508166142089e-1035)

(57.33406404223607, 1.58585357211292e-50)

(82.46680701446898, 2.34553232900166e-72)

(63.61724725136229, 5.53041433277473e-56)

(91.8915852168499, 1.52750732049582e-80)

(1093.450396664145, 3.10076189112941e-951)

(29.059731110112104, 5.74165976634959e-26)

(54.19244199096452, 8.49211354750576e-48)

(2174.2161976290536, 7.53716242697009e-1890)

(73.04202830231262, 3.60163374183124e-64)

(1276.2312542861546, 2.78082220127653e-1109)

(3.912860043654276, 0.000388356826050093)

(69.9004271695477, 1.92864481500706e-61)

(101.3163612759689, 9.94775721194786e-89)

(41.626098577256194, 6.98275208545944e-37)

(215.96333787259363, -2.72276659498928e-188)

(178.62650457068557, -3.34665320918683e-156)

(68.68124699571136, -1.02332162001827e-60)

(16.49311355060181, 4.7211552792339e-15)

(51.05087970643329, 4.54745594245833e-45)

(353.55555094293646, -6.33228077428679e-307)

(85.90412500546552, 4.54908258335329e-75)

(130.55305052630084, -2.24197532672518e-113)

(19.634954597654616, 8.81648711164915e-18)

(10.21020214076764, 1.35379747770255e-9)

(76.18359197395908, 6.72584475345676e-67)

(25.91813946894386, 3.07461089374248e-23)

(375.94961745260514, -4.86605609924963e-327)

(104.94829169996466, 2.29241132778391e-91)

(111.98896830068516, -1.0714508524121e-97)

(415.7233983191736, 1.35470509547705e-361)

(54.192473327019606, 8.49211354750611e-48)

(101.56811624186737, 1.01764698135817e-88)

(38.48449736726518, 3.73920547436167e-34)

(16.493356301057688, 4.72115527932978e-15)

(85.60840042190057, 4.38014729978027e-75)

(1705.3242090818685, -3.7327202566071e-1482)

(119.83935617011134, 4.00482841367776e-105)

(32.20129191272966, 1.07222207986092e-28)

(1910.2345613894888, 9.10926310678595e-1661)

(79.32521265959404, 1.25601298994396e-69)

(95.03317689776057, 2.85253244329066e-83)

(41.626103203307274, 6.98275208545944e-37)

(19.634949900266303, 8.81648711164915e-18)

(16.493361265320694, 4.72115527932978e-15)

(38.48450985169134, 3.73920547436168e-34)

(135.56426144606013, 9.17067291307826e-119)

(85.60839592268708, 4.38014729978027e-75)

(197.68263834325762, -4.77923012662488e-173)

(76.18362191361852, 6.725844753457e-67)


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=1.03841563726656x_{1} = 1.03841563726656
x2=3.94073313569291x_{2} = 3.94073313569291
x3=44.7676948914779x_{3} = 44.7676948914779
x4=69.9004366341518x_{4} = 69.9004366341518
x5=51.0508797064333x_{5} = 51.0508797064333
x6=10.2102021407676x_{6} = 10.2102021407676
x7=54.1924733270196x_{7} = 54.1924733270196
x8=85.6083959226871x_{8} = 85.6083959226871
Puntos máximos de la función:
x8=7.06798102285062x_{8} = 7.06798102285062
x8=7.06798104991329x_{8} = 7.06798104991329
x8=3.91286004365428x_{8} = 3.91286004365428
Decrece en los intervalos
[85.6083959226871,∞)\left[85.6083959226871, \infty\right)
Crece en los intervalos
(−∞,1.03841563726656]\left(-\infty, 1.03841563726656\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
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⁡(x)e2x−1)y = \lim_{x \to -\infty}\left(\frac{\tan{\left(x \right)}}{e^{2 x} - 1}\right)
lim⁡x→∞(tan⁡(x)e2x−1)=0\lim_{x \to \infty}\left(\frac{\tan{\left(x \right)}}{e^{2 x} - 1}\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 tan(x)/(-1 + E^(2*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⁡(x)x(e2x−1))y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(x \right)}}{x \left(e^{2 x} - 1\right)}\right)
lim⁡x→∞(tan⁡(x)x(e2x−1))=0\lim_{x \to \infty}\left(\frac{\tan{\left(x \right)}}{x \left(e^{2 x} - 1\right)}\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:
tan⁡(x)e2x−1=−tan⁡(x)−1+e−2x\frac{\tan{\left(x \right)}}{e^{2 x} - 1} = - \frac{\tan{\left(x \right)}}{-1 + e^{- 2 x}}
- No
tan⁡(x)e2x−1=tan⁡(x)−1+e−2x\frac{\tan{\left(x \right)}}{e^{2 x} - 1} = \frac{\tan{\left(x \right)}}{-1 + e^{- 2 x}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор