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Trazado el gráfico de la función/ acot(e^x-2)^(3)*x

Gráfico de la función y = acot(e^x-2)^(3)*x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
           3/ x    \  
f(x) = acot \E  - 2/*x
f(x)=xacot⁡3(ex−2)f{\left(x \right)} = x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} 
f = x*acot(E^x - 2)^3
Gráfico de la función
02468-8-6-4-2-10105-5
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:
xacot⁡3(ex−2)=0x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
Solución numérica
x1=51.225746017791x_{1} = 51.225746017791
x2=71.2109903191926x_{2} = 71.2109903191926
x3=27.2774204575398x_{3} = 27.2774204575398
x4=69.212057413326x_{4} = 69.212057413326
x5=0x_{5} = 0
x6=19.3319392486224x_{6} = 19.3319392486224
x7=81.2064858323066x_{7} = 81.2064858323066
x8=99.2007659285103x_{8} = 99.2007659285103
x9=105.199312006586x_{9} = 105.199312006586
x10=103.199777082893x_{10} = 103.199777082893
x11=93.2024157018913x_{11} = 93.2024157018913
x12=65.2144013921226x_{12} = 65.2144013921226
x13=21.3134065138082x_{13} = 21.3134065138082
x14=59.2185563042126x_{14} = 59.2185563042126
x15=45.2329802228957x_{15} = 45.2329802228957
x16=53.2237284855986x_{16} = 53.2237284855986
x17=77.2081396420156x_{17} = 77.2081396420156
x18=75.2090363714161x_{18} = 75.2090363714161
x19=33.256449060482x_{19} = 33.256449060482
x20=79.207290703384x_{20} = 79.207290703384
x21=61.2170741788082x_{21} = 61.2170741788082
x22=95.2018416261232x_{22} = 95.2018416261232
x23=73.2099850466567x_{23} = 73.2099850466567
x24=83.2057216827134x_{24} = 83.2057216827134
x25=49.2279429446814x_{25} = 49.2279429446814
x26=15.3895419635228x_{26} = 15.3895419635228
x27=89.2036448268923x_{27} = 89.2036448268923
x28=87.2043037765913x_{28} = 87.2043037765913
x29=17.3563135364062x_{29} = 17.3563135364062
x30=14.8531173062288x_{30} = 14.8531173062288
x31=91.2030161486236x_{31} = 91.2030161486236
x32=101.200261320377x_{32} = 101.200261320377
x33=12.2660631361198x_{33} = 12.2660631361198
x34=43.2358867450193x_{34} = 43.2358867450193
x35=47.2303443480487x_{35} = 47.2303443480487
x36=85.204995239083x_{36} = 85.204995239083
x37=37.2467243212378x_{37} = 37.2467243212378
x38=25.287100268446x_{38} = 25.287100268446
x39=57.220150259181x_{39} = 57.220150259181
x40=39.2426980145042x_{40} = 39.2426980145042
x41=97.201292220781x_{41} = 97.201292220781
x42=41.2391079532926x_{42} = 41.2391079532926
x43=29.2693033287281x_{43} = 29.2693033287281
x44=55.2218692119898x_{44} = 55.2218692119898
x45=35.2512718048271x_{45} = 35.2512718048271
x46=23.2988463344553x_{46} = 23.2988463344553
x47=31.2623972438193x_{47} = 31.2623972438193
x48=107.198864975899x_{48} = 107.198864975899
x49=63.2156925031801x_{49} = 63.2156925031801
x50=11.4852367707726x_{50} = 11.4852367707726
x51=13.4352706873666x_{51} = 13.4352706873666
x52=67.2131922172625x_{52} = 67.2131922172625
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 acot(E^x - 2)^3*x.
0acot⁡3(−2+e0)0 \operatorname{acot}^{3}{\left(-2 + e^{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
−3xexacot⁡2(ex−2)(ex−2)2+1+acot⁡3(ex−2)=0- \frac{3 x e^{x} \operatorname{acot}^{2}{\left(e^{x} - 2 \right)}}{\left(e^{x} - 2\right)^{2} + 1} + \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=81.2066170635637x_{1} = 81.2066170635637
x2=11202.9152038375x_{2} = 11202.9152038375
x3=62.9464469449249x_{3} = 62.9464469449249
x4=21.3161799499045x_{4} = 21.3161799499045
x5=57.2204276859673x_{5} = 57.2204276859673
x6=15.9748702207887x_{6} = 15.9748702207887
x7=101.200343972977x_{7} = 101.200343972977
x8=435756.71327721x_{8} = 435756.71327721
x9=89.2037524917503x_{9} = 89.2037524917503
x10=1.3411453739227⋅1024x_{10} = 1.3411453739227 \cdot 10^{24}
x11=9.4911826462222⋅1024x_{11} = 9.4911826462222 \cdot 10^{24}
x12=39.2433367216319x_{12} = 39.2433367216319
x13=17.3611400068309x_{13} = 17.3611400068309
x14=5577343301.70551x_{14} = 5577343301.70551
x15=11.4910367368311x_{15} = 11.4910367368311
x16=1798087101800.44x_{16} = 1798087101800.44
x17=6.16926872004443⋅1025x_{17} = 6.16926872004443 \cdot 10^{25}
x18=2814141.47938232x_{18} = 2814141.47938232
x19=122716981.807067x_{19} = 122716981.807067
x20=107.198938272575x_{20} = 107.198938272575
x21=105.199388237106x_{21} = 105.199388237106
x22=87.2044166988034x_{22} = 87.2044166988034
x23=35.2520875952893x_{23} = 35.2520875952893
x24=3.71201054170155⋅1021x_{24} = 3.71201054170155 \cdot 10^{21}
x25=41.2396790452484x_{25} = 41.2396790452484
x26=95.2019355481259x_{26} = 95.2019355481259
x27=75.2091907575095x_{27} = 75.2091907575095
x28=823839054.567737x_{28} = 823839054.567737
x29=5.22510526196966⋅1020x_{29} = 5.22510526196966 \cdot 10^{20}
x30=71.211163724783x_{30} = 71.211163724783
x31=604061239657243x_{31} = 604061239657243
x32=99.2008521009502x_{32} = 99.2008521009502
x33=2.08773765801678⋅1017x_{33} = 2.08773765801678 \cdot 10^{17}
x34=2.96717930780489⋅1016x_{34} = 2.96717930780489 \cdot 10^{16}
x35=53.2240532231067x_{35} = 53.2240532231067
x36=47.230766485132x_{36} = 47.230766485132
x37=73.2101485281618x_{37} = 73.2101485281618
x38=85.2051138135339x_{38} = 85.2051138135339
x39=37.2474434418124x_{39} = 37.2474434418124
x40=67.213388389416x_{40} = 67.213388389416
x41=19.2608907157928x_{41} = 19.2608907157928
x42=2.64180225673672⋅1022x_{42} = 2.64180225673672 \cdot 10^{22}
x43=29.2705640251349x_{43} = 29.2705640251349
x44=43.2364004365405x_{44} = 43.2364004365405
x45=91.2031189150526x_{45} = 91.2031189150526
x46=13.4443140003808x_{46} = 13.4443140003808
x47=12.6168443384873x_{47} = 12.6168443384873
x48=12452388552173.1x_{48} = 12452388552173.1
x49=7.36685176936684⋅1019x_{49} = 7.36685176936684 \cdot 10^{19}
x50=55.2221688971376x_{50} = 55.2221688971376
x51=25.2888979350529x_{51} = 25.2888979350529
x52=18466691.6785173x_{52} = 18466691.6785173
x53=65.2146106683664x_{53} = 65.2146106683664
x54=49.2283282355158x_{54} = 49.2283282355158
x55=27.2789138899985x_{55} = 27.2789138899985
x56=1.87801178692372⋅1023x_{56} = 1.87801178692372 \cdot 10^{23}
x57=260807590866.014x_{57} = 260807590866.014
x58=77.2082856715642x_{58} = 77.2082856715642
x59=103.199856427053x_{59} = 103.199856427053
x60=1.47231292416477⋅1018x_{60} = 1.47231292416477 \cdot 10^{18}
x61=31.2634758553134x_{61} = 31.2634758553134
x62=4.22771667798254⋅1015x_{62} = 4.22771667798254 \cdot 10^{15}
x63=86578155840378.2x_{63} = 86578155840378.2
x64=61.2173139366234x_{64} = 61.2173139366234
x65=15.3962525794656x_{65} = 15.3962525794656
x66=33.2573824925357x_{66} = 33.2573824925357
x67=63.2159162429921x_{67} = 63.2159162429921
x68=83.2058463448682x_{68} = 83.2058463448682
x69=59.2188138657047x_{69} = 59.2188138657047
x70=69.2122416755635x_{70} = 69.2122416755635
x71=23.3010526040499x_{71} = 23.3010526040499
x72=93.2025138968605x_{72} = 93.2025138968605
x73=51.2260990903392x_{73} = 51.2260990903392
x74=19.3355318037991x_{74} = 19.3355318037991
x75=38025247357.1215x_{75} = 38025247357.1215
x76=79.2074290372987x_{76} = 79.2074290372987
x77=1892.33413331107x_{77} = 1892.33413331107
x78=335.860928704143x_{78} = 335.860928704143
x79=97.2013821428693x_{79} = 97.2013821428693
x80=68897.4625531287x_{80} = 68897.4625531287
x81=1.04046593101803⋅1019x_{81} = 1.04046593101803 \cdot 10^{19}
x82=45.2334447667465x_{82} = 45.2334447667465
Signos de extremos en los puntos:
(81.2066170635637, 1.27889345462002e-104)

(11202.915203837545, 9.04832682085008e-14593)

(62.9464469449249, 6.12473820909545e-81)

(21.316179949904463, 3.59924489060771e-27)

(57.22042768596732, 1.60695276440122e-73)

(15.974870220788716, 2.45495582266907e-20)

(101.200343972977, 1.42209669175625e-130)

(435756.7132772101, 2.69872304226625e-567735)

(89.2037524917503, 5.34922304997794e-115)

(1.3411453739227018e+24, 6.14165875224495e-1747356105974108123557918)

(9.491182646222198e+24, 3.82505952155843e-12365904749970612734908931)

(39.24333672163195, 2.91254173839687e-50)

(17.361140006830873, 4.16904325465347e-22)

(5577343301.705511, 8.20590944724203e-7266628250)

(11.491036736831134, 1.22716881159532e-14)

(1798087101800.4448, 1.67253912009196e-2342697918868)

(6.169268720044429e+25, 5.3063980011521e-80378380874808982776908185)

(2814141.479382323, 1.2646592870528e-3666492)

(122716981.80706692, 9.66077447697893e-159885917)

(107.19893827257506, 2.30392539085296e-138)

(105.19938823710596, 9.10902263734796e-136)

(87.2044166988034, 2.10546279646155e-112)

(35.2520875952893, 4.14785423588043e-45)

(3.712010541701547e+21, 3.29757987800178e-4836317085083047423593)

(41.23967904524842, 7.67043761720469e-53)

(95.20193554812587, 8.74218419961682e-123)

(75.2091907575095, 7.71722766586551e-97)

(823839054.5677369, 6.17109310378871e-1073366258)

(5.225105261969665e+20, 7.60160218769333e-680770314791121160036)

(71.21116372478305, 1.1822292937602e-91)

(604061239657243, 4.21844592677326e-787021389344321)

(99.20085210095021, 5.61522806447129e-128)

(2.0877376580167843e+17, 1.19880942744089e-272007883361492290)

(2.967179307804888e+16, 9.84801384947669e-38658888005915181)

(53.22405322310665, 2.4064125660709e-68)

(47.230766485132044, 1.3741723694926e-60)

(73.21014852816181, 3.02190434178697e-94)

(85.20511381353388, 8.2819648590489e-110)

(37.24744344181235, 1.10158753754464e-47)

(67.21338838941597, 1.80403403687617e-86)

(19.260890715792833, 1.5487478451344e-24)

(2.6418022567367213e+22, 1.35936404745447e-34419604271409474809317)

(29.270564025134945, 2.13942849643934e-37)

(43.23640043654049, 2.01307126458314e-55)

(91.20311891505256, 1.35823794398429e-117)

(13.444314000380833, 4.09419264810298e-17)

(12.61684433848732, 4.59919431882857e-16)

(12452388552173.055, 1.42060869768117e-16224010904159)

(7.366851769366837e+19, 1.15496478381979e-95981492173056732822)

(55.222168897137564, 6.22391664503449e-71)

(25.2888979350529, 2.84736684547902e-32)

(18466691.67851731, 2.4067046377274e-24059940)

(65.2146106683664, 7.03571514176132e-84)

(49.22832823551577, 3.57635951232471e-63)

(27.278913889998492, 7.84479773799957e-35)

(1.8780117869237227e+23, 3.09365333876181e-244683046803071494842357)

(260807590866.01425, 4.40069154378558e-339801892644)

(77.20828567156421, 1.96909485036193e-99)

(103.19985642705348, 3.59993413291946e-133)

(1.4723129241647734e+18, 7.10817294446069e-1918252135798805837)

(31.263475855313434, 5.78591585983824e-40)

(4227716677982540.5, 3.28883637222096e-5508222072894478)

(86578155840378.19, 6.50974195774999e-112801246004495)

(61.217313936623434, 1.06622620242944e-78)

(15.396252579465552, 1.3424340269228e-19)

(33.257382492535655, 1.55379946691675e-42)

(63.21591624299207, 2.74066313797393e-81)

(83.20584634486819, 3.25562259138391e-107)

(59.218813865704675, 4.1423562299988e-76)

(69.21224167556348, 4.62060662036689e-89)

(23.301052604049925, 1.02051603989212e-29)

(93.20251389686047, 3.44679275755927e-120)

(51.22609909033916, 9.28655835627647e-66)

(19.33553180379907, 1.24283029406746e-24)

(38025247357.12148, 9.28669938617438e-49542465291)

(79.2074290372987, 5.02016332931213e-102)

(1892.3341333110686, 6.1119779755313e-2463)

(335.8609287041425, 8.67991385941079e-436)

(97.20138214286932, 2.21615813431594e-125)

(68897.46255312875, 2.98394867060924e-89761)

(1.040465931018027e+19, 3.11855043364218e-13556058373483757828)

(45.2334447667465, 5.26687830530526e-58)


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
Decrece en todo el eje numérico
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
3(x(−acot⁡(ex−2)+2(ex−2)exacot⁡(ex−2)(ex−2)2+1+2ex(ex−2)2+1)−2acot⁡(ex−2))exacot⁡(ex−2)(ex−2)2+1=0\frac{3 \left(x \left(- \operatorname{acot}{\left(e^{x} - 2 \right)} + \frac{2 \left(e^{x} - 2\right) e^{x} \operatorname{acot}{\left(e^{x} - 2 \right)}}{\left(e^{x} - 2\right)^{2} + 1} + \frac{2 e^{x}}{\left(e^{x} - 2\right)^{2} + 1}\right) - 2 \operatorname{acot}{\left(e^{x} - 2 \right)}\right) e^{x} \operatorname{acot}{\left(e^{x} - 2 \right)}}{\left(e^{x} - 2\right)^{2} + 1} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=71.2113388720181x_{1} = 71.2113388720181
x2=−121.06914228288x_{2} = -121.06914228288
x3=43.2369230750385x_{3} = 43.2369230750385
x4=−103.109329237227x_{4} = -103.109329237227
x5=−34.0912794933585x_{5} = -34.0912794933585
x6=57.2207086464134x_{6} = 57.2207086464134
x7=47.2311952754312x_{7} = 47.2311952754312
x8=59.2190745867129x_{8} = 59.2190745867129
x9=−45.5740005054363x_{9} = -45.5740005054363
x10=−87.1619388762717x_{10} = -87.1619388762717
x11=−95.1329980618501x_{11} = -95.1329980618501
x12=−55.3950840173981x_{12} = -55.3950840173981
x13=107.199012046333x_{13} = 107.199012046333
x14=−57.369883839131x_{14} = -57.369883839131
x15=−115.080930865701x_{15} = -115.080930865701
x16=55.2224725516522x_{16} = 55.2224725516522
x17=−81.1882678183563x_{17} = -81.1882678183563
x18=75.2093466059269x_{18} = 75.2093466059269
x19=13.4536839666432x_{19} = 13.4536839666432
x20=−105.10407015753x_{20} = -105.10407015753
x21=29.2718595375184x_{21} = 29.2718595375184
x22=−75.2198969347223x_{22} = -75.2198969347223
x23=81.2067494400359x_{23} = 81.2067494400359
x24=33.2583379969627x_{24} = 33.2583379969627
x25=−28.9353867047966x_{25} = -28.9353867047966
x26=77.2084330460014x_{26} = 77.2084330460014
x27=−67.2735421114241x_{27} = -67.2735421114241
x28=−113.085180982879x_{28} = -113.085180982879
x29=35.2529213858742x_{29} = 35.2529213858742
x30=−93.1396752246407x_{30} = -93.1396752246407
x31=−107.099039845199x_{31} = -107.099039845199
x32=17.3662305513467x_{32} = 17.3662305513467
x33=−49.4891864944484x_{33} = -49.4891864944484
x34=−69.2586229734047x_{34} = -69.2586229734047
x35=−43.6261544550314x_{35} = -43.6261544550314
x36=−53.4230249783973x_{36} = -53.4230249783973
x37=61.2175565308653x_{37} = 61.2175565308653
x38=19.3392956889366x_{38} = 19.3392956889366
x39=−71.2447823410302x_{39} = -71.2447823410302
x40=49.2287193234193x_{40} = 49.2287193234193
x41=53.2243824404727x_{41} = 53.2243824404727
x42=63.2161425387687x_{42} = 63.2161425387687
x43=−65.2896724119287x_{43} = -65.2896724119287
x44=−79.1981473783759x_{44} = -79.1981473783759
x45=−117.076847342498x_{45} = -117.076847342498
x46=91.2032224743629x_{46} = 91.2032224743629
x47=23.3033404871282x_{47} = 23.3033404871282
x48=−111.089608132217x_{48} = -111.089608132217
x49=−47.5287883412207x_{49} = -47.5287883412207
x50=21.3190690959477x_{50} = 21.3190690959477
x51=−61.3262172000187x_{51} = -61.3262172000187
x52=67.2135866585187x_{52} = 67.2135866585187
x53=−119.072920781941x_{53} = -119.072920781941
x54=83.2059720671165x_{54} = 83.2059720671165
x55=−39.7592415415509x_{55} = -39.7592415415509
x56=51.226457244805x_{56} = 51.226457244805
x57=−1.36879108843811x_{57} = -1.36879108843811
x58=105.199464973693x_{58} = 105.199464973693
x59=95.2020301626753x_{59} = 95.2020301626753
x60=−63.3071694941258x_{60} = -63.3071694941258
x61=−97.1266472537626x_{61} = -97.1266472537626
x62=−89.1541152286569x_{62} = -89.1541152286569
x63=101.200427197063x_{63} = 101.200427197063
x64=65.2148222559304x_{64} = 65.2148222559304
x65=−37.8463758148287x_{65} = -37.8463758148287
x66=89.2038610069901x_{66} = 89.2038610069901
x67=−109.094223645316x_{67} = -109.094223645316
x68=−59.3470343910748x_{68} = -59.3470343910748
x69=37.2481774358624x_{69} = 37.2481774358624
x70=31.2645819452763x_{70} = 31.2645819452763
x71=15.4033604368634x_{71} = 15.4033604368634
x72=−32.2738873612552x_{72} = -32.2738873612552
x73=87.2045305345977x_{73} = 87.2045305345977
x74=−41.6870582936533x_{74} = -41.6870582936533
x75=−73.2319064024203x_{75} = -73.2319064024203
x76=−83.1789726997072x_{76} = -83.1789726997072
x77=−35.9540458413012x_{77} = -35.9540458413012
x78=−85.1702113647074x_{78} = -85.1702113647074
x79=103.199936308665x_{79} = 103.199936308665
x80=97.2014727136456x_{80} = 97.2014727136456
x81=69.2124278461082x_{81} = 69.2124278461082
x82=99.2009388818469x_{82} = 99.2009388818469
x83=11.4943014725406x_{83} = 11.4943014725406
x84=27.2804523595265x_{84} = 27.2804523595265
x85=−30.5325780745648x_{85} = -30.5325780745648
x86=−77.2086687051389x_{86} = -77.2086687051389
x87=79.2075686109183x_{87} = 79.2075686109183
x88=−99.1205993527235x_{88} = -99.1205993527235
x89=−91.146704685936x_{89} = -91.146704685936
x90=93.2026128322817x_{90} = 93.2026128322817
x91=85.2052333711915x_{91} = 85.2052333711915
x92=73.2103136035163x_{92} = 73.2103136035163
x93=45.2339169975625x_{93} = 45.2339169975625
x94=25.2907553231121x_{94} = 25.2907553231121
x95=39.2439878613196x_{95} = 39.2439878613196
x96=41.240260636074x_{96} = 41.240260636074
x97=−51.4541901054401x_{97} = -51.4541901054401
x98=−101.114833112977x_{98} = -101.114833112977

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
(−∞,−1.36879108843811]\left(-\infty, -1.36879108843811\right]
Convexa en los intervalos
[−1.36879108843811,∞)\left[-1.36879108843811, \infty\right)
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xacot⁡3(ex−2))=∞\lim_{x \to -\infty}\left(x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)}\right) = \infty
Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda
lim⁡x→∞(xacot⁡3(ex−2))=−∞\lim_{x \to \infty}\left(x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)}\right) = -\infty
Tomamos como el límite
es decir,
no hay asíntota horizontal a la derecha
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función acot(E^x - 2)^3*x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞acot⁡3(ex−2)=−acot⁡3(2)\lim_{x \to -\infty} \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = - \operatorname{acot}^{3}{\left(2 \right)}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=−xacot⁡3(2)y = - x \operatorname{acot}^{3}{\left(2 \right)}
lim⁡x→∞acot⁡3(ex−2)=−π3\lim_{x \to \infty} \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = - \pi^{3}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=−π3xy = - \pi^{3} x
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:
xacot⁡3(ex−2)=xacot⁡3(2−e−x)x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = x \operatorname{acot}^{3}{\left(2 - e^{- x} \right)}
- No
xacot⁡3(ex−2)=−xacot⁡3(2−e−x)x \operatorname{acot}^{3}{\left(e^{x} - 2 \right)} = - x \operatorname{acot}^{3}{\left(2 - e^{- x} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор