Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ x(ln(2x-1)-ln(2x+1))

Gráfico de la función y = x(ln(2x-1)-ln(2x+1))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*(log(2*x - 1) - log(2*x + 1))
f(x)=x(log⁡(2x−1)−log⁡(2x+1))f{\left(x \right)} = x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right) 
f = x*(log(2*x - 1) - log(2*x + 1))
Gráfico de la función
02468-8-6-4-2-1010-2.0-0.5
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:
x(log⁡(2x−1)−log⁡(2x+1))=0x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−3.22609812321022⋅1026x_{1} = -3.22609812321022 \cdot 10^{26}
x2=−6.47402782793718⋅1025x_{2} = -6.47402782793718 \cdot 10^{25}
x3=7.50094552608037⋅1025x_{3} = 7.50094552608037 \cdot 10^{25}
x4=−2.40823234120046⋅1026x_{4} = -2.40823234120046 \cdot 10^{26}
x5=5.02102112419634⋅1025x_{5} = 5.02102112419634 \cdot 10^{25}
x6=−1.05366520306426⋅1026x_{6} = -1.05366520306426 \cdot 10^{26}
x7=−2.40080856410126⋅1026x_{7} = -2.40080856410126 \cdot 10^{26}
x8=2.76727486741566⋅1025x_{8} = 2.76727486741566 \cdot 10^{25}
x9=1.96009803304089⋅1026x_{9} = 1.96009803304089 \cdot 10^{26}
x10=1.0686920447928⋅1026x_{10} = 1.0686920447928 \cdot 10^{26}
x11=−8.59182912193446⋅1025x_{11} = -8.59182912193446 \cdot 10^{25}
x12=−2.2080134785649⋅1026x_{12} = -2.2080134785649 \cdot 10^{26}
x13=−2.94938798820719⋅1025x_{13} = -2.94938798820719 \cdot 10^{25}
x14=1.45858998581264⋅1026x_{14} = 1.45858998581264 \cdot 10^{26}
x15=3.64687156486423⋅1026x_{15} = 3.64687156486423 \cdot 10^{26}
x16=−3.50804162675416⋅1025x_{16} = -3.50804162675416 \cdot 10^{25}
x17=9.1832414483614⋅1026x_{17} = 9.1832414483614 \cdot 10^{26}
x18=5.32570993256929⋅1025x_{18} = 5.32570993256929 \cdot 10^{25}
x19=8.67399842068681⋅1025x_{19} = 8.67399842068681 \cdot 10^{25}
x20=3.25967628538509⋅1025x_{20} = 3.25967628538509 \cdot 10^{25}
x21=1.32434139824402⋅1026x_{21} = 1.32434139824402 \cdot 10^{26}
x22=8.31133238780096⋅1025x_{22} = 8.31133238780096 \cdot 10^{25}
x23=1.06029282506316⋅1026x_{23} = 1.06029282506316 \cdot 10^{26}
x24=−5.64838158907187⋅1025x_{24} = -5.64838158907187 \cdot 10^{25}
x25=−9.75343758251088⋅1025x_{25} = -9.75343758251088 \cdot 10^{25}
x26=5.78802719796909⋅1027x_{26} = 5.78802719796909 \cdot 10^{27}
x27=3.09485072783018⋅1025x_{27} = 3.09485072783018 \cdot 10^{25}
x28=−2.02413740845105⋅1026x_{28} = -2.02413740845105 \cdot 10^{26}
x29=−3.57275160519401⋅1025x_{29} = -3.57275160519401 \cdot 10^{25}
x30=−8.86769590437601⋅1025x_{30} = -8.86769590437601 \cdot 10^{25}
x31=−4.39888940252873⋅1025x_{31} = -4.39888940252873 \cdot 10^{25}
x32=−1.87904803772021⋅1026x_{32} = -1.87904803772021 \cdot 10^{26}
x33=4.95429959116116⋅1025x_{33} = 4.95429959116116 \cdot 10^{25}
x34=−9.30731399006709⋅1025x_{34} = -9.30731399006709 \cdot 10^{25}
x35=−8.14781718983478⋅1025x_{35} = -8.14781718983478 \cdot 10^{25}
x36=1.38152324182664⋅1026x_{36} = 1.38152324182664 \cdot 10^{26}
x37=−1.17039779234401⋅1026x_{37} = -1.17039779234401 \cdot 10^{26}
x38=−7.65000147575217⋅1025x_{38} = -7.65000147575217 \cdot 10^{25}
x39=7.3707451630513⋅1025x_{39} = 7.3707451630513 \cdot 10^{25}
x40=1.51176997139963⋅1026x_{40} = 1.51176997139963 \cdot 10^{26}
x41=1.32881811432645⋅1026x_{41} = 1.32881811432645 \cdot 10^{26}
x42=−6.33503017760262⋅1025x_{42} = -6.33503017760262 \cdot 10^{25}
x43=2.70495072944396⋅1025x_{43} = 2.70495072944396 \cdot 10^{25}
x44=−3.65837285181693⋅1026x_{44} = -3.65837285181693 \cdot 10^{26}
x45=3.11427711214079⋅1025x_{45} = 3.11427711214079 \cdot 10^{25}
x46=6.06993494643769⋅1025x_{46} = 6.06993494643769 \cdot 10^{25}
x47=1.517907059167⋅1026x_{47} = 1.517907059167 \cdot 10^{26}
x48=−4.06812926448392⋅1025x_{48} = -4.06812926448392 \cdot 10^{25}
x49=0x_{49} = 0
x50=1.49997190283908⋅1026x_{50} = 1.49997190283908 \cdot 10^{26}
x51=−6.86356674995671⋅1025x_{51} = -6.86356674995671 \cdot 10^{25}
x52=1.07616847500344⋅1026x_{52} = 1.07616847500344 \cdot 10^{26}
x53=−6.04072446326113⋅1025x_{53} = -6.04072446326113 \cdot 10^{25}
x54=1.02622717203066⋅1026x_{54} = 1.02622717203066 \cdot 10^{26}
x55=6.29716874707299⋅1025x_{55} = 6.29716874707299 \cdot 10^{25}
x56=−6.24442863316537⋅1025x_{56} = -6.24442863316537 \cdot 10^{25}
x57=−4.50957906342187⋅1025x_{57} = -4.50957906342187 \cdot 10^{25}
x58=2.72244328065554⋅1025x_{58} = 2.72244328065554 \cdot 10^{25}
x59=1.26882193023152⋅1026x_{59} = 1.26882193023152 \cdot 10^{26}
x60=2.15570709377169⋅1026x_{60} = 2.15570709377169 \cdot 10^{26}
x61=4.97153982257293⋅1025x_{61} = 4.97153982257293 \cdot 10^{25}
x62=−1.17148386284775⋅1026x_{62} = -1.17148386284775 \cdot 10^{26}
x63=−8.70020357895223⋅1025x_{63} = -8.70020357895223 \cdot 10^{25}
x64=1.03750401165811⋅1026x_{64} = 1.03750401165811 \cdot 10^{26}
x65=1.199905918542⋅1026x_{65} = 1.199905918542 \cdot 10^{26}
x66=−4.1226096889333⋅1026x_{66} = -4.1226096889333 \cdot 10^{26}
x67=4.21409747757619⋅1026x_{67} = 4.21409747757619 \cdot 10^{26}
x68=−4.63292243808114⋅1025x_{68} = -4.63292243808114 \cdot 10^{25}
x69=−1.34025979809347⋅1027x_{69} = -1.34025979809347 \cdot 10^{27}
x70=−2.30401785325728⋅1025x_{70} = -2.30401785325728 \cdot 10^{25}
x71=2.93439524050673⋅1025x_{71} = 2.93439524050673 \cdot 10^{25}
x72=−3.5515406358993⋅1025x_{72} = -3.5515406358993 \cdot 10^{25}
x73=−7.63907746896755⋅1025x_{73} = -7.63907746896755 \cdot 10^{25}
x74=3.00702335121376⋅1025x_{74} = 3.00702335121376 \cdot 10^{25}
x75=−4.81726084986691⋅1025x_{75} = -4.81726084986691 \cdot 10^{25}
x76=−8.1510969108869⋅1025x_{76} = -8.1510969108869 \cdot 10^{25}
x77=5.85159856415722⋅1025x_{77} = 5.85159856415722 \cdot 10^{25}
x78=−5.14949768550572⋅1025x_{78} = -5.14949768550572 \cdot 10^{25}
x79=2.63567969306403⋅1025x_{79} = 2.63567969306403 \cdot 10^{25}
x80=−4.03169358616203⋅1025x_{80} = -4.03169358616203 \cdot 10^{25}
x81=7.33885223556569⋅1025x_{81} = 7.33885223556569 \cdot 10^{25}
x82=−5.34355586916431⋅1025x_{82} = -5.34355586916431 \cdot 10^{25}
x83=−5.22613218397941⋅1026x_{83} = -5.22613218397941 \cdot 10^{26}
x84=−7.25740919630976⋅1025x_{84} = -7.25740919630976 \cdot 10^{25}
x85=8.64872190345139⋅1025x_{85} = 8.64872190345139 \cdot 10^{25}
x86=−4.05390791861746⋅1025x_{86} = -4.05390791861746 \cdot 10^{25}
x87=6.86352979208891⋅1026x_{87} = 6.86352979208891 \cdot 10^{26}
x88=−2.4649219065448⋅1025x_{88} = -2.4649219065448 \cdot 10^{25}
x89=−4.23684732824908⋅1026x_{89} = -4.23684732824908 \cdot 10^{26}
x90=−1.26467358703299⋅1026x_{90} = -1.26467358703299 \cdot 10^{26}
x91=−3.05611542500579⋅1025x_{91} = -3.05611542500579 \cdot 10^{25}
x92=3.49997350705541⋅1025x_{92} = 3.49997350705541 \cdot 10^{25}
x93=8.50004943111367⋅1025x_{93} = 8.50004943111367 \cdot 10^{25}
x94=9.98075871555385⋅1025x_{94} = 9.98075871555385 \cdot 10^{25}
x95=1.09074207665668⋅1026x_{95} = 1.09074207665668 \cdot 10^{26}
x96=3.56443131629294⋅1025x_{96} = 3.56443131629294 \cdot 10^{25}
x97=5.26475236252101⋅1026x_{97} = 5.26475236252101 \cdot 10^{26}
x98=9.92298950862112⋅1025x_{98} = 9.92298950862112 \cdot 10^{25}
x99=5.1807262487873⋅1026x_{99} = 5.1807262487873 \cdot 10^{26}
x100=4.69291866261227⋅1025x_{100} = 4.69291866261227 \cdot 10^{25}
x101=−6.60361686599096⋅1025x_{101} = -6.60361686599096 \cdot 10^{25}
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 x*(log(2*x - 1) - log(2*x + 1)).
0(−log⁡(0⋅2+1)+log⁡(−1+0⋅2))0 \left(- \log{\left(0 \cdot 2 + 1 \right)} + \log{\left(-1 + 0 \cdot 2 \right)}\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
x(−22x+1+22x−1)+log⁡(2x−1)−log⁡(2x+1)=0x \left(- \frac{2}{2 x + 1} + \frac{2}{2 x - 1}\right) + \log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−32142.7621782406x_{1} = -32142.7621782406
x2=34816.8526385191x_{2} = 34816.8526385191
x3=13625.9107386977x_{3} = 13625.9107386977
x4=16168.9394711881x_{4} = 16168.9394711881
x5=21254.8418612082x_{5} = 21254.8418612082
x6=24645.3799465062x_{6} = 24645.3799465062
x7=6843.71590474159x_{7} = 6843.71590474159
x8=23797.7486613497x_{8} = 23797.7486613497
x9=−27904.6525692875x_{9} = -27904.6525692875
x10=33121.6166527357x_{10} = 33121.6166527357
x11=7691.62151268173x_{11} = 7691.62151268173
x12=27188.2636823476x_{12} = 27188.2636823476
x13=28883.5125581417x_{13} = 28883.5125581417
x14=−23666.5112905186x_{14} = -23666.5112905186
x15=5995.72506323764x_{15} = 5995.72506323764
x16=−42314.1529693663x_{16} = -42314.1529693663
x17=−7560.34665462058x_{17} = -7560.34665462058
x18=−15190.0276944355x_{18} = -15190.0276944355
x19=−19428.3176170057x_{19} = -19428.3176170057
x20=−13494.6644627574x_{20} = -13494.6644627574
x21=−12646.967288922x_{21} = -12646.967288922
x22=−14342.3506515978x_{22} = -14342.3506515978
x23=−18580.6694399672x_{23} = -18580.6694399672
x24=25493.009432894x_{24} = 25493.009432894
x25=40750.1605612703x_{25} = 40750.1605612703
x26=38207.3172854108x_{26} = 38207.3172854108
x27=5147.60685938721x_{27} = 5147.60685938721
x28=−17733.0170623745x_{28} = -17733.0170623745
x29=−38076.0825601956x_{29} = -38076.0825601956
x30=39902.5465688638x_{30} = 39902.5465688638
x31=−25361.7726184844x_{31} = -25361.7726184844
x32=−21971.2418063629x_{32} = -21971.2418063629
x33=19559.5570689242x_{33} = 19559.5570689242
x34=17016.6013671353x_{34} = 17016.6013671353
x35=36512.0860693594x_{35} = 36512.0860693594
x36=26340.6372941876x_{36} = 26340.6372941876
x37=11930.5070870505x_{37} = 11930.5070870505
x38=−5864.42287902783x_{38} = -5864.42287902783
x39=−22818.8776815696x_{39} = -22818.8776815696
x40=32273.9975759261x_{40} = 32273.9975759261
x41=33969.2349888874x_{41} = 33969.2349888874
x42=31426.3776985327x_{42} = 31426.3776985327
x43=29731.1352681699x_{43} = 29731.1352681699
x44=15321.2711950046x_{44} = 15321.2711950046
x45=10235.0387730651x_{45} = 10235.0387730651
x46=−38923.6974995969x_{46} = -38923.6974995969
x47=35664.4696505573x_{47} = 35664.4696505573
x48=−27057.02732333x_{48} = -27057.02732333
x49=−32990.3813736861x_{49} = -32990.3813736861
x50=−28752.2765765372x_{50} = -28752.2765765372
x51=−26209.4007184741x_{51} = -26209.4007184741
x52=−34685.6175712743x_{52} = -34685.6175712743
x53=−40618.926038451x_{53} = -40618.926038451
x54=28035.8887310277x_{54} = 28035.8887310277
x55=−29599.8994514668x_{55} = -29599.8994514668
x56=37359.7019353925x_{56} = 37359.7019353925
x57=−21123.6033920841x_{57} = -21123.6033920841
x58=18711.9094867874x_{58} = 18711.9094867874
x59=−20275.9621202975x_{59} = -20275.9621202975
x60=−16037.6970414573x_{60} = -16037.6970414573
x61=−31295.1421724324x_{61} = -31295.1421724324
x62=−33837.9998197249x_{62} = -33837.9998197249
x63=8539.46727846485x_{63} = 8539.46727846485
x64=22950.1153781196x_{64} = 22950.1153781196
x65=−6712.42993452474x_{65} = -6712.42993452474
x66=9387.26941795865x_{66} = 9387.26941795865
x67=−39771.3119828419x_{67} = -39771.3119828419
x68=41597.7741560983x_{68} = 41597.7741560983
x69=−35533.234678033x_{69} = -35533.234678033
x70=−9256.00838465814x_{70} = -9256.00838465814
x71=−36380.8511850373x_{71} = -36380.8511850373
x72=−41466.5396925675x_{72} = -41466.5396925675
x73=−37228.4671333377x_{73} = -37228.4671333377
x74=39054.9321529674x_{74} = 39054.9321529674
x75=−24514.142868273x_{75} = -24514.142868273
x76=17864.2577911088x_{76} = 17864.2577911088
x77=−8408.20036681627x_{77} = -8408.20036681627
x78=−10103.7822101052x_{78} = -10103.7822101052
x79=42445.3873771332x_{79} = 42445.3873771332
x80=−30447.5212886495x_{80} = -30447.5212886495
x81=−10951.5297833693x_{81} = -10951.5297833693
x82=12778.2153869264x_{82} = 12778.2153869264
x83=−11799.2567626242x_{83} = -11799.2567626242
x84=22102.4798669204x_{84} = 22102.4798669204
x85=14473.5954175247x_{85} = 14473.5954175247
x86=11082.7828677272x_{86} = 11082.7828677272
x87=30578.7569539954x_{87} = 30578.7569539954
x88=20407.2010501152x_{88} = 20407.2010501152
x89=−16885.3598516464x_{89} = -16885.3598516464
Signos de extremos en los puntos:
(-32142.76217824058, -1.00000000009397)

(34816.85263851907, -1.00000000005849)

(13625.91073869772, -1.0000000004538)

(16168.939471188081, -1.00000000032051)

(21254.841861208162, -1.00000000018187)

(24645.379946506233, -1.00000000014779)

(6843.715904741594, -1.00000000177557)

(23797.748661349662, -1.00000000015047)

(-27904.65256928748, -1.0000000001342)

(33121.616652735735, -1.00000000006463)

(7691.621512681734, -1.00000000140612)

(27188.26368234756, -1.00000000012507)

(28883.512558141654, -1.0000000000804)

(-23666.511290518647, -1.00000000017358)

(5995.725063237641, -1.00000000231788)

(-42314.15296936629, -1.00000000005032)

(-7560.346654620577, -1.00000000145689)

(-15190.027694435537, -1.00000000035668)

(-19428.317617005716, -1.00000000021279)

(-13494.664462757368, -1.00000000044828)

(-12646.96728892199, -1.00000000051586)

(-14342.35065159777, -1.00000000042465)

(-18580.669439967234, -1.0000000002531)

(25493.009432893992, -1.00000000009865)

(40750.1605612703, -1.00000000004154)

(38207.31728541079, -1.00000000007514)

(5147.606859387208, -1.00000000314434)

(-17733.017062374503, -1.00000000024231)

(-38076.08256019559, -1.00000000006003)

(39902.54656886377, -1.00000000011465)

(-25361.772618484407, -1.00000000013227)

(-21971.241806362927, -1.00000000016288)

(19559.55706892419, -1.00000000021371)

(17016.601367135318, -1.00000000027847)

(36512.08606935942, -1.00000000006436)

(26340.637294187607, -1.00000000012102)

(11930.50708705048, -1.00000000058398)

(-5864.422879027826, -1.00000000241938)

(-22818.87768156959, -1.00000000015835)

(32273.9975759261, -1.00000000009919)

(33969.234988887445, -1.00000000002054)

(31426.3776985327, -1.00000000008825)

(29731.135268169943, -1.0000000001061)

(15321.271195004578, -1.00000000034588)

(10235.038773065076, -1.00000000078083)

(-38923.69749959692, -1.00000000006937)

(35664.469650557265, -1.00000000007405)

(-27057.027323330018, -1.00000000013016)

(-32990.381373686076, -1.00000000010153)

(-28752.276576537166, -1.0000000000753)

(-26209.400718474084, -1.00000000015827)

(-34685.61757127434, -1.00000000010832)

(-40618.92603845096, -0.999999999994731)

(28035.88873102775, -1.00000000009697)

(-29599.899451466816, -1.00000000010004)

(37359.70193539255, -1.0000000001093)

(-21123.60339208412, -1.00000000017673)

(18711.909486787434, -1.00000000026384)

(-20275.96212029752, -1.00000000019756)

(-16037.69704145727, -1.000000000317)

(-31295.14217243237, -1.00000000007547)

(-33837.999819724886, -1.00000000006912)

(8539.467278464846, -1.00000000114199)

(22950.115378119608, -1.00000000014847)

(-6712.429934524745, -1.00000000184614)

(9387.269417958652, -1.00000000094669)

(-39771.3119828419, -1.00000000003715)

(41597.77415609826, -1.00000000010347)

(-35533.234678033, -1.00000000001538)

(-9256.008384658142, -1.00000000098165)

(-36380.85118503728, -1.00000000002941)

(-41466.539692567516, -1.00000000002145)

(-37228.46713333767, -1.00000000004591)

(39054.93215296742, -1.0000000000444)

(-24514.142868273026, -1.00000000016455)

(17864.25779110885, -1.0000000002475)

(-8408.20036681627, -1.00000000116987)

(-10103.782210105152, -1.00000000081791)

(42445.38737713322, -1.00000000001121)

(-30447.52128864948, -1.00000000006992)

(-10951.529783369335, -1.00000000069498)

(12778.215386926386, -1.00000000052139)

(-11799.25676262423, -1.0000000006006)

(22102.47986692036, -1.00000000017326)

(14473.595417524735, -1.00000000041239)

(11082.782867727186, -1.00000000068077)

(30578.756953995446, -1.00000000004564)

(20407.201050115164, -1.00000000020884)

(-16885.359851646383, -1.00000000028967)


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=−27904.6525692875x_{1} = -27904.6525692875
x2=27188.2636823476x_{2} = 27188.2636823476
x3=−23666.5112905186x_{3} = -23666.5112905186
x4=−14342.3506515978x_{4} = -14342.3506515978
x5=−18580.6694399672x_{5} = -18580.6694399672
x6=−38076.0825601956x_{6} = -38076.0825601956
x7=39902.5465688638x_{7} = 39902.5465688638
x8=32273.9975759261x_{8} = 32273.9975759261
x9=31426.3776985327x_{9} = 31426.3776985327
x10=−27057.02732333x_{10} = -27057.02732333
x11=−32990.3813736861x_{11} = -32990.3813736861
x12=−26209.4007184741x_{12} = -26209.4007184741
x13=−34685.6175712743x_{13} = -34685.6175712743
x14=−29599.8994514668x_{14} = -29599.8994514668
x15=37359.7019353925x_{15} = 37359.7019353925
x16=18711.9094867874x_{16} = 18711.9094867874
x17=−39771.3119828419x_{17} = -39771.3119828419
x18=41597.7741560983x_{18} = 41597.7741560983
x19=−9256.00838465814x_{19} = -9256.00838465814
x20=−10103.7822101052x_{20} = -10103.7822101052
x21=12778.2153869264x_{21} = 12778.2153869264
x22=14473.5954175247x_{22} = 14473.5954175247
x23=20407.2010501152x_{23} = 20407.2010501152
Puntos máximos de la función:
x23=7691.62151268173x_{23} = 7691.62151268173
x23=−15190.0276944355x_{23} = -15190.0276944355
x23=−12646.967288922x_{23} = -12646.967288922
x23=25493.009432894x_{23} = 25493.009432894
x23=−17733.0170623745x_{23} = -17733.0170623745
x23=−21971.2418063629x_{23} = -21971.2418063629
x23=−5864.42287902783x_{23} = -5864.42287902783
x23=33969.2349888874x_{23} = 33969.2349888874
x23=29731.1352681699x_{23} = 29731.1352681699
x23=10235.0387730651x_{23} = 10235.0387730651
x23=−40618.926038451x_{23} = -40618.926038451
x23=28035.8887310277x_{23} = 28035.8887310277
x23=−21123.6033920841x_{23} = -21123.6033920841
x23=−33837.9998197249x_{23} = -33837.9998197249
x23=8539.46727846485x_{23} = 8539.46727846485
x23=−6712.42993452474x_{23} = -6712.42993452474
x23=−35533.234678033x_{23} = -35533.234678033
x23=−36380.8511850373x_{23} = -36380.8511850373
x23=−41466.5396925675x_{23} = -41466.5396925675
x23=17864.2577911088x_{23} = 17864.2577911088
x23=−8408.20036681627x_{23} = -8408.20036681627
x23=42445.3873771332x_{23} = 42445.3873771332
x23=−30447.5212886495x_{23} = -30447.5212886495
x23=30578.7569539954x_{23} = 30578.7569539954
Decrece en los intervalos
[41597.7741560983,∞)\left[41597.7741560983, \infty\right)
Crece en los intervalos
(−∞,−39771.3119828419]\left(-\infty, -39771.3119828419\right]
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
4(x(1(2x+1)2−1(2x−1)2)−12x+1+12x−1)=04 \left(x \left(\frac{1}{\left(2 x + 1\right)^{2}} - \frac{1}{\left(2 x - 1\right)^{2}}\right) - \frac{1}{2 x + 1} + \frac{1}{2 x - 1}\right) = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x(log⁡(2x−1)−log⁡(2x+1)))=−1\lim_{x \to -\infty}\left(x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right)\right) = -1
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=−1y = -1
lim⁡x→∞(x(log⁡(2x−1)−log⁡(2x+1)))=−1\lim_{x \to \infty}\left(x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right)\right) = -1
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=−1y = -1
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*(log(2*x - 1) - log(2*x + 1)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(log⁡(2x−1)−log⁡(2x+1))=0\lim_{x \to -\infty}\left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(log⁡(2x−1)−log⁡(2x+1))=0\lim_{x \to \infty}\left(\log{\left(2 x - 1 \right)} - \log{\left(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:
x(log⁡(2x−1)−log⁡(2x+1))=−x(−log⁡(1−2x)+log⁡(−2x−1))x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right) = - x \left(- \log{\left(1 - 2 x \right)} + \log{\left(- 2 x - 1 \right)}\right)
- No
x(log⁡(2x−1)−log⁡(2x+1))=x(−log⁡(1−2x)+log⁡(−2x−1))x \left(\log{\left(2 x - 1 \right)} - \log{\left(2 x + 1 \right)}\right) = x \left(- \log{\left(1 - 2 x \right)} + \log{\left(- 2 x - 1 \right)}\right)
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор