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Trazado el gráfico de la función/ x*sin(x*x)

Gráfico de la función y = x*sin(x*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*sin(x*x)
f(x)=xsin⁡(xx)f{\left(x \right)} = x \sin{\left(x x \right)} 
f = x*sin(x*x)
Gráfico de la función
-3.0-2.5-2.0-1.5-1.0-0.52.00.00.51.01.55-5
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:
xsin⁡(xx)=0x \sin{\left(x x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−πx_{2} = - \sqrt{\pi}
x3=πx_{3} = \sqrt{\pi}
Solución numérica
x1=5.87856438167413x_{1} = 5.87856438167413
x2=−83.9065500225979x_{2} = -83.9065500225979
x3=52.2498231190263x_{3} = 52.2498231190263
x4=−55.8533929588406x_{4} = -55.8533929588406
x5=60.0806953935677x_{5} = 60.0806953935677
x6=0x_{6} = 0
x7=99.0197488981554x_{7} = 99.0197488981554
x8=56.3294645822743x_{8} = 56.3294645822743
x9=−65.3167882215203x_{9} = -65.3167882215203
x10=96.4482029240534x_{10} = 96.4482029240534
x11=−38.5075542263383x_{11} = -38.5075542263383
x12=10.7814158709709x_{12} = 10.7814158709709
x13=28.2482660354898x_{13} = 28.2482660354898
x14=42.2796194388336x_{14} = 42.2796194388336
x15=−76.1949028730527x_{15} = -76.1949028730527
x16=3.96332729760601x_{16} = 3.96332729760601
x17=94.1238082693386x_{17} = 94.1238082693386
x18=−86.2695368966023x_{18} = -86.2695368966023
x19=3.06998012383947x_{19} = 3.06998012383947
x20=11.0689707511585x_{20} = 11.0689707511585
x21=33.9553310080679x_{21} = 33.9553310080679
x22=−43.8480866628973x_{22} = -43.8480866628973
x23=78.2292943160867x_{23} = 78.2292943160867
x24=82.1853040708499x_{24} = 82.1853040708499
x25=4.68947209983475x_{25} = 4.68947209983475
x26=−30.1838014428441x_{26} = -30.1838014428441
x27=−97.7906336901818x_{27} = -97.7906336901818
x28=6.13996024767893x_{28} = 6.13996024767893
x29=−1.77245385090552x_{29} = -1.77245385090552
x30=86.2148955714351x_{30} = 86.2148955714351
x31=16.244807875181x_{31} = 16.244807875181
x32=−61.7567282282506x_{32} = -61.7567282282506
x33=−15.5532194199919x_{33} = -15.5532194199919
x34=−13.2638300879131x_{34} = -13.2638300879131
x35=7.37324357953091⋅10−5x_{35} = 7.37324357953091 \cdot 10^{-5}
x36=2.506628274631x_{36} = 2.506628274631
x37=1.4484073226336⋅10−5x_{37} = 1.4484073226336 \cdot 10^{-5}
x38=−5.87856438167413x_{38} = -5.87856438167413
x39=−59.634577921401x_{39} = -59.634577921401
x40=1.77245385090552x_{40} = 1.77245385090552
x41=−82.7756822833816x_{41} = -82.7756822833816
x42=−26.1699674910493x_{42} = -26.1699674910493
x43=64.8097938420541x_{43} = 64.8097938420541
x44=−41.8314129339366x_{44} = -41.8314129339366
x45=−89.7498945058111x_{45} = -89.7498945058111
x46=−30.4944490926231x_{46} = -30.4944490926231
x47=−35.9331960814148x_{47} = -35.9331960814148
x48=−7.72594721818665x_{48} = -7.72594721818665
x49=−9.86860538583257x_{49} = -9.86860538583257
x50=−45.9814294674049x_{50} = -45.9814294674049
x51=9.86860538583257x_{51} = 9.86860538583257
x52=−54.0235094674987x_{52} = -54.0235094674987
x53=18.2485292908913x_{53} = 18.2485292908913
x54=−57.0774174413368x_{54} = -57.0774174413368
x55=20.053026197048x_{55} = 20.053026197048
x56=−3.96332729760601x_{56} = -3.96332729760601
x57=22.137941502317x_{57} = 22.137941502317
x58=−95.8600986425016x_{58} = -95.8600986425016
x59=−39.7914902637393x_{59} = -39.7914902637393
x60=66.2954607976453x_{60} = 66.2954607976453
x61=46.1519210773927x_{61} = 46.1519210773927
x62=8.1224039375905x_{62} = 8.1224039375905
x63=26.2897391350647x_{63} = 26.2897391350647
x64=28.4145968117194x_{64} = 28.4145968117194
x65=−4.68947209983475x_{65} = -4.68947209983475
x66=−91.8432157259783x_{66} = -91.8432157259783
x67=−64.0295120466702x_{67} = -64.0295120466702
x68=−19.8166364880301x_{68} = -19.8166364880301
x69=−5.60499121639793x_{69} = -5.60499121639793
x70=80.212104788192x_{70} = 80.212104788192
x71=64.2499240996983x_{71} = 64.2499240996983
x72=−15.7539144225679x_{72} = -15.7539144225679
x73=−74.0410641503361x_{73} = -74.0410641503361
x74=−69.9165085583206x_{74} = -69.9165085583206
x75=67.1664131136608x_{75} = 67.1664131136608
x76=70.096012084957x_{76} = 70.096012084957
x77=47.9218554500359x_{77} = 47.9218554500359
x78=−11.6227571644753x_{78} = -11.6227571644753
x79=−33.862683274665x_{79} = -33.862683274665
x80=−22.0668724858422x_{80} = -22.0668724858422
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*sin(x*x).
0sin⁡(0⋅0)0 \sin{\left(0 \cdot 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
2x2cos⁡(xx)+sin⁡(xx)=02 x^{2} \cos{\left(x x \right)} + \sin{\left(x x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−1.35521112862614x_{1} = -1.35521112862614
x2=−3.76462907532733x_{2} = -3.76462907532733
x3=20.2479396696885x_{3} = 20.2479396696885
x4=6.26758611849278x_{4} = 6.26758611849278
x5=−13.3230177428884x_{5} = -13.3230177428884
x6=18.1189943237946x_{6} = 18.1189943237946
x7=55.698500038955x_{7} = 55.698500038955
x8=−23.4138597867238x_{8} = -23.4138597867238
x9=−93.7978159831513x_{9} = -93.7978159831513
x10=−8.95080183389482x_{10} = -8.95080183389482
x11=12.7198707532056x_{11} = 12.7198707532056
x12=−44.0803279657641x_{12} = -44.0803279657641
x13=−83.5970868479093x_{13} = -83.5970868479093
x14=70.1520134668099x_{14} = 70.1520134668099
x15=58.2083140493455x_{15} = 58.2083140493455
x16=84.2708150182891x_{16} = 84.2708150182891
x17=−38.3235554977812x_{17} = -38.3235554977812
x18=−47.8726650497299x_{18} = -47.8726650497299
x19=−70.1072165206277x_{19} = -70.1072165206277
x20=60.2503979153653x_{20} = 60.2503979153653
x21=18.2915584905206x_{21} = 18.2915584905206
x22=33.0409428606701x_{22} = 33.0409428606701
x23=0x_{23} = 0
x24=26.438704217983x_{24} = 26.438704217983
x25=−18.0320929835385x_{25} = -18.0320929835385
x26=58.5580782403786x_{26} = 58.5580782403786
x27=−97.7504685831282x_{27} = -97.7504685831282
x28=−5.74472561217197x_{28} = -5.74472561217197
x29=91.8517671603543x_{29} = 91.8517671603543
x30=−68.7040251218618x_{30} = -68.7040251218618
x31=−85.7673554818607x_{31} = -85.7673554818607
x32=−4.16024524967154x_{32} = -4.16024524967154
x33=−42.3724023394102x_{33} = -42.3724023394102
x34=77.3509100937384x_{34} = 77.3509100937384
x35=6.01183407098084x_{35} = 6.01183407098084
x36=−14.3449206558669x_{36} = -14.3449206558669
x37=5.16935647582827x_{37} = 5.16935647582827
x38=−65.8556662221908x_{38} = -65.8556662221908
x39=−9.78896285608669x_{39} = -9.78896285608669
x40=−6.97889329812938x_{40} = -6.97889329812938
x41=−29.8962149672115x_{41} = -29.8962149672115
x42=2.19450274956445x_{42} = 2.19450274956445
x43=−33.7930372624299x_{43} = -33.7930372624299
x44=32.1249695905524x_{44} = 32.1249695905524
x45=−17.8570216542223x_{45} = -17.8570216542223
x46=−42.0000542670678x_{46} = -42.0000542670678
x47=37.0735370544564x_{47} = 37.0735370544564
x48=−91.8517671603543x_{48} = -91.8517671603543
x49=−11.1398805605465x_{49} = -11.1398805605465
x50=4.16024524967154x_{50} = 4.16024524967154
x51=−26.7928090700661x_{51} = -26.7928090700661
x52=10.2590498848041x_{52} = 10.2590498848041
x53=8.40790743485922x_{53} = 8.40790743485922
x54=−7.82746557122563x_{54} = -7.82746557122563
x55=35.4269200396297x_{55} = 35.4269200396297
x56=−53.6002486537402x_{56} = -53.6002486537402
x57=−16.0013047615368x_{57} = -16.0013047615368
x58=18.7997496853775x_{58} = 18.7997496853775
x59=−90.0556577728139x_{59} = -90.0556577728139
x60=−2.19450274956445x_{60} = -2.19450274956445
x61=34.2088247492311x_{61} = 34.2088247492311
x62=1.35521112862614x_{62} = 1.35521112862614
x63=54.1251819410153x_{63} = 54.1251819410153
x64=−21.7442119165177x_{64} = -21.7442119165177
x65=−75.8953899598703x_{65} = -75.8953899598703
x66=56.1199322342945x_{66} = 56.1199322342945
x67=−69.7703226268241x_{67} = -69.7703226268241
x68=−35.6038344867429x_{68} = -35.6038344867429
x69=41.2071732071487x_{69} = 41.2071732071487
x70=46.0326458158356x_{70} = 46.0326458158356
x71=96.048356995137x_{71} = 96.048356995137
x72=94.2155512590465x_{72} = 94.2155512590465
x73=26.6163455262094x_{73} = 26.6163455262094
x74=80.182725342438x_{74} = 80.182725342438
x75=22.3146463051457x_{75} = 22.3146463051457
x76=−43.3979845304653x_{76} = -43.3979845304653
x77=40.1647623864471x_{77} = 40.1647623864471
x78=−81.0594911844327x_{78} = -81.0594911844327
x79=82.5952088232899x_{79} = 82.5952088232899
x80=27.996928491633x_{80} = 27.996928491633
x81=90.2299142368658x_{81} = 90.2299142368658
x82=62.2255018033701x_{82} = 62.2255018033701
x83=−52.1143649402824x_{83} = -52.1143649402824
x84=14.1242217429234x_{84} = 14.1242217429234
x85=36.0423216116322x_{85} = 36.0423216116322
Signos de extremos en los puntos:
(-1.3552111286261361, -1.30761941299144)

(-3.7646290753273344, -3.76228841574689)

(20.247939669688456, 20.2479246116981)

(6.26758611849278, 6.26707847792961)

(-13.323017742888373, -13.3229648862414)

(18.11899432379457, 18.1189733098786)

(55.69850003895503, -55.6984993155534)

(-23.413859786723755, -23.4138500482544)

(-93.79781598315132, -93.7978158316795)

(-8.950801833894822, 8.95062752823053)

(12.719870753205562, -12.7198100154406)

(-44.08032796576413, -44.0803265063601)

(-83.59708684790927, -83.5970866339473)

(70.1520134668099, 70.1520131047424)

(58.20831404934549, 58.2083134155415)

(84.27081501828906, 84.2708148094179)

(-38.32355549778122, 38.3235532769651)

(-47.87266504972991, 47.8726639104061)

(-70.10721652062774, -70.1072161578657)

(60.25039791536535, -60.2503973438469)

(18.291558490520618, 18.2915380657515)

(33.04094286067008, -33.0409393952758)

(0, 0)

(26.438704217982963, 26.4386974542049)

(-18.032092983538494, 18.0320716643422)

(58.5580782403786, -58.558077617864)

(-97.75046858312821, 97.7504684492982)

(-5.744725612171971, -5.74406639671223)

(91.85176716035429, -91.8517669990494)

(-68.70402512186176, -68.7040247364158)

(-85.7673554818607, 85.7673552837336)

(-4.160245249671543, 4.15851032158028)

(-42.372402339410215, 42.3724006963226)

(77.35091009373836, 77.3509098236451)

(6.011834070980841, -6.01125886058877)

(-14.344920655866918, 14.3448783097455)

(5.169356475828274, 5.16845181340769)

(-65.8556662221908, -65.8556657845372)

(-9.78896285608669, -9.78882959875799)

(-6.97889329812938, 6.97852557917854)

(-29.89621496721153, -29.8962102892)

(2.194502749564451, -2.18276978467772)

(-33.79303726242993, 33.7930340233007)

(32.124969590552375, 32.1249658202016)

(-17.857021654222304, 17.8569997018158)

(-42.00005426706781, 42.0000525798916)

(37.07353705445637, -37.0735346013414)

(-91.85176716035429, 91.8517669990494)

(-11.139880560546503, 11.139790140834)

(4.160245249671543, -4.15851032158028)

(-26.79280907006613, -26.7928025709379)

(10.259049884804105, -10.2589341187482)

(8.407907434859222, 8.40769713937167)

(-7.8274655712256305, 7.82720494097395)

(35.42692003962967, -35.426917228313)

(-53.600248653740245, -53.600247842014)

(-16.001304761536776, 16.0012742515106)

(18.799749685377474, 18.7997308725895)

(-90.05565777281386, 90.0556576016638)

(-2.194502749564451, 2.18276978467772)

(34.20882474923113, 34.2088216267811)

(1.3552111286261361, 1.30761941299144)

(54.125181941015335, 54.1251811526784)

(-21.744211916517738, -21.744199758056)

(-75.89538995987029, 75.8953896739376)

(56.119932234294495, 56.1199315270679)

(-69.77032262682411, 69.7703222587817)

(-35.60383448674287, 35.6038317171263)

(41.20717320714869, 41.207171420696)

(46.03264581583564, 46.0326445343546)

(96.04835699513701, 96.0483568540652)

(94.21555125904652, -94.2155511095806)

(26.616345526209365, -26.6163388969567)

(80.18272534243798, 80.1827250999626)

(22.314646305145708, 22.3146350554788)

(-43.39798453046534, 43.397983001135)

(40.1647623864471, -40.1647604572599)

(-81.05949118443273, 81.0594909497407)

(82.5952088232899, -82.595208601447)

(27.996928491632993, -27.9969227955184)

(90.22991423686584, -90.2299140667055)

(62.22550180337009, 62.2255012845643)

(-52.11436494028237, -52.1143640571259)

(14.124221742923448, -14.1241773805896)

(36.042321611632175, -36.0423189418754)


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=−1.35521112862614x_{1} = -1.35521112862614
x2=−3.76462907532733x_{2} = -3.76462907532733
x3=−13.3230177428884x_{3} = -13.3230177428884
x4=55.698500038955x_{4} = 55.698500038955
x5=−23.4138597867238x_{5} = -23.4138597867238
x6=−93.7978159831513x_{6} = -93.7978159831513
x7=12.7198707532056x_{7} = 12.7198707532056
x8=−44.0803279657641x_{8} = -44.0803279657641
x9=−83.5970868479093x_{9} = -83.5970868479093
x10=−70.1072165206277x_{10} = -70.1072165206277
x11=60.2503979153653x_{11} = 60.2503979153653
x12=33.0409428606701x_{12} = 33.0409428606701
x13=58.5580782403786x_{13} = 58.5580782403786
x14=−5.74472561217197x_{14} = -5.74472561217197
x15=91.8517671603543x_{15} = 91.8517671603543
x16=−68.7040251218618x_{16} = -68.7040251218618
x17=6.01183407098084x_{17} = 6.01183407098084
x18=−65.8556662221908x_{18} = -65.8556662221908
x19=−9.78896285608669x_{19} = -9.78896285608669
x20=−29.8962149672115x_{20} = -29.8962149672115
x21=2.19450274956445x_{21} = 2.19450274956445
x22=37.0735370544564x_{22} = 37.0735370544564
x23=4.16024524967154x_{23} = 4.16024524967154
x24=−26.7928090700661x_{24} = -26.7928090700661
x25=10.2590498848041x_{25} = 10.2590498848041
x26=35.4269200396297x_{26} = 35.4269200396297
x27=−53.6002486537402x_{27} = -53.6002486537402
x28=−21.7442119165177x_{28} = -21.7442119165177
x29=94.2155512590465x_{29} = 94.2155512590465
x30=26.6163455262094x_{30} = 26.6163455262094
x31=40.1647623864471x_{31} = 40.1647623864471
x32=82.5952088232899x_{32} = 82.5952088232899
x33=27.996928491633x_{33} = 27.996928491633
x34=90.2299142368658x_{34} = 90.2299142368658
x35=−52.1143649402824x_{35} = -52.1143649402824
x36=14.1242217429234x_{36} = 14.1242217429234
x37=36.0423216116322x_{37} = 36.0423216116322
Puntos máximos de la función:
x37=20.2479396696885x_{37} = 20.2479396696885
x37=6.26758611849278x_{37} = 6.26758611849278
x37=18.1189943237946x_{37} = 18.1189943237946
x37=−8.95080183389482x_{37} = -8.95080183389482
x37=70.1520134668099x_{37} = 70.1520134668099
x37=58.2083140493455x_{37} = 58.2083140493455
x37=84.2708150182891x_{37} = 84.2708150182891
x37=−38.3235554977812x_{37} = -38.3235554977812
x37=−47.8726650497299x_{37} = -47.8726650497299
x37=18.2915584905206x_{37} = 18.2915584905206
x37=26.438704217983x_{37} = 26.438704217983
x37=−18.0320929835385x_{37} = -18.0320929835385
x37=−97.7504685831282x_{37} = -97.7504685831282
x37=−85.7673554818607x_{37} = -85.7673554818607
x37=−4.16024524967154x_{37} = -4.16024524967154
x37=−42.3724023394102x_{37} = -42.3724023394102
x37=77.3509100937384x_{37} = 77.3509100937384
x37=−14.3449206558669x_{37} = -14.3449206558669
x37=5.16935647582827x_{37} = 5.16935647582827
x37=−6.97889329812938x_{37} = -6.97889329812938
x37=−33.7930372624299x_{37} = -33.7930372624299
x37=32.1249695905524x_{37} = 32.1249695905524
x37=−17.8570216542223x_{37} = -17.8570216542223
x37=−42.0000542670678x_{37} = -42.0000542670678
x37=−91.8517671603543x_{37} = -91.8517671603543
x37=−11.1398805605465x_{37} = -11.1398805605465
x37=8.40790743485922x_{37} = 8.40790743485922
x37=−7.82746557122563x_{37} = -7.82746557122563
x37=−16.0013047615368x_{37} = -16.0013047615368
x37=18.7997496853775x_{37} = 18.7997496853775
x37=−90.0556577728139x_{37} = -90.0556577728139
x37=−2.19450274956445x_{37} = -2.19450274956445
x37=34.2088247492311x_{37} = 34.2088247492311
x37=1.35521112862614x_{37} = 1.35521112862614
x37=54.1251819410153x_{37} = 54.1251819410153
x37=−75.8953899598703x_{37} = -75.8953899598703
x37=56.1199322342945x_{37} = 56.1199322342945
x37=−69.7703226268241x_{37} = -69.7703226268241
x37=−35.6038344867429x_{37} = -35.6038344867429
x37=41.2071732071487x_{37} = 41.2071732071487
x37=46.0326458158356x_{37} = 46.0326458158356
x37=96.048356995137x_{37} = 96.048356995137
x37=80.182725342438x_{37} = 80.182725342438
x37=22.3146463051457x_{37} = 22.3146463051457
x37=−43.3979845304653x_{37} = -43.3979845304653
x37=−81.0594911844327x_{37} = -81.0594911844327
x37=62.2255018033701x_{37} = 62.2255018033701
Decrece en los intervalos
[94.2155512590465,∞)\left[94.2155512590465, \infty\right)
Crece en los intervalos
(−∞,−93.7978159831513]\left(-\infty, -93.7978159831513\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
2x(−2x2sin⁡(x2)+3cos⁡(x2))=02 x \left(- 2 x^{2} \sin{\left(x^{2} \right)} + 3 \cos{\left(x^{2} \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−87.8035794627719x_{1} = -87.8035794627719
x2=−7.72757234170916x_{2} = -7.72757234170916
x3=−1.88206439251153x_{3} = -1.88206439251153
x4=24.0427877576748x_{4} = 24.0427877576748
x5=6.14319442831165x_{5} = 6.14319442831165
x6=−81.2433775297909x_{6} = -81.2433775297909
x7=40.3403757581099x_{7} = 40.3403757581099
x8=95.9092459191474x_{8} = 95.9092459191474
x9=−62.010561988096x_{9} = -62.010561988096
x10=42.5019600275937x_{10} = 42.5019600275937
x11=−91.9457775443788x_{11} = -91.9457775443788
x12=−22.0669422824152x_{12} = -22.0669422824152
x13=52.2498283768574x_{13} = 52.2498283768574
x14=56.3573477467582x_{14} = 56.3573477467582
x15=4.35070519313685x_{15} = 4.35070519313685
x16=80.2121062414459x_{16} = 80.2121062414459
x17=−45.3969768662765x_{17} = -45.3969768662765
x18=−84.3918879768863x_{18} = -84.3918879768863
x19=70.0287543665084x_{19} = 70.0287543665084
x20=−25.6241126501789x_{20} = -25.6241126501789
x21=−41.8314231799115x_{21} = -41.8314231799115
x22=29.9749423415538x_{22} = 29.9749423415538
x23=−89.7498955432426x_{23} = -89.7498955432426
x24=−59.8711753367813x_{24} = -59.8711753367813
x25=16.2449828200284x_{25} = 16.2449828200284
x26=−80.9916396263613x_{26} = -80.9916396263613
x27=0x_{27} = 0
x28=−20.2091740980058x_{28} = -20.2091740980058
x29=70.4759411950435x_{29} = 70.4759411950435
x30=−70.4090442339662x_{30} = -70.4090442339662
x31=−53.5562752223296x_{31} = -53.5562752223296
x32=60.3415801705031x_{32} = 60.3415801705031
x33=−13.956591457499x_{33} = -13.956591457499
x34=12.4075695960596x_{34} = 12.4075695960596
x35=−97.210651992103x_{35} = -97.210651992103
x36=−95.8600994939291x_{36} = -95.8600994939291
x37=−19.8167328629527x_{37} = -19.8167328629527
x38=−15.7541062352466x_{38} = -15.7541062352466
x39=29.5527405699079x_{39} = 29.5527405699079
x40=31.3078015557213x_{40} = 31.3078015557213
x41=18.248652705729x_{41} = 18.248652705729
x42=−3.97524852094956x_{42} = -3.97524852094956
x43=−20.5941386070623x_{43} = -20.5941386070623
x44=−58.167823848281x_{44} = -58.167823848281
x45=98.1433809873861x_{45} = 98.1433809873861
x46=−5.32233379663163x_{46} = -5.32233379663163
x47=82.1853054219226x_{47} = 82.1853054219226
x48=24.4958506003749x_{48} = 24.4958506003749
x49=−53.8779373088248x_{49} = -53.8779373088248
x50=28.2482993078868x_{50} = 28.2482993078868
x51=19.9746345778427x_{51} = 19.9746345778427
x52=−73.1016373582204x_{52} = -73.1016373582204
x53=82.5476510009072x_{53} = 82.5476510009072
x54=15.7541062352466x_{54} = 15.7541062352466
x55=−33.8627025897352x_{55} = -33.8627025897352
x56=−77.5435915368253x_{56} = -77.5435915368253
x57=−74.0410659980864x_{57} = -74.0410659980864
x58=−46.7941317323039x_{58} = -46.7941317323039
x59=−10.1826825135632x_{59} = -10.1826825135632
x60=78.2292958826682x_{60} = 78.2292958826682
x61=3.97524852094956x_{61} = 3.97524852094956
x62=34.0015792865219x_{62} = 34.0015792865219
x63=−39.7915021676646x_{63} = -39.7915021676646
x64=8.12380270589791x_{64} = 8.12380270589791
x65=44.3821963776835x_{65} = 44.3821963776835
x66=11.487308570426x_{66} = 11.487308570426
x67=−43.848095559189x_{67} = -43.848095559189
x68=−72.3673630855497x_{68} = -72.3673630855497
x69=−35.0928131991141x_{69} = -35.0928131991141
x70=−67.8875301383577x_{70} = -67.8875301383577
x71=94.1238091687591x_{71} = 94.1238091687591
x72=1.88206439251153x_{72} = 1.88206439251153
x73=−88.2852851046244x_{73} = -88.2852851046244
x74=−9.86938552801094x_{74} = -9.86938552801094
x75=64.2499269274634x_{75} = 64.2499269274634
x76=−65.6526120480487x_{76} = -65.6526120480487
x77=24.1080323085044x_{77} = 24.1080323085044
x78=9.86938552801094x_{78} = 9.86938552801094
x79=21.6356305619669x_{79} = 21.6356305619669
x80=−55.853397263239x_{80} = -55.853397263239
x81=86.1784499457929x_{81} = 86.1784499457929
x82=−11.6232347721659x_{82} = -11.6232347721659
x83=50.2264820133132x_{83} = 50.2264820133132
x84=−5.88224817621418x_{84} = -5.88224817621418
x85=22.1380106288555x_{85} = 22.1380106288555
x86=−14.2902367964909x_{86} = -14.2902367964909
x87=39.8309582553183x_{87} = 39.8309582553183

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
[82.5476510009072,∞)\left[82.5476510009072, \infty\right)
Convexa en los intervalos
(−∞,−95.8600994939291]\left(-\infty, -95.8600994939291\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡(xx))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \sin{\left(x x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞(xsin⁡(xx))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \sin{\left(x x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*sin(x*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞sin⁡(xx)=⟨−1,1⟩\lim_{x \to -\infty} \sin{\left(x x \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞sin⁡(xx)=⟨−1,1⟩\lim_{x \to \infty} \sin{\left(x x \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle 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:
xsin⁡(xx)=−xsin⁡(x2)x \sin{\left(x x \right)} = - x \sin{\left(x^{2} \right)}
- No
xsin⁡(xx)=xsin⁡(x2)x \sin{\left(x x \right)} = x \sin{\left(x^{2} \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор