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Trazado el gráfico de la función/ x*sinx*cosx

Gráfico de la función y = x*sinx*cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*sin(x)*cos(x)
f(x)=xsin⁡(x)cos⁡(x)f{\left(x \right)} = x \sin{\left(x \right)} \cos{\left(x \right)} 
f = (x*sin(x))*cos(x)
Gráfico de la función
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.02-2
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⁡(x)cos⁡(x)=0x \sin{\left(x \right)} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Solución numérica
x1=48.6946861306418x_{1} = 48.6946861306418
x2=81.6814089933346x_{2} = 81.6814089933346
x3=−4.71238898038469x_{3} = -4.71238898038469
x4=−14.1371669411541x_{4} = -14.1371669411541
x5=−86.3937979737193x_{5} = -86.3937979737193
x6=−1.5707963267949x_{6} = -1.5707963267949
x7=23.5619449019235x_{7} = 23.5619449019235
x8=59.6902604182061x_{8} = 59.6902604182061
x9=73.8274273593601x_{9} = 73.8274273593601
x10=4.71238898038469x_{10} = 4.71238898038469
x11=34.5575191894877x_{11} = 34.5575191894877
x12=−21.9911485751286x_{12} = -21.9911485751286
x13=−20.4203522483337x_{13} = -20.4203522483337
x14=15.707963267949x_{14} = 15.707963267949
x15=−95.8185759344887x_{15} = -95.8185759344887
x16=26.7035375555132x_{16} = 26.7035375555132
x17=−81.6814089933346x_{17} = -81.6814089933346
x18=20.4203522483337x_{18} = 20.4203522483337
x19=−94.2477796076938x_{19} = -94.2477796076938
x20=67.5442420521806x_{20} = 67.5442420521806
x21=−59.6902604182061x_{21} = -59.6902604182061
x22=36.1283155162826x_{22} = 36.1283155162826
x23=−43.9822971502571x_{23} = -43.9822971502571
x24=58.1194640914112x_{24} = 58.1194640914112
x25=−29.845130209103x_{25} = -29.845130209103
x26=−31.4159265358979x_{26} = -31.4159265358979
x27=12.5663706143592x_{27} = 12.5663706143592
x28=43.9822971502571x_{28} = 43.9822971502571
x29=7.85398163397448x_{29} = 7.85398163397448
x30=−15.707963267949x_{30} = -15.707963267949
x31=9.42477796076938x_{31} = 9.42477796076938
x32=0x_{32} = 0
x33=89.5353906273091x_{33} = 89.5353906273091
x34=−65.9734457253857x_{34} = -65.9734457253857
x35=−62.8318530717959x_{35} = -62.8318530717959
x36=−28.2743338823081x_{36} = -28.2743338823081
x37=51.8362787842316x_{37} = 51.8362787842316
x38=70.6858347057703x_{38} = 70.6858347057703
x39=−50.2654824574367x_{39} = -50.2654824574367
x40=80.1106126665397x_{40} = 80.1106126665397
x41=−75.398223686155x_{41} = -75.398223686155
x42=45.553093477052x_{42} = 45.553093477052
x43=14.1371669411541x_{43} = 14.1371669411541
x44=28.2743338823081x_{44} = 28.2743338823081
x45=65.9734457253857x_{45} = 65.9734457253857
x46=−67.5442420521806x_{46} = -67.5442420521806
x47=42.4115008234622x_{47} = 42.4115008234622
x48=−45.553093477052x_{48} = -45.553093477052
x49=−58.1194640914112x_{49} = -58.1194640914112
x50=−87.9645943005142x_{50} = -87.9645943005142
x51=−6.28318530717959x_{51} = -6.28318530717959
x52=−83.2522053201295x_{52} = -83.2522053201295
x53=−97.3893722612836x_{53} = -97.3893722612836
x54=94.2477796076938x_{54} = 94.2477796076938
x55=−17.2787595947439x_{55} = -17.2787595947439
x56=95.8185759344887x_{56} = 95.8185759344887
x57=−39.2699081698724x_{57} = -39.2699081698724
x58=72.2566310325652x_{58} = 72.2566310325652
x59=3.14159265358979x_{59} = 3.14159265358979
x60=−36.1283155162826x_{60} = -36.1283155162826
x61=1.5707963267949x_{61} = 1.5707963267949
x62=−9.42477796076938x_{62} = -9.42477796076938
x63=−64.4026493985908x_{63} = -64.4026493985908
x64=56.5486677646163x_{64} = 56.5486677646163
x65=92.6769832808989x_{65} = 92.6769832808989
x66=−51.8362787842316x_{66} = -51.8362787842316
x67=100.530964914873x_{67} = 100.530964914873
x68=−89.5353906273091x_{68} = -89.5353906273091
x69=6.28318530717959x_{69} = 6.28318530717959
x70=−61.261056745001x_{70} = -61.261056745001
x71=−53.4070751110265x_{71} = -53.4070751110265
x72=−73.8274273593601x_{72} = -73.8274273593601
x73=21.9911485751286x_{73} = 21.9911485751286
x74=29.845130209103x_{74} = 29.845130209103
x75=87.9645943005142x_{75} = 87.9645943005142
x76=−72.2566310325652x_{76} = -72.2566310325652
x77=37.6991118430775x_{77} = 37.6991118430775
x78=50.2654824574367x_{78} = 50.2654824574367
x79=86.3937979737193x_{79} = 86.3937979737193
x80=64.4026493985908x_{80} = 64.4026493985908
x81=−37.6991118430775x_{81} = -37.6991118430775
x82=−23.5619449019235x_{82} = -23.5619449019235
x83=78.5398163397448x_{83} = 78.5398163397448
x84=−42.4115008234622x_{84} = -42.4115008234622
x85=−80.1106126665397x_{85} = -80.1106126665397
x86=−7.85398163397448x_{86} = -7.85398163397448
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))*cos(x).
0sin⁡(0)cos⁡(0)0 \sin{\left(0 \right)} \cos{\left(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
−xsin⁡2(x)+(xcos⁡(x)+sin⁡(x))cos⁡(x)=0- x \sin^{2}{\left(x \right)} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−24.3576053587789x_{1} = -24.3576053587789
x2=−49.4851361441979x_{2} = -49.4851361441979
x3=98.1773168157084x_{3} = 98.1773168157084
x4=−25.927780364576x_{4} = -25.927780364576
x5=19.6476754907365x_{5} = 19.6476754907365
x6=7.10371836259559x_{6} = 7.10371836259559
x7=−82.469838530885x_{7} = -82.469838530885
x8=76.186903206326x_{8} = 76.186903206326
x9=3.98933285620662x_{9} = 3.98933285620662
x10=74.6161759525405x_{10} = 74.6161759525405
x11=−77.757633250469x_{11} = -77.757633250469
x12=41.6321073520443x_{12} = 41.6321073520443
x13=−27.4980262787482x_{13} = -27.4980262787482
x14=−55.7677523585655x_{14} = -55.7677523585655
x15=90.3235565896713x_{15} = 90.3235565896713
x16=−69.9040128139871x_{16} = -69.9040128139871
x17=33.7795214194042x_{17} = 33.7795214194042
x18=−60.479792099527x_{18} = -60.479792099527
x19=−76.186903206326x_{19} = -76.186903206326
x20=−57.3384258953415x_{20} = -57.3384258953415
x21=27.4980262787482x_{21} = 27.4980262787482
x22=−1.01437891905522x_{22} = -1.01437891905522
x23=−93.4650562152248x_{23} = -93.4650562152248
x24=−13.3704580073937x_{24} = -13.3704580073937
x25=18.0779832097684x_{25} = 18.0779832097684
x26=−90.3235565896713x_{26} = -90.3235565896713
x27=85.6113199516972x_{27} = 85.6113199516972
x28=0x_{28} = 0
x29=66.7625884309285x_{29} = 66.7625884309285
x30=32.2090858609196x_{30} = 32.2090858609196
x31=−11.8021423864902x_{31} = -11.8021423864902
x32=−33.7795214194042x_{32} = -33.7795214194042
x33=−19.6476754907365x_{33} = -19.6476754907365
x34=40.0615464074251x_{34} = 40.0615464074251
x35=96.6065618907118x_{35} = 96.6065618907118
x36=−10.2345837013705x_{36} = -10.2345837013705
x37=38.4910046652094x_{37} = 38.4910046652094
x38=11.8021423864902x_{38} = 11.8021423864902
x39=−84.0405782018796x_{39} = -84.0405782018796
x40=−47.9145054045097x_{40} = -47.9145054045097
x41=77.757633250469x_{41} = 77.757633250469
x42=63.6211806632638x_{42} = 63.6211806632638
x43=25.927780364576x_{43} = 25.927780364576
x44=71.4747305517771x_{44} = 71.4747305517771
x45=84.0405782018796x_{45} = 84.0405782018796
x46=62.0504837986507x_{46} = 62.0504837986507
x47=30.6386872667848x_{47} = 30.6386872667848
x48=91.8943056074308x_{48} = 91.8943056074308
x49=55.7677523585655x_{49} = 55.7677523585655
x50=8.66818896199168x_{50} = 8.66818896199168
x51=−38.4910046652094x_{51} = -38.4910046652094
x52=−79.3283659192419x_{52} = -79.3283659192419
x53=−71.4747305517771x_{53} = -71.4747305517771
x54=82.469838530885x_{54} = 82.469838530885
x55=−18.0779832097684x_{55} = -18.0779832097684
x56=52.6264272696834x_{56} = 52.6264272696834
x57=−98.1773168157084x_{57} = -98.1773168157084
x58=−16.5085005166786x_{58} = -16.5085005166786
x59=−2.45659021971744x_{59} = -2.45659021971744
x60=5.54276920324851x_{60} = 5.54276920324851
x61=−32.2090858609196x_{61} = -32.2090858609196
x62=−63.6211806632638x_{62} = -63.6211806632638
x63=10.2345837013705x_{63} = 10.2345837013705
x64=−41.6321073520443x_{64} = -41.6321073520443
x65=−99.7480730445654x_{65} = -99.7480730445654
x66=60.479792099527x_{66} = 60.479792099527
x67=47.9145054045097x_{67} = 47.9145054045097
x68=99.7480730445654x_{68} = 99.7480730445654
x69=−85.6113199516972x_{69} = -85.6113199516972
x70=−40.0615464074251x_{70} = -40.0615464074251
x71=−35.349989019305x_{71} = -35.349989019305
x72=16.5085005166786x_{72} = 16.5085005166786
x73=−68.3332986887281x_{73} = -68.3332986887281
x74=−5.54276920324851x_{74} = -5.54276920324851
x75=69.9040128139871x_{75} = 69.9040128139871
x76=54.1970859376957x_{76} = 54.1970859376957
x77=88.752809246359x_{77} = 88.752809246359
x78=2.45659021971744x_{78} = 2.45659021971744
x79=24.3576053587789x_{79} = 24.3576053587789
x80=49.4851361441979x_{80} = 49.4851361441979
x81=−54.1970859376957x_{81} = -54.1970859376957
x82=−46.3438858860085x_{82} = -46.3438858860085
x83=−62.0504837986507x_{83} = -62.0504837986507
x84=68.3332986887281x_{84} = 68.3332986887281
x85=46.3438858860085x_{85} = 46.3438858860085
x86=−3.98933285620662x_{86} = -3.98933285620662
x87=−91.8943056074308x_{87} = -91.8943056074308
Signos de extremos en los puntos:
(-24.357605358778862, -12.176237556342)

(-49.48513614419785, -24.7413051632797)

(98.17731681570837, 49.088021816977)

(-25.927780364575984, 12.9614803125504)

(19.647675490736493, 9.82065825172294)

(7.103718362595594, 3.54309352844357)

(-82.46983853088497, 41.2341614335109)

(76.186903206326, 38.092631278691)

(3.9893328562066204, 1.97918184289695)

(74.61617595254046, -37.3072503844953)

(-77.75763325046901, -38.8780128705513)

(41.63210735204432, 20.8145525932383)

(-27.498026278748195, -13.7467408124244)

(-55.7677523585655, -27.88275552748)

(90.32355658967134, -45.1610863539292)

(-69.90401281398711, 34.9511123581481)

(33.7795214194042, -16.8879107802431)

(-60.47979209952698, 30.2388626997097)

(-76.186903206326, 38.092631278691)

(-57.338425895341494, 28.6681229903721)

(27.498026278748195, -13.7467408124244)

(-1.014378919055217, 0.454926435289913)

(-93.46505621522485, -46.7318594228538)

(-13.370458007393655, 6.68055941617435)

(18.07798320976836, -9.03553634306052)

(-90.32355658967134, -45.1610863539292)

(85.61131995169717, 42.80492995088)

(0, 0)

(66.76258843092853, 33.3803581018047)

(32.20908586091958, 16.1026028348438)

(-11.802142386490203, -5.89578266240834)

(-33.7795214194042, -16.8879107802431)

(-19.647675490736493, 9.82065825172294)

(40.061546407425126, -20.0292132864148)

(96.6065618907118, -48.3026340043701)

(-10.234583701370475, 5.11119601456306)

(38.49100466520936, 19.2438787820659)

(11.802142386490203, -5.89578266240834)

(-84.04057820187961, -42.0195454323196)

(-47.91450540450974, 23.9559484021164)

(77.75763325046901, -38.8780128705513)

(63.62118066326382, 31.8096079998942)

(25.927780364575984, 12.9614803125504)

(71.47473055177714, -35.7364908730653)

(84.04057820187961, -42.0195454323196)

(62.050483798650674, -31.0242347040109)

(30.638687266784828, -15.3173041361191)

(91.89430560743084, 45.9464726896225)

(55.7677523585655, -27.88275552748)

(8.66818896199168, -4.32690215196463)

(-38.49100466520936, 19.2438787820659)

(-79.32836591924193, 39.6633951186369)

(-71.47473055177714, -35.7364908730653)

(82.46983853088497, 41.2341614335109)

(-18.07798320976836, -9.03553634306052)

(52.6264272696834, -26.3120260989921)

(-98.17731681570837, 49.088021816977)

(-16.508500516678623, 8.25046693271134)

(-2.456590219717442, -1.20361747242807)

(5.542769203248511, -2.7601770039825)

(-32.20908586091958, 16.1026028348438)

(-63.62118066326382, 31.8096079998942)

(10.234583701370475, 5.11119601456306)

(-41.63210735204432, 20.8145525932383)

(-99.74807304456543, -49.87340995557)

(60.47979209952698, 30.2388626997097)

(47.91450540450974, 23.9559484021164)

(99.74807304456543, -49.87340995557)

(-85.61131995169717, 42.80492995088)

(-40.061546407425126, -20.0292132864148)

(-35.349989019305, 17.6732267403983)

(16.508500516678623, 8.25046693271134)

(-68.33329868872808, -34.1657347464792)

(-5.542769203248511, -2.7601770039825)

(69.90401281398711, 34.9511123581481)

(54.197085937695654, 27.0973898439224)

(88.75280924635904, 44.3757004368798)

(2.456590219717442, -1.20361747242807)

(24.357605358778862, -12.176237556342)

(49.48513614419785, -24.7413051632797)

(-54.197085937695654, 27.0973898439224)

(-46.3438858860085, -23.1705944470148)

(-62.050483798650674, -31.0242347040109)

(68.33329868872808, -34.1657347464792)

(46.3438858860085, -23.1705944470148)

(-3.9893328562066204, 1.97918184289695)

(-91.89430560743084, 45.9464726896225)


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=−24.3576053587789x_{1} = -24.3576053587789
x2=−49.4851361441979x_{2} = -49.4851361441979
x3=74.6161759525405x_{3} = 74.6161759525405
x4=−77.757633250469x_{4} = -77.757633250469
x5=−27.4980262787482x_{5} = -27.4980262787482
x6=−55.7677523585655x_{6} = -55.7677523585655
x7=90.3235565896713x_{7} = 90.3235565896713
x8=33.7795214194042x_{8} = 33.7795214194042
x9=27.4980262787482x_{9} = 27.4980262787482
x10=−93.4650562152248x_{10} = -93.4650562152248
x11=18.0779832097684x_{11} = 18.0779832097684
x12=−90.3235565896713x_{12} = -90.3235565896713
x13=0x_{13} = 0
x14=−11.8021423864902x_{14} = -11.8021423864902
x15=−33.7795214194042x_{15} = -33.7795214194042
x16=40.0615464074251x_{16} = 40.0615464074251
x17=96.6065618907118x_{17} = 96.6065618907118
x18=11.8021423864902x_{18} = 11.8021423864902
x19=−84.0405782018796x_{19} = -84.0405782018796
x20=77.757633250469x_{20} = 77.757633250469
x21=71.4747305517771x_{21} = 71.4747305517771
x22=84.0405782018796x_{22} = 84.0405782018796
x23=62.0504837986507x_{23} = 62.0504837986507
x24=30.6386872667848x_{24} = 30.6386872667848
x25=55.7677523585655x_{25} = 55.7677523585655
x26=8.66818896199168x_{26} = 8.66818896199168
x27=−71.4747305517771x_{27} = -71.4747305517771
x28=−18.0779832097684x_{28} = -18.0779832097684
x29=52.6264272696834x_{29} = 52.6264272696834
x30=−2.45659021971744x_{30} = -2.45659021971744
x31=5.54276920324851x_{31} = 5.54276920324851
x32=−99.7480730445654x_{32} = -99.7480730445654
x33=99.7480730445654x_{33} = 99.7480730445654
x34=−40.0615464074251x_{34} = -40.0615464074251
x35=−68.3332986887281x_{35} = -68.3332986887281
x36=−5.54276920324851x_{36} = -5.54276920324851
x37=2.45659021971744x_{37} = 2.45659021971744
x38=24.3576053587789x_{38} = 24.3576053587789
x39=49.4851361441979x_{39} = 49.4851361441979
x40=−46.3438858860085x_{40} = -46.3438858860085
x41=−62.0504837986507x_{41} = -62.0504837986507
x42=68.3332986887281x_{42} = 68.3332986887281
x43=46.3438858860085x_{43} = 46.3438858860085
Puntos máximos de la función:
x43=98.1773168157084x_{43} = 98.1773168157084
x43=−25.927780364576x_{43} = -25.927780364576
x43=19.6476754907365x_{43} = 19.6476754907365
x43=7.10371836259559x_{43} = 7.10371836259559
x43=−82.469838530885x_{43} = -82.469838530885
x43=76.186903206326x_{43} = 76.186903206326
x43=3.98933285620662x_{43} = 3.98933285620662
x43=41.6321073520443x_{43} = 41.6321073520443
x43=−69.9040128139871x_{43} = -69.9040128139871
x43=−60.479792099527x_{43} = -60.479792099527
x43=−76.186903206326x_{43} = -76.186903206326
x43=−57.3384258953415x_{43} = -57.3384258953415
x43=−1.01437891905522x_{43} = -1.01437891905522
x43=−13.3704580073937x_{43} = -13.3704580073937
x43=85.6113199516972x_{43} = 85.6113199516972
x43=66.7625884309285x_{43} = 66.7625884309285
x43=32.2090858609196x_{43} = 32.2090858609196
x43=−19.6476754907365x_{43} = -19.6476754907365
x43=−10.2345837013705x_{43} = -10.2345837013705
x43=38.4910046652094x_{43} = 38.4910046652094
x43=−47.9145054045097x_{43} = -47.9145054045097
x43=63.6211806632638x_{43} = 63.6211806632638
x43=25.927780364576x_{43} = 25.927780364576
x43=91.8943056074308x_{43} = 91.8943056074308
x43=−38.4910046652094x_{43} = -38.4910046652094
x43=−79.3283659192419x_{43} = -79.3283659192419
x43=82.469838530885x_{43} = 82.469838530885
x43=−98.1773168157084x_{43} = -98.1773168157084
x43=−16.5085005166786x_{43} = -16.5085005166786
x43=−32.2090858609196x_{43} = -32.2090858609196
x43=−63.6211806632638x_{43} = -63.6211806632638
x43=10.2345837013705x_{43} = 10.2345837013705
x43=−41.6321073520443x_{43} = -41.6321073520443
x43=60.479792099527x_{43} = 60.479792099527
x43=47.9145054045097x_{43} = 47.9145054045097
x43=−85.6113199516972x_{43} = -85.6113199516972
x43=−35.349989019305x_{43} = -35.349989019305
x43=16.5085005166786x_{43} = 16.5085005166786
x43=69.9040128139871x_{43} = 69.9040128139871
x43=54.1970859376957x_{43} = 54.1970859376957
x43=88.752809246359x_{43} = 88.752809246359
x43=−54.1970859376957x_{43} = -54.1970859376957
x43=−3.98933285620662x_{43} = -3.98933285620662
x43=−91.8943056074308x_{43} = -91.8943056074308
Decrece en los intervalos
[99.7480730445654,∞)\left[99.7480730445654, \infty\right)
Crece en los intervalos
(−∞,−99.7480730445654]\left(-\infty, -99.7480730445654\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
−(xsin⁡(x)cos⁡(x)+(xsin⁡(x)−2cos⁡(x))cos⁡(x)+2(xcos⁡(x)+sin⁡(x))sin⁡(x))=0- (x \sin{\left(x \right)} \cos{\left(x \right)} + \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)} + 2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−75.4048541703099x_{1} = -75.4048541703099
x2=56.5575074028724x_{2} = 56.5575074028724
x3=−59.6986350358615x_{3} = -59.6986350358615
x4=29.8618677162152x_{4} = 29.8618677162152
x5=59.6986350358615x_{5} = 59.6986350358615
x6=45.5640652755696x_{6} = 45.5640652755696
x7=26.7222398348818x_{7} = 26.7222398348818
x8=42.4232846216546x_{8} = 42.4232846216546
x9=−53.4164344328533x_{9} = -53.4164344328533
x10=−23.5831338013883x_{10} = -23.5831338013883
x11=−58.1280649399539x_{11} = -58.1280649399539
x12=−94.2530842748465x_{12} = -94.2530842748465
x13=64.4104114951368x_{13} = 64.4104114951368
x14=−73.8341988749761x_{14} = -73.8341988749761
x15=−6.36114938588332x_{15} = -6.36114938588332
x16=80.1168532266283x_{16} = 80.1168532266283
x17=78.5461816776562x_{17} = 78.5461816776562
x18=−50.275426362712x_{18} = -50.275426362712
x19=−15.739687460157x_{19} = -15.739687460157
x20=73.8341988749761x_{20} = 73.8341988749761
x21=50.275426362712x_{21} = 50.275426362712
x22=12.6059515321053x_{22} = 12.6059515321053
x23=9.47734088326452x_{23} = 9.47734088326452
x24=−86.3995847801759x_{24} = -86.3995847801759
x25=−64.4104114951368x_{25} = -64.4104114951368
x26=20.4447888830204x_{26} = 20.4447888830204
x27=58.1280649399539x_{27} = 58.1280649399539
x28=−28.2919993689317x_{28} = -28.2919993689317
x29=−61.2692167254242x_{29} = -61.2692167254242
x30=−17.3076165276153x_{30} = -17.3076165276153
x31=65.9810230816998x_{31} = 65.9810230816998
x32=95.8237936557983x_{32} = 95.8237936557983
x33=−14.1723884348932x_{33} = -14.1723884348932
x34=−89.5409744308928x_{34} = -89.5409744308928
x35=70.6929070794294x_{35} = 70.6929070794294
x36=67.5516432560125x_{36} = 67.5516432560125
x37=1.8217985837127x_{37} = 1.8217985837127
x38=−72.2635497085721x_{38} = -72.2635497085721
x39=51.8459215486945x_{39} = 51.8459215486945
x40=89.5409744308928x_{40} = 89.5409744308928
x41=37.7123669872618x_{41} = 37.7123669872618
x42=23.5831338013883x_{42} = 23.5831338013883
x43=−39.2826336922998x_{43} = -39.2826336922998
x44=81.6875295729143x_{44} = 81.6875295729143
x45=−81.6875295729143x_{45} = -81.6875295729143
x46=28.2919993689317x_{46} = 28.2919993689317
x47=22.0138459496239x_{47} = 22.0138459496239
x48=−22.0138459496239x_{48} = -22.0138459496239
x49=87.9702777935942x_{49} = 87.9702777935942
x50=−43.9936604673443x_{50} = -43.9936604673443
x51=−87.9702777935942x_{51} = -87.9702777935942
x52=43.9936604673443x_{52} = 43.9936604673443
x53=0.538436993155902x_{53} = 0.538436993155902
x54=−65.9810230816998x_{54} = -65.9810230816998
x55=−37.7123669872618x_{55} = -37.7123669872618
x56=−45.5640652755696x_{56} = -45.5640652755696
x57=−29.8618677162152x_{57} = -29.8618677162152
x58=36.1421462518412x_{58} = 36.1421462518412
x59=−95.8237936557983x_{59} = -95.8237936557983
x60=48.7049505853361x_{60} = 48.7049505853361
x61=−36.1421462518412x_{61} = -36.1421462518412
x62=14.1723884348932x_{62} = 14.1723884348932
x63=−102.10665792544x_{63} = -102.10665792544
x64=−1.8217985837127x_{64} = -1.8217985837127
x65=−97.3945058407034x_{65} = -97.3945058407034
x66=6.36114938588332x_{66} = 6.36114938588332
x67=−20.4447888830204x_{67} = -20.4447888830204
x68=92.682377840368x_{68} = 92.682377840368
x69=3.28916686636117x_{69} = 3.28916686636117
x70=−3.28916686636117x_{70} = -3.28916686636117
x71=15.739687460157x_{71} = 15.739687460157
x72=−80.1168532266283x_{72} = -80.1168532266283
x73=100.535938096812x_{73} = 100.535938096812
x74=34.5719777382463x_{74} = 34.5719777382463
x75=−7.91680570747386x_{75} = -7.91680570747386
x76=−51.8459215486945x_{76} = -51.8459215486945
x77=86.3995847801759x_{77} = 86.3995847801759
x78=−42.4232846216546x_{78} = -42.4232846216546
x79=7.91680570747386x_{79} = 7.91680570747386
x80=−31.4318286143515x_{80} = -31.4318286143515
x81=−67.5516432560125x_{81} = -67.5516432560125
x82=94.2530842748465x_{82} = 94.2530842748465
x83=−9.47734088326452x_{83} = -9.47734088326452
x84=−83.2582104451025x_{84} = -83.2582104451025
x85=72.2635497085721x_{85} = 72.2635497085721

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
[95.8237936557983,∞)\left[95.8237936557983, \infty\right)
Convexa en los intervalos
(−∞,−97.3945058407034]\left(-\infty, -97.3945058407034\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡(x)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \sin{\left(x \right)} \cos{\left(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⁡(x)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \sin{\left(x \right)} \cos{\left(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))*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(x)cos⁡(x))=⟨−1,1⟩\lim_{x \to -\infty}\left(\sin{\left(x \right)} \cos{\left(x \right)}\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⁡(x)cos⁡(x))=⟨−1,1⟩\lim_{x \to \infty}\left(\sin{\left(x \right)} \cos{\left(x \right)}\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⁡(x)cos⁡(x)=xsin⁡(x)cos⁡(x)x \sin{\left(x \right)} \cos{\left(x \right)} = x \sin{\left(x \right)} \cos{\left(x \right)}
- Sí
xsin⁡(x)cos⁡(x)=−xsin⁡(x)cos⁡(x)x \sin{\left(x \right)} \cos{\left(x \right)} = - x \sin{\left(x \right)} \cos{\left(x \right)}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор