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

Gráfico de la función y = x*sin(x)*cos(x)

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
02468-8-6-4-2-1010-1010
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=73.8274273593601x_{1} = 73.8274273593601
x2=70.6858347057703x_{2} = 70.6858347057703
x3=−89.5353906273091x_{3} = -89.5353906273091
x4=42.4115008234622x_{4} = 42.4115008234622
x5=−64.4026493985908x_{5} = -64.4026493985908
x6=14.1371669411541x_{6} = 14.1371669411541
x7=−1.5707963267949x_{7} = -1.5707963267949
x8=−53.4070751110265x_{8} = -53.4070751110265
x9=−67.5442420521806x_{9} = -67.5442420521806
x10=89.5353906273091x_{10} = 89.5353906273091
x11=−9.42477796076938x_{11} = -9.42477796076938
x12=−20.4203522483337x_{12} = -20.4203522483337
x13=28.2743338823081x_{13} = 28.2743338823081
x14=9.42477796076938x_{14} = 9.42477796076938
x15=−80.1106126665397x_{15} = -80.1106126665397
x16=50.2654824574367x_{16} = 50.2654824574367
x17=36.1283155162826x_{17} = 36.1283155162826
x18=−97.3893722612836x_{18} = -97.3893722612836
x19=95.8185759344887x_{19} = 95.8185759344887
x20=45.553093477052x_{20} = 45.553093477052
x21=92.6769832808989x_{21} = 92.6769832808989
x22=34.5575191894877x_{22} = 34.5575191894877
x23=1.5707963267949x_{23} = 1.5707963267949
x24=−29.845130209103x_{24} = -29.845130209103
x25=65.9734457253857x_{25} = 65.9734457253857
x26=0x_{26} = 0
x27=3.14159265358979x_{27} = 3.14159265358979
x28=23.5619449019235x_{28} = 23.5619449019235
x29=20.4203522483337x_{29} = 20.4203522483337
x30=78.5398163397448x_{30} = 78.5398163397448
x31=59.6902604182061x_{31} = 59.6902604182061
x32=100.530964914873x_{32} = 100.530964914873
x33=−72.2566310325652x_{33} = -72.2566310325652
x34=21.9911485751286x_{34} = 21.9911485751286
x35=7.85398163397448x_{35} = 7.85398163397448
x36=−17.2787595947439x_{36} = -17.2787595947439
x37=−62.8318530717959x_{37} = -62.8318530717959
x38=4.71238898038469x_{38} = 4.71238898038469
x39=−37.6991118430775x_{39} = -37.6991118430775
x40=−81.6814089933346x_{40} = -81.6814089933346
x41=−21.9911485751286x_{41} = -21.9911485751286
x42=26.7035375555132x_{42} = 26.7035375555132
x43=−58.1194640914112x_{43} = -58.1194640914112
x44=12.5663706143592x_{44} = 12.5663706143592
x45=−87.9645943005142x_{45} = -87.9645943005142
x46=−42.4115008234622x_{46} = -42.4115008234622
x47=−14.1371669411541x_{47} = -14.1371669411541
x48=−94.2477796076938x_{48} = -94.2477796076938
x49=−51.8362787842316x_{49} = -51.8362787842316
x50=15.707963267949x_{50} = 15.707963267949
x51=−43.9822971502571x_{51} = -43.9822971502571
x52=−6.28318530717959x_{52} = -6.28318530717959
x53=58.1194640914112x_{53} = 58.1194640914112
x54=−4.71238898038469x_{54} = -4.71238898038469
x55=−28.2743338823081x_{55} = -28.2743338823081
x56=48.6946861306418x_{56} = 48.6946861306418
x57=−83.2522053201295x_{57} = -83.2522053201295
x58=−95.8185759344887x_{58} = -95.8185759344887
x59=81.6814089933346x_{59} = 81.6814089933346
x60=−75.398223686155x_{60} = -75.398223686155
x61=−36.1283155162826x_{61} = -36.1283155162826
x62=94.2477796076938x_{62} = 94.2477796076938
x63=86.3937979737193x_{63} = 86.3937979737193
x64=−59.6902604182061x_{64} = -59.6902604182061
x65=87.9645943005142x_{65} = 87.9645943005142
x66=−15.707963267949x_{66} = -15.707963267949
x67=−23.5619449019235x_{67} = -23.5619449019235
x68=−61.261056745001x_{68} = -61.261056745001
x69=−7.85398163397448x_{69} = -7.85398163397448
x70=67.5442420521806x_{70} = 67.5442420521806
x71=80.1106126665397x_{71} = 80.1106126665397
x72=6.28318530717959x_{72} = 6.28318530717959
x73=29.845130209103x_{73} = 29.845130209103
x74=−50.2654824574367x_{74} = -50.2654824574367
x75=−73.8274273593601x_{75} = -73.8274273593601
x76=37.6991118430775x_{76} = 37.6991118430775
x77=−86.3937979737193x_{77} = -86.3937979737193
x78=51.8362787842316x_{78} = 51.8362787842316
x79=43.9822971502571x_{79} = 43.9822971502571
x80=56.5486677646163x_{80} = 56.5486677646163
x81=−45.553093477052x_{81} = -45.553093477052
x82=−65.9734457253857x_{82} = -65.9734457253857
x83=−39.2699081698724x_{83} = -39.2699081698724
x84=−31.4159265358979x_{84} = -31.4159265358979
x85=72.2566310325652x_{85} = 72.2566310325652
x86=64.4026493985908x_{86} = 64.4026493985908
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=63.6211806632638x_{1} = 63.6211806632638
x2=85.6113199516972x_{2} = 85.6113199516972
x3=−19.6476754907365x_{3} = -19.6476754907365
x4=54.1970859376957x_{4} = 54.1970859376957
x5=−98.1773168157084x_{5} = -98.1773168157084
x6=−16.5085005166786x_{6} = -16.5085005166786
x7=−82.469838530885x_{7} = -82.469838530885
x8=−5.54276920324851x_{8} = -5.54276920324851
x9=3.98933285620662x_{9} = 3.98933285620662
x10=−79.3283659192419x_{10} = -79.3283659192419
x11=−10.2345837013705x_{11} = -10.2345837013705
x12=7.10371836259559x_{12} = 7.10371836259559
x13=−77.757633250469x_{13} = -77.757633250469
x14=11.8021423864902x_{14} = 11.8021423864902
x15=−40.0615464074251x_{15} = -40.0615464074251
x16=52.6264272696834x_{16} = 52.6264272696834
x17=−76.186903206326x_{17} = -76.186903206326
x18=−32.2090858609196x_{18} = -32.2090858609196
x19=24.3576053587789x_{19} = 24.3576053587789
x20=2.45659021971744x_{20} = 2.45659021971744
x21=16.5085005166786x_{21} = 16.5085005166786
x22=25.927780364576x_{22} = 25.927780364576
x23=−71.4747305517771x_{23} = -71.4747305517771
x24=62.0504837986507x_{24} = 62.0504837986507
x25=41.6321073520443x_{25} = 41.6321073520443
x26=18.0779832097684x_{26} = 18.0779832097684
x27=82.469838530885x_{27} = 82.469838530885
x28=74.6161759525405x_{28} = 74.6161759525405
x29=71.4747305517771x_{29} = 71.4747305517771
x30=91.8943056074308x_{30} = 91.8943056074308
x31=−1.01437891905522x_{31} = -1.01437891905522
x32=69.9040128139871x_{32} = 69.9040128139871
x33=0x_{33} = 0
x34=99.7480730445654x_{34} = 99.7480730445654
x35=−18.0779832097684x_{35} = -18.0779832097684
x36=8.66818896199168x_{36} = 8.66818896199168
x37=84.0405782018796x_{37} = 84.0405782018796
x38=−35.349989019305x_{38} = -35.349989019305
x39=−41.6321073520443x_{39} = -41.6321073520443
x40=−99.7480730445654x_{40} = -99.7480730445654
x41=−11.8021423864902x_{41} = -11.8021423864902
x42=−85.6113199516972x_{42} = -85.6113199516972
x43=−68.3332986887281x_{43} = -68.3332986887281
x44=49.4851361441979x_{44} = 49.4851361441979
x45=−25.927780364576x_{45} = -25.927780364576
x46=−24.3576053587789x_{46} = -24.3576053587789
x47=−27.4980262787482x_{47} = -27.4980262787482
x48=−54.1970859376957x_{48} = -54.1970859376957
x49=−90.3235565896713x_{49} = -90.3235565896713
x50=−13.3704580073937x_{50} = -13.3704580073937
x51=98.1773168157084x_{51} = 98.1773168157084
x52=−62.0504837986507x_{52} = -62.0504837986507
x53=−60.479792099527x_{53} = -60.479792099527
x54=−3.98933285620662x_{54} = -3.98933285620662
x55=−49.4851361441979x_{55} = -49.4851361441979
x56=46.3438858860085x_{56} = 46.3438858860085
x57=−93.4650562152248x_{57} = -93.4650562152248
x58=−47.9145054045097x_{58} = -47.9145054045097
x59=−84.0405782018796x_{59} = -84.0405782018796
x60=77.757633250469x_{60} = 77.757633250469
x61=38.4910046652094x_{61} = 38.4910046652094
x62=19.6476754907365x_{62} = 19.6476754907365
x63=−33.7795214194042x_{63} = -33.7795214194042
x64=−2.45659021971744x_{64} = -2.45659021971744
x65=47.9145054045097x_{65} = 47.9145054045097
x66=−38.4910046652094x_{66} = -38.4910046652094
x67=55.7677523585655x_{67} = 55.7677523585655
x68=30.6386872667848x_{68} = 30.6386872667848
x69=−69.9040128139871x_{69} = -69.9040128139871
x70=−63.6211806632638x_{70} = -63.6211806632638
x71=−46.3438858860085x_{71} = -46.3438858860085
x72=10.2345837013705x_{72} = 10.2345837013705
x73=96.6065618907118x_{73} = 96.6065618907118
x74=88.752809246359x_{74} = 88.752809246359
x75=−57.3384258953415x_{75} = -57.3384258953415
x76=−91.8943056074308x_{76} = -91.8943056074308
x77=76.186903206326x_{77} = 76.186903206326
x78=60.479792099527x_{78} = 60.479792099527
x79=−55.7677523585655x_{79} = -55.7677523585655
x80=27.4980262787482x_{80} = 27.4980262787482
x81=66.7625884309285x_{81} = 66.7625884309285
x82=40.0615464074251x_{82} = 40.0615464074251
x83=33.7795214194042x_{83} = 33.7795214194042
x84=68.3332986887281x_{84} = 68.3332986887281
x85=5.54276920324851x_{85} = 5.54276920324851
x86=32.2090858609196x_{86} = 32.2090858609196
x87=90.3235565896713x_{87} = 90.3235565896713
Signos de extremos en los puntos:
(63.62118066326382, 31.8096079998942)

(85.61131995169717, 42.80492995088)

(-19.647675490736493, 9.82065825172294)

(54.197085937695654, 27.0973898439224)

(-98.17731681570837, 49.088021816977)

(-16.508500516678623, 8.25046693271134)

(-82.46983853088497, 41.2341614335109)

(-5.542769203248511, -2.7601770039825)

(3.9893328562066204, 1.97918184289695)

(-79.32836591924193, 39.6633951186369)

(-10.234583701370475, 5.11119601456306)

(7.103718362595594, 3.54309352844357)

(-77.75763325046901, -38.8780128705513)

(11.802142386490203, -5.89578266240834)

(-40.061546407425126, -20.0292132864148)

(52.6264272696834, -26.3120260989921)

(-76.186903206326, 38.092631278691)

(-32.20908586091958, 16.1026028348438)

(24.357605358778862, -12.176237556342)

(2.456590219717442, -1.20361747242807)

(16.508500516678623, 8.25046693271134)

(25.927780364575984, 12.9614803125504)

(-71.47473055177714, -35.7364908730653)

(62.050483798650674, -31.0242347040109)

(41.63210735204432, 20.8145525932383)

(18.07798320976836, -9.03553634306052)

(82.46983853088497, 41.2341614335109)

(74.61617595254046, -37.3072503844953)

(71.47473055177714, -35.7364908730653)

(91.89430560743084, 45.9464726896225)

(-1.014378919055217, 0.454926435289913)

(69.90401281398711, 34.9511123581481)

(0, 0)

(99.74807304456543, -49.87340995557)

(-18.07798320976836, -9.03553634306052)

(8.66818896199168, -4.32690215196463)

(84.04057820187961, -42.0195454323196)

(-35.349989019305, 17.6732267403983)

(-41.63210735204432, 20.8145525932383)

(-99.74807304456543, -49.87340995557)

(-11.802142386490203, -5.89578266240834)

(-85.61131995169717, 42.80492995088)

(-68.33329868872808, -34.1657347464792)

(49.48513614419785, -24.7413051632797)

(-25.927780364575984, 12.9614803125504)

(-24.357605358778862, -12.176237556342)

(-27.498026278748195, -13.7467408124244)

(-54.197085937695654, 27.0973898439224)

(-90.32355658967134, -45.1610863539292)

(-13.370458007393655, 6.68055941617435)

(98.17731681570837, 49.088021816977)

(-62.050483798650674, -31.0242347040109)

(-60.47979209952698, 30.2388626997097)

(-3.9893328562066204, 1.97918184289695)

(-49.48513614419785, -24.7413051632797)

(46.3438858860085, -23.1705944470148)

(-93.46505621522485, -46.7318594228538)

(-47.91450540450974, 23.9559484021164)

(-84.04057820187961, -42.0195454323196)

(77.75763325046901, -38.8780128705513)

(38.49100466520936, 19.2438787820659)

(19.647675490736493, 9.82065825172294)

(-33.7795214194042, -16.8879107802431)

(-2.456590219717442, -1.20361747242807)

(47.91450540450974, 23.9559484021164)

(-38.49100466520936, 19.2438787820659)

(55.7677523585655, -27.88275552748)

(30.638687266784828, -15.3173041361191)

(-69.90401281398711, 34.9511123581481)

(-63.62118066326382, 31.8096079998942)

(-46.3438858860085, -23.1705944470148)

(10.234583701370475, 5.11119601456306)

(96.6065618907118, -48.3026340043701)

(88.75280924635904, 44.3757004368798)

(-57.338425895341494, 28.6681229903721)

(-91.89430560743084, 45.9464726896225)

(76.186903206326, 38.092631278691)

(60.47979209952698, 30.2388626997097)

(-55.7677523585655, -27.88275552748)

(27.498026278748195, -13.7467408124244)

(66.76258843092853, 33.3803581018047)

(40.061546407425126, -20.0292132864148)

(33.7795214194042, -16.8879107802431)

(68.33329868872808, -34.1657347464792)

(5.542769203248511, -2.7601770039825)

(32.20908586091958, 16.1026028348438)

(90.32355658967134, -45.1610863539292)


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

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
Gráfico
Gráfico de la función y = x*sin(x)*cos(x)
    © Sr Examen – Калькулятор