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Trazado el gráfico de la función/ (x*sin(2*x))/4

Gráfico de la función y = (x*sin(2*x))/4

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       x*sin(2*x)
f(x) = ----------
           4
f(x)=xsin⁡(2x)4f{\left(x \right)} = \frac{x \sin{\left(2 x \right)}}{4} 
f = (x*sin(2*x))/4
Gráfico de la función
02468-8-6-4-2-10105-5
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
xsin⁡(2x)4=0\frac{x \sin{\left(2 x \right)}}{4} = 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}
x4=πx_{4} = \pi
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(2*x))/4.
0sin⁡(0⋅2)4\frac{0 \sin{\left(0 \cdot 2 \right)}}{4}
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
xcos⁡(2x)2+sin⁡(2x)4=0\frac{x \cos{\left(2 x \right)}}{2} + \frac{\sin{\left(2 x \right)}}{4} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−93.4650562152248x_{1} = -93.4650562152248
x2=−82.469838530885x_{2} = -82.469838530885
x3=−33.7795214194042x_{3} = -33.7795214194042
x4=60.479792099527x_{4} = 60.479792099527
x5=−77.757633250469x_{5} = -77.757633250469
x6=−11.8021423864902x_{6} = -11.8021423864902
x7=25.927780364576x_{7} = 25.927780364576
x8=46.3438858860085x_{8} = 46.3438858860085
x9=55.7677523585655x_{9} = 55.7677523585655
x10=−16.5085005166786x_{10} = -16.5085005166786
x11=−18.0779832097684x_{11} = -18.0779832097684
x12=−62.0504837986507x_{12} = -62.0504837986507
x13=−3.98933285620662x_{13} = -3.98933285620662
x14=−71.4747305517771x_{14} = -71.4747305517771
x15=74.6161759525405x_{15} = 74.6161759525405
x16=98.1773168157084x_{16} = 98.1773168157084
x17=71.4747305517771x_{17} = 71.4747305517771
x18=−27.4980262787482x_{18} = -27.4980262787482
x19=−57.3384258953415x_{19} = -57.3384258953415
x20=−46.3438858860085x_{20} = -46.3438858860085
x21=99.7480730445654x_{21} = 99.7480730445654
x22=−38.4910046652094x_{22} = -38.4910046652094
x23=7.10371836259559x_{23} = 7.10371836259559
x24=−25.927780364576x_{24} = -25.927780364576
x25=41.6321073520443x_{25} = 41.6321073520443
x26=88.752809246359x_{26} = 88.752809246359
x27=−98.1773168157084x_{27} = -98.1773168157084
x28=−63.6211806632638x_{28} = -63.6211806632638
x29=19.6476754907365x_{29} = 19.6476754907365
x30=−41.6321073520443x_{30} = -41.6321073520443
x31=−91.8943056074308x_{31} = -91.8943056074308
x32=62.0504837986507x_{32} = 62.0504837986507
x33=84.0405782018796x_{33} = 84.0405782018796
x34=54.1970859376957x_{34} = 54.1970859376957
x35=−2.45659021971744x_{35} = -2.45659021971744
x36=47.9145054045097x_{36} = 47.9145054045097
x37=32.2090858609196x_{37} = 32.2090858609196
x38=−1.01437891905522x_{38} = -1.01437891905522
x39=52.6264272696834x_{39} = 52.6264272696834
x40=77.757633250469x_{40} = 77.757633250469
x41=−69.9040128139871x_{41} = -69.9040128139871
x42=66.7625884309285x_{42} = 66.7625884309285
x43=−99.7480730445654x_{43} = -99.7480730445654
x44=8.66818896199168x_{44} = 8.66818896199168
x45=16.5085005166786x_{45} = 16.5085005166786
x46=−47.9145054045097x_{46} = -47.9145054045097
x47=69.9040128139871x_{47} = 69.9040128139871
x48=−60.479792099527x_{48} = -60.479792099527
x49=38.4910046652094x_{49} = 38.4910046652094
x50=−79.3283659192419x_{50} = -79.3283659192419
x51=10.2345837013705x_{51} = 10.2345837013705
x52=76.186903206326x_{52} = 76.186903206326
x53=33.7795214194042x_{53} = 33.7795214194042
x54=2.45659021971744x_{54} = 2.45659021971744
x55=−85.6113199516972x_{55} = -85.6113199516972
x56=18.0779832097684x_{56} = 18.0779832097684
x57=49.4851361441979x_{57} = 49.4851361441979
x58=−68.3332986887281x_{58} = -68.3332986887281
x59=63.6211806632638x_{59} = 63.6211806632638
x60=−76.186903206326x_{60} = -76.186903206326
x61=−5.54276920324851x_{61} = -5.54276920324851
x62=−35.349989019305x_{62} = -35.349989019305
x63=−54.1970859376957x_{63} = -54.1970859376957
x64=0x_{64} = 0
x65=3.98933285620662x_{65} = 3.98933285620662
x66=−55.7677523585655x_{66} = -55.7677523585655
x67=24.3576053587789x_{67} = 24.3576053587789
x68=−40.0615464074251x_{68} = -40.0615464074251
x69=30.6386872667848x_{69} = 30.6386872667848
x70=96.6065618907118x_{70} = 96.6065618907118
x71=−13.3704580073937x_{71} = -13.3704580073937
x72=−24.3576053587789x_{72} = -24.3576053587789
x73=−84.0405782018796x_{73} = -84.0405782018796
x74=11.8021423864902x_{74} = 11.8021423864902
x75=−32.2090858609196x_{75} = -32.2090858609196
x76=5.54276920324851x_{76} = 5.54276920324851
x77=91.8943056074308x_{77} = 91.8943056074308
x78=−49.4851361441979x_{78} = -49.4851361441979
x79=90.3235565896713x_{79} = 90.3235565896713
x80=−19.6476754907365x_{80} = -19.6476754907365
x81=−10.2345837013705x_{81} = -10.2345837013705
x82=68.3332986887281x_{82} = 68.3332986887281
x83=27.4980262787482x_{83} = 27.4980262787482
x84=82.469838530885x_{84} = 82.469838530885
x85=−90.3235565896713x_{85} = -90.3235565896713
x86=85.6113199516972x_{86} = 85.6113199516972
x87=40.0615464074251x_{87} = 40.0615464074251
Signos de extremos en los puntos:
(-93.46505621522485, -23.3659297114269)

(-82.46983853088497, 20.6170807167555)

(-33.7795214194042, -8.44395539012157)

(60.47979209952698, 15.1194313498549)

(-77.75763325046901, -19.4390064352756)

(-11.802142386490203, -2.94789133120417)

(25.927780364575984, 6.48074015627518)

(46.3438858860085, -11.5852972235074)

(55.7677523585655, -13.94137776374)

(-16.508500516678623, 4.12523346635567)

(-18.07798320976836, -4.51776817153026)

(-62.050483798650674, -15.5121173520054)

(-3.9893328562066204, 0.989590921448473)

(-71.47473055177714, -17.8682454365327)

(74.61617595254046, -18.6536251922476)

(98.17731681570837, 24.5440109084885)

(71.47473055177714, -17.8682454365327)

(-27.498026278748195, -6.8733704062122)

(-57.338425895341494, 14.334061495186)

(-46.3438858860085, -11.5852972235074)

(99.74807304456543, -24.936704977785)

(-38.49100466520936, 9.62193939103296)

(7.103718362595594, 1.77154676422179)

(-25.927780364575984, 6.48074015627518)

(41.63210735204432, 10.4072762966192)

(88.75280924635904, 22.1878502184399)

(-98.17731681570837, 24.5440109084885)

(-63.62118066326382, 15.9048039999471)

(19.647675490736493, 4.91032912586147)

(-41.63210735204432, 10.4072762966192)

(-91.89430560743084, 22.9732363448112)

(62.050483798650674, -15.5121173520054)

(84.04057820187961, -21.0097727161598)

(54.197085937695654, 13.5486949219612)

(-2.456590219717442, -0.601808736214034)

(47.91450540450974, 11.9779742010582)

(32.20908586091958, 8.05130141742191)

(-1.014378919055217, 0.227463217644957)

(52.6264272696834, -13.156013049496)

(77.75763325046901, -19.4390064352756)

(-69.90401281398711, 17.4755561790741)

(66.76258843092853, 16.6901790509024)

(-99.74807304456543, -24.936704977785)

(8.66818896199168, -2.16345107598231)

(16.508500516678623, 4.12523346635567)

(-47.91450540450974, 11.9779742010582)

(69.90401281398711, 17.4755561790741)

(-60.47979209952698, 15.1194313498549)

(38.49100466520936, 9.62193939103296)

(-79.32836591924193, 19.8316975593184)

(10.234583701370475, 2.55559800728153)

(76.186903206326, 19.0463156393455)

(33.7795214194042, -8.44395539012157)

(2.456590219717442, -0.601808736214034)

(-85.61131995169717, 21.40246497544)

(18.07798320976836, -4.51776817153026)

(49.48513614419785, -12.3706525816398)

(-68.33329868872808, -17.0828673732396)

(63.62118066326382, 15.9048039999471)

(-76.186903206326, 19.0463156393455)

(-5.542769203248511, -1.38008850199125)

(-35.349989019305, 8.83661337019914)

(-54.197085937695654, 13.5486949219612)

(0, 0)

(3.9893328562066204, 0.989590921448473)

(-55.7677523585655, -13.94137776374)

(24.357605358778862, -6.08811877817099)

(-40.061546407425126, -10.0146066432074)

(30.638687266784828, -7.65865206805957)

(96.6065618907118, -24.1513170021851)

(-13.370458007393655, 3.34027970808717)

(-24.357605358778862, -6.08811877817099)

(-84.04057820187961, -21.0097727161598)

(11.802142386490203, -2.94789133120417)

(-32.20908586091958, 8.05130141742191)

(5.542769203248511, -1.38008850199125)

(91.89430560743084, 22.9732363448112)

(-49.48513614419785, -12.3706525816398)

(90.32355658967134, -22.5805431769646)

(-19.647675490736493, 4.91032912586147)

(-10.234583701370475, 2.55559800728153)

(68.33329868872808, -17.0828673732396)

(27.498026278748195, -6.8733704062122)

(82.46983853088497, 20.6170807167555)

(-90.32355658967134, -22.5805431769646)

(85.61131995169717, 21.40246497544)

(40.061546407425126, -10.0146066432074)


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

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⁡(2x)4)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{x \sin{\left(2 x \right)}}{4}\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⁡(2x)4)=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{x \sin{\left(2 x \right)}}{4}\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(2*x))/4, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(2x)4)=⟨−14,14⟩\lim_{x \to -\infty}\left(\frac{\sin{\left(2 x \right)}}{4}\right) = \left\langle - \frac{1}{4}, \frac{1}{4}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−14,14⟩xy = \left\langle - \frac{1}{4}, \frac{1}{4}\right\rangle x
lim⁡x→∞(sin⁡(2x)4)=⟨−14,14⟩\lim_{x \to \infty}\left(\frac{\sin{\left(2 x \right)}}{4}\right) = \left\langle - \frac{1}{4}, \frac{1}{4}\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−14,14⟩xy = \left\langle - \frac{1}{4}, \frac{1}{4}\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⁡(2x)4=xsin⁡(2x)4\frac{x \sin{\left(2 x \right)}}{4} = \frac{x \sin{\left(2 x \right)}}{4}
- Sí
xsin⁡(2x)4=−xsin⁡(2x)4\frac{x \sin{\left(2 x \right)}}{4} = - \frac{x \sin{\left(2 x \right)}}{4}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор