Sr Examen

Otras calculadoras

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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        2         
f(x) = x *sin(2*x)
f(x)=x2sin⁡(2x)f{\left(x \right)} = x^{2} \sin{\left(2 x \right)} 
f = x^2*sin(2*x)
Gráfico de la función
02468-8-6-4-2-1010-200200
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:
x2sin⁡(2x)=0x^{2} \sin{\left(2 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}
x4=πx_{4} = \pi
Solución numérica
x1=73.8274273593601x_{1} = 73.8274273593601
x2=34.5575191894877x_{2} = 34.5575191894877
x3=−4.71238898038469x_{3} = -4.71238898038469
x4=14.1371669411541x_{4} = 14.1371669411541
x5=58.1194640914112x_{5} = 58.1194640914112
x6=92.6769832808989x_{6} = 92.6769832808989
x7=−43.9822971502571x_{7} = -43.9822971502571
x8=28.2743338823081x_{8} = 28.2743338823081
x9=−103.672557568463x_{9} = -103.672557568463
x10=36.1283155162826x_{10} = 36.1283155162826
x11=−7.85398163397448x_{11} = -7.85398163397448
x12=−58.1194640914112x_{12} = -58.1194640914112
x13=86.3937979737193x_{13} = 86.3937979737193
x14=51.8362787842316x_{14} = 51.8362787842316
x15=−42.4115008234622x_{15} = -42.4115008234622
x16=−89.5353906273091x_{16} = -89.5353906273091
x17=59.6902604182061x_{17} = 59.6902604182061
x18=1.5707963267949x_{18} = 1.5707963267949
x19=56.5486677646163x_{19} = 56.5486677646163
x20=100.530964914873x_{20} = 100.530964914873
x21=15.707963267949x_{21} = 15.707963267949
x22=−15.707963267949x_{22} = -15.707963267949
x23=−37.6991118430775x_{23} = -37.6991118430775
x24=−72.2566310325652x_{24} = -72.2566310325652
x25=65.9734457253857x_{25} = 65.9734457253857
x26=−36.1283155162826x_{26} = -36.1283155162826
x27=12.5663706143592x_{27} = 12.5663706143592
x28=21.9911485751286x_{28} = 21.9911485751286
x29=−3.14159265358979x_{29} = -3.14159265358979
x30=−6.28318530717959x_{30} = -6.28318530717959
x31=−65.9734457253857x_{31} = -65.9734457253857
x32=81.6814089933346x_{32} = 81.6814089933346
x33=−14.1371669411541x_{33} = -14.1371669411541
x34=80.1106126665397x_{34} = 80.1106126665397
x35=95.8185759344887x_{35} = 95.8185759344887
x36=−64.4026493985908x_{36} = -64.4026493985908
x37=78.5398163397448x_{37} = 78.5398163397448
x38=45.553093477052x_{38} = 45.553093477052
x39=−17.2787595947439x_{39} = -17.2787595947439
x40=4.71238898038469x_{40} = 4.71238898038469
x41=20.4203522483337x_{41} = 20.4203522483337
x42=−23.5619449019235x_{42} = -23.5619449019235
x43=−51.8362787842316x_{43} = -51.8362787842316
x44=−29.845130209103x_{44} = -29.845130209103
x45=7.85398163397448x_{45} = 7.85398163397448
x46=−95.8185759344887x_{46} = -95.8185759344887
x47=−97.3893722612836x_{47} = -97.3893722612836
x48=−39.2699081698724x_{48} = -39.2699081698724
x49=37.6991118430775x_{49} = 37.6991118430775
x50=−21.9911485751286x_{50} = -21.9911485751286
x51=3.14159265358979x_{51} = 3.14159265358979
x52=−50.2654824574367x_{52} = -50.2654824574367
x53=−94.2477796076938x_{53} = -94.2477796076938
x54=−53.4070751110265x_{54} = -53.4070751110265
x55=23.5619449019235x_{55} = 23.5619449019235
x56=−86.3937979737193x_{56} = -86.3937979737193
x57=−61.261056745001x_{57} = -61.261056745001
x58=−67.5442420521806x_{58} = -67.5442420521806
x59=−59.6902604182061x_{59} = -59.6902604182061
x60=−45.553093477052x_{60} = -45.553093477052
x61=−87.9645943005142x_{61} = -87.9645943005142
x62=−83.2522053201295x_{62} = -83.2522053201295
x63=−28.2743338823081x_{63} = -28.2743338823081
x64=42.4115008234622x_{64} = 42.4115008234622
x65=67.5442420521806x_{65} = 67.5442420521806
x66=6.28318530717959x_{66} = 6.28318530717959
x67=−73.8274273593601x_{67} = -73.8274273593601
x68=0x_{68} = 0
x69=−1.5707963267949x_{69} = -1.5707963267949
x70=87.9645943005142x_{70} = 87.9645943005142
x71=43.9822971502571x_{71} = 43.9822971502571
x72=70.6858347057703x_{72} = 70.6858347057703
x73=−75.398223686155x_{73} = -75.398223686155
x74=−9.42477796076938x_{74} = -9.42477796076938
x75=−31.4159265358979x_{75} = -31.4159265358979
x76=72.2566310325652x_{76} = 72.2566310325652
x77=26.7035375555132x_{77} = 26.7035375555132
x78=94.2477796076938x_{78} = 94.2477796076938
x79=48.6946861306418x_{79} = 48.6946861306418
x80=−81.6814089933346x_{80} = -81.6814089933346
x81=−20.4203522483337x_{81} = -20.4203522483337
x82=−80.1106126665397x_{82} = -80.1106126665397
x83=64.4026493985908x_{83} = 64.4026493985908
x84=29.845130209103x_{84} = 29.845130209103
x85=89.5353906273091x_{85} = 89.5353906273091
x86=50.2654824574367x_{86} = 50.2654824574367
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^2*sin(2*x).
02sin⁡(0⋅2)0^{2} \sin{\left(0 \cdot 2 \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⁡(2x)+2xsin⁡(2x)=02 x^{2} \cos{\left(2 x \right)} + 2 x \sin{\left(2 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−44.7788594413622x_{1} = -44.7788594413622
x2=25.9374070267134x_{2} = 25.9374070267134
x3=−18.0917665453763x_{3} = -18.0917665453763
x4=−63.6251091208926x_{4} = -63.6251091208926
x5=−84.0435524991391x_{5} = -84.0435524991391
x6=−10.2587614549708x_{6} = -10.2587614549708
x7=−41.6381085824888x_{7} = -41.6381085824888
x8=−55.7722336752062x_{8} = -55.7722336752062
x9=35.3570550332742x_{9} = 35.3570550332742
x10=−54.2016970313842x_{10} = -54.2016970313842
x11=−5.58635293416499x_{11} = -5.58635293416499
x12=55.7722336752062x_{12} = 55.7722336752062
x13=63.6251091208926x_{13} = 63.6251091208926
x14=−90.3263240494369x_{14} = -90.3263240494369
x15=−3.16473361148914⋅10−7x_{15} = -3.16473361148914 \cdot 10^{-7}
x16=33.7869153354295x_{16} = 33.7869153354295
x17=90.3263240494369x_{17} = 90.3263240494369
x18=68.3369563786298x_{18} = 68.3369563786298
x19=2.54349254705114x_{19} = 2.54349254705114
x20=−21.2292853858495x_{20} = -21.2292853858495
x21=69.9075883539626x_{21} = 69.9075883539626
x22=41.6381085824888x_{22} = 41.6381085824888
x23=−85.6142396947314x_{23} = -85.6142396947314
x24=7.13817645916824x_{24} = 7.13817645916824
x25=85.6142396947314x_{25} = 85.6142396947314
x26=8.69662198229738x_{26} = 8.69662198229738
x27=−57.3427845371101x_{27} = -57.3427845371101
x28=−60.4839244878466x_{28} = -60.4839244878466
x29=74.6195257807054x_{29} = 74.6195257807054
x30=−47.9197205706165x_{30} = -47.9197205706165
x31=38.4974949445838x_{31} = 38.4974949445838
x32=−40.0677825970372x_{32} = -40.0677825970372
x33=71.4782275499213x_{33} = 71.4782275499213
x34=−93.4677306800165x_{34} = -93.4677306800165
x35=49.4901859325761x_{35} = 49.4901859325761
x36=−79.3315168346756x_{36} = -79.3315168346756
x37=40.0677825970372x_{37} = 40.0677825970372
x38=−3.42962943093331⋅10−7x_{38} = -3.42962943093331 \cdot 10^{-7}
x39=0x_{39} = 0
x40=−32.2168395518658x_{40} = -32.2168395518658
x41=−24.3678503974527x_{41} = -24.3678503974527
x42=60.4839244878466x_{42} = 60.4839244878466
x43=82.4728694594266x_{43} = 82.4728694594266
x44=−82.4728694594266x_{44} = -82.4728694594266
x45=76.1901839979235x_{45} = 76.1901839979235
x46=−71.4782275499213x_{46} = -71.4782275499213
x47=30.6468374831214x_{47} = 30.6468374831214
x48=−4.04808180161146x_{48} = -4.04808180161146
x49=84.0435524991391x_{49} = 84.0435524991391
x50=99.7505790857949x_{50} = 99.7505790857949
x51=46.3492776216985x_{51} = 46.3492776216985
x52=91.8970257752571x_{52} = 91.8970257752571
x53=−13.3890435377793x_{53} = -13.3890435377793
x54=−68.3369563786298x_{54} = -68.3369563786298
x55=−46.3492776216985x_{55} = -46.3492776216985
x56=−69.9075883539626x_{56} = -69.9075883539626
x57=95.0384386061415x_{57} = 95.0384386061415
x58=−25.9374070267134x_{58} = -25.9374070267134
x59=4.04808180161146x_{59} = 4.04808180161146
x60=16.5235843473527x_{60} = 16.5235843473527
x61=11.8231619098018x_{61} = 11.8231619098018
x62=88.7556256712795x_{62} = 88.7556256712795
x63=−49.4901859325761x_{63} = -49.4901859325761
x64=18.0917665453763x_{64} = 18.0917665453763
x65=−98.1798629425939x_{65} = -98.1798629425939
x66=98.1798629425939x_{66} = 98.1798629425939
x67=19.6603640661261x_{67} = 19.6603640661261
x68=−33.7869153354295x_{68} = -33.7869153354295
x69=−11.8231619098018x_{69} = -11.8231619098018
x70=−99.7505790857949x_{70} = -99.7505790857949
x71=−62.0545116429054x_{71} = -62.0545116429054
x72=−35.3570550332742x_{72} = -35.3570550332742
x73=−2.54349254705114x_{73} = -2.54349254705114
x74=62.0545116429054x_{74} = 62.0545116429054
x75=−19.6603640661261x_{75} = -19.6603640661261
x76=5.58635293416499x_{76} = 5.58635293416499
x77=−91.8970257752571x_{77} = -91.8970257752571
x78=32.2168395518658x_{78} = 32.2168395518658
x79=24.3678503974527x_{79} = 24.3678503974527
x80=65.1957161761796x_{80} = 65.1957161761796
x81=96.6091494063022x_{81} = 96.6091494063022
x82=27.5071048394191x_{82} = 27.5071048394191
x83=−76.1901839979235x_{83} = -76.1901839979235
x84=−27.5071048394191x_{84} = -27.5071048394191
x85=47.9197205706165x_{85} = 47.9197205706165
x86=−77.760847792972x_{86} = -77.760847792972
x87=54.2016970313842x_{87} = 54.2016970313842
x88=77.760847792972x_{88} = 77.760847792972
x89=52.6311758774383x_{89} = 52.6311758774383
x90=−38.4974949445838x_{90} = -38.4974949445838
x91=10.2587614549708x_{91} = 10.2587614549708
Signos de extremos en los puntos:
(-44.77885944136221, -2004.64643981036)

(25.937407026713387, 672.24963999419)

(-18.09176654537629, 326.813159519034)

(-63.62510912089261, -4047.65460326123)

(-84.04355249913914, 7062.81876976048)

(-10.258761454970845, -104.745721818108)

(-41.63810858248877, -1733.23230251961)

(-55.772233675206174, 3110.04216964728)

(35.35705503327425, 1249.62164039704)

(-54.2016970313842, -2937.32408869126)

(-5.586352934164992, 30.719043378479)

(55.772233675206174, -3110.04216964728)

(63.62510912089261, 4047.65460326123)

(-90.32632404943689, 8158.34486224158)

(-3.1647336114891426e-07, -6.33930247556382e-20)

(33.7869153354295, -1141.05597614296)

(90.32632404943689, -8158.34486224158)

(68.3369563786298, -4669.43968738125)

(2.543492547051135, -6.02074005576708)

(-21.229285385849522, 450.183388529538)

(69.90758835396257, 4886.57098618708)

(41.63810858248877, 1733.23230251961)

(-85.6142396947314, -7329.29808966213)

(7.138176459168239, 50.4608044704652)

(85.6142396947314, 7329.29808966213)

(8.696621982297376, -75.1361381644989)

(-57.3427845371101, -3287.69505248487)

(-60.48392448784664, -3657.80522393468)

(74.61952578070536, -5567.57369507552)

(-47.91972057061652, -2295.79978281294)

(38.4974949445838, 1481.55736989275)

(-40.06778259703722, 1604.92743570495)

(71.47822754992126, -5108.63708706427)

(-93.46773068001654, 8735.71672139277)

(49.49018593257614, -2448.7786566952)

(-79.33151683467557, -6292.98962286791)

(40.06778259703722, -1604.92743570495)

(-3.4296294309333057e-07, -8.06810585778905e-20)

(0, 0)

(-32.21683955186578, -1037.4251117187)

(-24.367850397452695, 593.292763641772)

(60.48392448784664, 3657.80522393468)

(82.47286945942662, 6801.27425199754)

(-82.47286945942662, -6801.27425199754)

(76.1901839979235, 5804.44420222827)

(-71.47822754992126, 5108.63708706427)

(30.64683748312145, -938.729046626741)

(-4.048081801611461, -15.9087454878886)

(84.04355249913914, -7062.81876976048)

(99.75057908579493, -9949.67806563604)

(46.34927762169846, -2147.75571054583)

(91.89702577525712, 8444.56339073853)

(-13.389043537779253, -178.768569037428)

(-68.3369563786298, 4669.43968738125)

(-46.34927762169846, 2147.75571054583)

(-69.90758835396257, -4886.57098618708)

(95.0384386061415, 9031.80485420714)

(-25.937407026713387, -672.24963999419)

(4.048081801611461, 15.9087454878886)

(16.52358434735268, 272.530208986636)

(11.82316190980181, -139.289824302256)

(88.75562567127952, 7877.06113589882)

(-49.49018593257614, 2448.7786566952)

(18.09176654537629, -326.813159519034)

(-98.17986294259394, -9638.78552632646)

(98.17986294259394, 9638.78552632646)

(19.660364066126064, 386.030883296424)

(-33.7869153354295, 1141.05597614296)

(-11.82316190980181, 139.289824302256)

(-99.75057908579493, 9949.67806563604)

(-62.054511642905446, 3850.26251260173)

(-35.35705503327425, -1249.62164039704)

(-2.543492547051135, 6.02074005576708)

(62.054511642905446, -3850.26251260173)

(-19.660364066126064, -386.030883296424)

(5.586352934164992, -30.719043378479)

(-91.89702577525712, -8444.56339073853)

(32.21683955186578, 1037.4251117187)

(24.367850397452695, -593.292763641772)

(65.19571617617964, -4249.98149593298)

(96.60914940630224, -9332.82778918424)

(27.50710483941906, -756.141311713221)

(-76.1901839979235, -5804.44420222827)

(-27.50710483941906, 756.141311713221)

(47.91972057061652, 2295.79978281294)

(-77.76084779297203, 6046.24951149001)

(54.2016970313842, 2937.32408869126)

(77.76084779297203, -6046.24951149001)

(52.63117587743834, -2769.54080957821)

(-38.4974949445838, -1481.55736989275)

(10.258761454970845, 104.745721818108)


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=−44.7788594413622x_{1} = -44.7788594413622
x2=−63.6251091208926x_{2} = -63.6251091208926
x3=−10.2587614549708x_{3} = -10.2587614549708
x4=−41.6381085824888x_{4} = -41.6381085824888
x5=−54.2016970313842x_{5} = -54.2016970313842
x6=55.7722336752062x_{6} = 55.7722336752062
x7=33.7869153354295x_{7} = 33.7869153354295
x8=90.3263240494369x_{8} = 90.3263240494369
x9=68.3369563786298x_{9} = 68.3369563786298
x10=2.54349254705114x_{10} = 2.54349254705114
x11=−85.6142396947314x_{11} = -85.6142396947314
x12=8.69662198229738x_{12} = 8.69662198229738
x13=−57.3427845371101x_{13} = -57.3427845371101
x14=−60.4839244878466x_{14} = -60.4839244878466
x15=74.6195257807054x_{15} = 74.6195257807054
x16=−47.9197205706165x_{16} = -47.9197205706165
x17=71.4782275499213x_{17} = 71.4782275499213
x18=49.4901859325761x_{18} = 49.4901859325761
x19=−79.3315168346756x_{19} = -79.3315168346756
x20=40.0677825970372x_{20} = 40.0677825970372
x21=−32.2168395518658x_{21} = -32.2168395518658
x22=−82.4728694594266x_{22} = -82.4728694594266
x23=30.6468374831214x_{23} = 30.6468374831214
x24=−4.04808180161146x_{24} = -4.04808180161146
x25=84.0435524991391x_{25} = 84.0435524991391
x26=99.7505790857949x_{26} = 99.7505790857949
x27=46.3492776216985x_{27} = 46.3492776216985
x28=−13.3890435377793x_{28} = -13.3890435377793
x29=−69.9075883539626x_{29} = -69.9075883539626
x30=−25.9374070267134x_{30} = -25.9374070267134
x31=11.8231619098018x_{31} = 11.8231619098018
x32=18.0917665453763x_{32} = 18.0917665453763
x33=−98.1798629425939x_{33} = -98.1798629425939
x34=−35.3570550332742x_{34} = -35.3570550332742
x35=62.0545116429054x_{35} = 62.0545116429054
x36=−19.6603640661261x_{36} = -19.6603640661261
x37=5.58635293416499x_{37} = 5.58635293416499
x38=−91.8970257752571x_{38} = -91.8970257752571
x39=24.3678503974527x_{39} = 24.3678503974527
x40=65.1957161761796x_{40} = 65.1957161761796
x41=96.6091494063022x_{41} = 96.6091494063022
x42=27.5071048394191x_{42} = 27.5071048394191
x43=−76.1901839979235x_{43} = -76.1901839979235
x44=77.760847792972x_{44} = 77.760847792972
x45=52.6311758774383x_{45} = 52.6311758774383
x46=−38.4974949445838x_{46} = -38.4974949445838
Puntos máximos de la función:
x46=25.9374070267134x_{46} = 25.9374070267134
x46=−18.0917665453763x_{46} = -18.0917665453763
x46=−84.0435524991391x_{46} = -84.0435524991391
x46=−55.7722336752062x_{46} = -55.7722336752062
x46=35.3570550332742x_{46} = 35.3570550332742
x46=−5.58635293416499x_{46} = -5.58635293416499
x46=63.6251091208926x_{46} = 63.6251091208926
x46=−90.3263240494369x_{46} = -90.3263240494369
x46=−21.2292853858495x_{46} = -21.2292853858495
x46=69.9075883539626x_{46} = 69.9075883539626
x46=41.6381085824888x_{46} = 41.6381085824888
x46=7.13817645916824x_{46} = 7.13817645916824
x46=85.6142396947314x_{46} = 85.6142396947314
x46=38.4974949445838x_{46} = 38.4974949445838
x46=−40.0677825970372x_{46} = -40.0677825970372
x46=−93.4677306800165x_{46} = -93.4677306800165
x46=−24.3678503974527x_{46} = -24.3678503974527
x46=60.4839244878466x_{46} = 60.4839244878466
x46=82.4728694594266x_{46} = 82.4728694594266
x46=76.1901839979235x_{46} = 76.1901839979235
x46=−71.4782275499213x_{46} = -71.4782275499213
x46=91.8970257752571x_{46} = 91.8970257752571
x46=−68.3369563786298x_{46} = -68.3369563786298
x46=−46.3492776216985x_{46} = -46.3492776216985
x46=95.0384386061415x_{46} = 95.0384386061415
x46=4.04808180161146x_{46} = 4.04808180161146
x46=16.5235843473527x_{46} = 16.5235843473527
x46=88.7556256712795x_{46} = 88.7556256712795
x46=−49.4901859325761x_{46} = -49.4901859325761
x46=98.1798629425939x_{46} = 98.1798629425939
x46=19.6603640661261x_{46} = 19.6603640661261
x46=−33.7869153354295x_{46} = -33.7869153354295
x46=−11.8231619098018x_{46} = -11.8231619098018
x46=−99.7505790857949x_{46} = -99.7505790857949
x46=−62.0545116429054x_{46} = -62.0545116429054
x46=−2.54349254705114x_{46} = -2.54349254705114
x46=32.2168395518658x_{46} = 32.2168395518658
x46=−27.5071048394191x_{46} = -27.5071048394191
x46=47.9197205706165x_{46} = 47.9197205706165
x46=−77.760847792972x_{46} = -77.760847792972
x46=54.2016970313842x_{46} = 54.2016970313842
x46=10.2587614549708x_{46} = 10.2587614549708
Decrece en los intervalos
[99.7505790857949,∞)\left[99.7505790857949, \infty\right)
Crece en los intervalos
(−∞,−98.1798629425939]\left(-\infty, -98.1798629425939\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
2(−2x2sin⁡(2x)+4xcos⁡(2x)+sin⁡(2x))=02 \left(- 2 x^{2} \sin{\left(2 x \right)} + 4 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=81.6936483190068x_{1} = 81.6936483190068
x2=−37.725603538235x_{2} = -37.725603538235
x3=29.8785678341332x_{3} = 29.8785678341332
x4=28.3096209125642x_{4} = 28.3096209125642
x5=−80.1230918433114x_{5} = -80.1230918433114
x6=−1.99722235787071x_{6} = -1.99722235787071
x7=58.1366607029306x_{7} = 58.1366607029306
x8=−28.3096209125642x_{8} = -28.3096209125642
x9=89.5465568422098x_{9} = 89.5465568422098
x10=65.9885969598317x_{10} = 65.9885969598317
x11=36.1559558691412x_{11} = 36.1559558691412
x12=34.5864121653729x_{12} = 34.5864121653729
x13=−9.52877807686926x_{13} = -9.52877807686926
x14=−95.829010241065x_{14} = -95.829010241065
x15=59.7070049585797x_{15} = 59.7070049585797
x16=67.5590412185413x_{16} = 67.5590412185413
x17=3.41607287346559x_{17} = 3.41607287346559
x18=−17.3362830681118x_{18} = -17.3362830681118
x19=−86.4053700369695x_{19} = -86.4053700369695
x20=87.9759598185177x_{20} = 87.9759598185177
x21=−6.43557028921917x_{21} = -6.43557028921917
x22=−36.1559558691412x_{22} = -36.1559558691412
x23=−29.8785678341332x_{23} = -29.8785678341332
x24=−22.0364503381404x_{24} = -22.0364503381404
x25=−76.9820082350865x_{25} = -76.9820082350865
x26=7.97773271487555x_{26} = 7.97773271487555
x27=−3.41607287346559x_{27} = -3.41607287346559
x28=−15.7711591859629x_{28} = -15.7711591859629
x29=−59.7070049585797x_{29} = -59.7070049585797
x30=−50.2853624109229x_{30} = -50.2853624109229
x31=95.829010241065x_{31} = 95.829010241065
x32=−31.4476986173355x_{32} = -31.4476986173355
x33=−81.6936483190068x_{33} = -81.6936483190068
x34=20.4691095857577x_{34} = 20.4691095857577
x35=0x_{35} = 0
x36=−45.5750265225894x_{36} = -45.5750265225894
x37=100.540910295039x_{37} = 100.540910295039
x38=73.8409679079427x_{38} = 73.8409679079427
x39=26.7408899940119x_{39} = 26.7408899940119
x40=−72.2704657365879x_{40} = -72.2704657365879
x41=−20.4691095857577x_{41} = -20.4691095857577
x42=45.5750265225894x_{42} = 45.5750265225894
x43=−26.7408899940119x_{43} = -26.7408899940119
x44=−23.6042469916597x_{44} = -23.6042469916597
x45=−73.8409679079427x_{45} = -73.8409679079427
x46=−64.418169852971x_{46} = -64.418169852971
x47=−53.4257872025938x_{47} = -53.4257872025938
x48=23.6042469916597x_{48} = 23.6042469916597
x49=−75.4114823236753x_{49} = -75.4114823236753
x50=−14.2072653485813x_{50} = -14.2072653485813
x51=−87.9759598185177x_{51} = -87.9759598185177
x52=92.6877711443551x_{52} = 92.6877711443551
x53=80.1230918433114x_{53} = 80.1230918433114
x54=70.6999766247443x_{54} = 70.6999766247443
x55=12.6450452480401x_{55} = 12.6450452480401
x56=−61.2773723625442x_{56} = -61.2773723625442
x57=9.52877807686926x_{57} = 9.52877807686926
x58=56.5663415203821x_{58} = 56.5663415203821
x59=72.2704657365879x_{59} = 72.2704657365879
x60=37.725603538235x_{60} = 37.725603538235
x61=86.4053700369695x_{61} = 86.4053700369695
x62=1.99722235787071x_{62} = 1.99722235787071
x63=−42.4350553508244x_{63} = -42.4350553508244
x64=−51.8555571480304x_{64} = -51.8555571480304
x65=42.4350553508244x_{65} = 42.4350553508244
x66=−83.2642138383723x_{66} = -83.2642138383723
x67=50.2853624109229x_{67} = 50.2853624109229
x68=51.8555571480304x_{68} = 51.8555571480304
x69=64.418169852971x_{69} = 64.418169852971
x70=48.7152063990254x_{70} = 48.7152063990254
x71=94.258387748226x_{71} = 94.258387748226
x72=−97.3996383381479x_{72} = -97.3996383381479
x73=14.2072653485813x_{73} = 14.2072653485813
x74=44.0050120637787x_{74} = 44.0050120637787
x75=−65.9885969598317x_{75} = -65.9885969598317
x76=6.43557028921917x_{76} = 6.43557028921917
x77=−94.258387748226x_{77} = -94.258387748226
x78=22.0364503381404x_{78} = 22.0364503381404
x79=−102.111553670193x_{79} = -102.111553670193
x80=−39.2953427597448x_{80} = -39.2953427597448
x81=−67.5590412185413x_{81} = -67.5590412185413
x82=−7.97773271487555x_{82} = -7.97773271487555
x83=−44.0050120637787x_{83} = -44.0050120637787
x84=15.7711591859629x_{84} = 15.7711591859629
x85=−89.5465568422098x_{85} = -89.5465568422098
x86=78.5525449532803x_{86} = 78.5525449532803
x87=−58.1366607029306x_{87} = -58.1366607029306

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
[95.829010241065,∞)\left[95.829010241065, \infty\right)
Convexa en los intervalos
(−∞,−102.111553670193]\left(-\infty, -102.111553670193\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x2sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{2} \sin{\left(2 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→∞(x2sin⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{2} \sin{\left(2 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^2*sin(2*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(xsin⁡(2x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(xsin⁡(2x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \sin{\left(2 x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\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:
x2sin⁡(2x)=−x2sin⁡(2x)x^{2} \sin{\left(2 x \right)} = - x^{2} \sin{\left(2 x \right)}
- No
x2sin⁡(2x)=x2sin⁡(2x)x^{2} \sin{\left(2 x \right)} = x^{2} \sin{\left(2 x \right)}
- Sí
es decir, función
es
impar
Gráfico
Gráfico de la función y = x^2*sin(2*x)
    © Sr Examen – Калькулятор