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Trazado el gráfico de la función/ (2*x+1)*sin(x)

Gráfico de la función y = (2*x+1)*sin(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = (2*x + 1)*sin(x)
f(x)=(2x+1)sin⁡(x)f{\left(x \right)} = \left(2 x + 1\right) \sin{\left(x \right)} 
f = (2*x + 1)*sin(x)
Gráfico de la función
02468-8-6-4-2-1010-5050
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:
(2x+1)sin⁡(x)=0\left(2 x + 1\right) \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−12x_{1} = - \frac{1}{2}
x2=0x_{2} = 0
x3=πx_{3} = \pi
Solución numérica
x1=69.1150383789755x_{1} = 69.1150383789755
x2=65.9734457253857x_{2} = 65.9734457253857
x3=−91.106186954104x_{3} = -91.106186954104
x4=−59.6902604182061x_{4} = -59.6902604182061
x5=−21.9911485751286x_{5} = -21.9911485751286
x6=12.5663706143592x_{6} = 12.5663706143592
x7=21.9911485751286x_{7} = 21.9911485751286
x8=−69.1150383789755x_{8} = -69.1150383789755
x9=−100.530964914873x_{9} = -100.530964914873
x10=3.14159265358979x_{10} = 3.14159265358979
x11=−3.14159265358979x_{11} = -3.14159265358979
x12=−25.1327412287183x_{12} = -25.1327412287183
x13=−15.707963267949x_{13} = -15.707963267949
x14=−53.4070751110265x_{14} = -53.4070751110265
x15=−72.2566310325652x_{15} = -72.2566310325652
x16=84.8230016469244x_{16} = 84.8230016469244
x17=−81.6814089933346x_{17} = -81.6814089933346
x18=−94.2477796076938x_{18} = -94.2477796076938
x19=−0.5x_{19} = -0.5
x20=18.8495559215388x_{20} = 18.8495559215388
x21=−65.9734457253857x_{21} = -65.9734457253857
x22=94.2477796076938x_{22} = 94.2477796076938
x23=9.42477796076938x_{23} = 9.42477796076938
x24=−40.8407044966673x_{24} = -40.8407044966673
x25=34.5575191894877x_{25} = 34.5575191894877
x26=0x_{26} = 0
x27=97.3893722612836x_{27} = 97.3893722612836
x28=53.4070751110265x_{28} = 53.4070751110265
x29=−62.8318530717959x_{29} = -62.8318530717959
x30=59.6902604182061x_{30} = 59.6902604182061
x31=−28.2743338823081x_{31} = -28.2743338823081
x32=−56.5486677646163x_{32} = -56.5486677646163
x33=91.106186954104x_{33} = 91.106186954104
x34=15.707963267949x_{34} = 15.707963267949
x35=−18.8495559215388x_{35} = -18.8495559215388
x36=6.28318530717959x_{36} = 6.28318530717959
x37=56.5486677646163x_{37} = 56.5486677646163
x38=87.9645943005142x_{38} = 87.9645943005142
x39=31.4159265358979x_{39} = 31.4159265358979
x40=−1036.72557568463x_{40} = -1036.72557568463
x41=25.1327412287183x_{41} = 25.1327412287183
x42=43.9822971502571x_{42} = 43.9822971502571
x43=−47.1238898038469x_{43} = -47.1238898038469
x44=72.2566310325652x_{44} = 72.2566310325652
x45=−34.5575191894877x_{45} = -34.5575191894877
x46=−97.3893722612836x_{46} = -97.3893722612836
x47=−50.2654824574367x_{47} = -50.2654824574367
x48=100.530964914873x_{48} = 100.530964914873
x49=81.6814089933346x_{49} = 81.6814089933346
x50=−75.398223686155x_{50} = -75.398223686155
x51=40.8407044966673x_{51} = 40.8407044966673
x52=−9.42477796076938x_{52} = -9.42477796076938
x53=78.5398163397448x_{53} = 78.5398163397448
x54=−87.9645943005142x_{54} = -87.9645943005142
x55=37.6991118430775x_{55} = 37.6991118430775
x56=−78.5398163397448x_{56} = -78.5398163397448
x57=−6.28318530717959x_{57} = -6.28318530717959
x58=50.2654824574367x_{58} = 50.2654824574367
x59=−37.6991118430775x_{59} = -37.6991118430775
x60=−43.9822971502571x_{60} = -43.9822971502571
x61=47.1238898038469x_{61} = 47.1238898038469
x62=28.2743338823081x_{62} = 28.2743338823081
x63=62.8318530717959x_{63} = 62.8318530717959
x64=−31.4159265358979x_{64} = -31.4159265358979
x65=−12.5663706143592x_{65} = -12.5663706143592
x66=75.398223686155x_{66} = 75.398223686155
x67=−84.8230016469244x_{67} = -84.8230016469244
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 (2*x + 1)*sin(x).
(0⋅2+1)sin⁡(0)\left(0 \cdot 2 + 1\right) \sin{\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
(2x+1)cos⁡(x)+2sin⁡(x)=0\left(2 x + 1\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=39.2950316476879x_{1} = 39.2950316476879
x2=92.6877138973701x_{2} = 92.6877138973701
x3=−7.98676475119172x_{3} = -7.98676475119172
x4=−33.0174658775265x_{4} = -33.0174658775265
x5=67.5589341430727x_{5} = 67.5589341430727
x6=−67.5591531543674x_{6} = -67.5591531543674
x7=−80.1231711644351x_{7} = -80.1231711644351
x8=7.97148100902349x_{8} = 7.97148100902349
x9=76.9819255322054x_{9} = 76.9819255322054
x10=83.2641430354848x_{10} = 83.2641430354848
x11=−95.829065529839x_{11} = -95.829065529839
x12=58.1365166573738x_{12} = 58.1365166573738
x13=−39.2956785303244x_{13} = -39.2956785303244
x14=−83.2642872382528x_{14} = -83.2642872382528
x15=−26.7416265193495x_{15} = -26.7416265193495
x16=80.123015436615x_{16} = 80.123015436615
x17=−11.0897262388501x_{17} = -11.0897262388501
x18=20.4680078422429x_{18} = 20.4680078422429
x19=29.8780368458978x_{19} = 29.8780368458978
x20=54.9958888407247x_{20} = 54.9958888407247
x21=−64.4182930958041x_{21} = -64.4182930958041
x22=95.8289566560771x_{22} = 95.8289566560771
x23=−92.6878302742345x_{23} = -92.6878302742345
x24=89.5464955446878x_{24} = 89.5464955446878
x25=51.8553766970605x_{25} = 51.8553766970605
x26=4.89564432915531x_{26} = 4.89564432915531
x27=26.7402314854239x_{27} = 26.7402314854239
x28=48.7150023424838x_{28} = 48.7150023424838
x29=42.4347877496486x_{29} = 42.4347877496486
x30=−36.1563536592178x_{30} = -36.1563536592178
x31=−70.700078740623x_{31} = -70.700078740623
x32=36.1555897201517x_{32} = 36.1555897201517
x33=−4.93419822854993x_{33} = -4.93419822854993
x34=−20.4703846071522x_{34} = -20.4703846071522
x35=61.2772425220152x_{35} = 61.2772425220152
x36=17.3347711916489x_{36} = 17.3347711916489
x37=−29.8791548121049x_{37} = -29.8791548121049
x38=23.6034090301611x_{38} = 23.6034090301611
x39=−14.2099775813926x_{39} = -14.2099775813926
x40=33.0165500205799x_{40} = 33.0165500205799
x41=−76.9820942237331x_{41} = -76.9820942237331
x42=−42.4353425392198x_{42} = -42.4353425392198
x43=−45.5752749499286x_{43} = -45.5752749499286
x44=105.252809626976x_{44} = 105.252809626976
x45=86.4053042434102x_{45} = 86.4053042434102
x46=−86.4054381545562x_{46} = -86.4054381545562
x47=−54.9962192754584x_{47} = -54.9962192754584
x48=−48.715423408888x_{48} = -48.715423408888
x49=70.699878750109x_{49} = 70.699878750109
x50=45.5747939110765x_{50} = 45.5747939110765
x51=−73.8410614412353x_{51} = -73.8410614412353
x52=1.95728275422062x_{52} = 1.95728275422062
x53=11.0817037582484x_{53} = 11.0817037582484
x54=−61.2775087154266x_{54} = -61.2775087154266
x55=98.9702215094204x_{55} = 98.9702215094204
x56=−98.9703235828905x_{56} = -98.9703235828905
x57=−89.5466202277414x_{57} = -89.5466202277414
x58=−23.6051982121417x_{58} = -23.6051982121417
x59=−58.1368123734526x_{59} = -58.1368123734526
x60=−0.247412484885142x_{60} = -0.247412484885142
x61=−17.3380791158534x_{61} = -17.3380791158534
x62=14.2050661771509x_{62} = 14.2050661771509
x63=64.4180522161792x_{63} = 64.4180522161792
x64=73.8408780976001x_{64} = 73.8408780976001
x65=−2.12300090681457x_{65} = -2.12300090681457
x66=−51.8557483406994x_{66} = -51.8557483406994
Signos de extremos en los puntos:
(39.29503164768789, 79.5649464248379)

(92.68771389737012, -186.364697693097)

(-7.986764751191716, 14.8417215197729)

(-33.01746587752653, 65.0042008467558)

(67.5589341430727, -136.103177516664)

(-67.55915315436735, -134.103396587937)

(-80.12317116443509, -159.233784656253)

(7.971481009023492, 16.8261383769496)

(76.98192553220542, 154.950946440755)

(83.26414303548475, 167.516349064459)

(-95.82906552983897, 190.647641945238)

(58.13651665737381, 117.255982814905)

(-39.2956785303244, 77.5655938310989)

(-83.2642872382528, 165.516493293226)

(-26.741626519349484, 52.4451870984841)

(80.12301543661505, -161.233628898112)

(-11.089726238850124, -21.0856482225243)

(20.46800784224292, 41.8884051837394)

(29.878036845897785, -60.7231819016979)

(54.995888840724724, -110.973762715585)

(-64.41829309580406, 127.820944089557)

(95.8289566560771, 192.647533056656)

(-92.68783027423446, -184.364814086894)

(89.54649554468782, 180.081886742599)

(51.85537669706051, 104.691658383599)

(4.895644329155311, -10.6105958362832)

(26.740231485423934, 54.4437896263579)

(48.715002342483764, -98.4096919670489)

(42.4347877496486, -85.8462938347437)

(-36.156353659217835, -71.2846783594538)

(-70.70007874062303, 140.385914650559)

(36.15558972015174, -73.283913689973)

(-4.934198228549927, -8.65112979640719)

(-20.470384607152152, 39.8907890373943)

(61.2772425220152, -123.538301033815)

(17.334771191648883, -35.6136040006033)

(-29.879154812104865, -58.7243014330717)

(23.60340903016115, -48.165383634478)

(-14.209977581392641, 27.3473053378206)

(33.016550020579906, 67.0032839397468)

(-76.98209422373313, 152.951115167863)

(-42.43534253921977, -83.8468490094031)

(-45.575274949928605, 90.1283729743018)

(105.25280962697555, -211.496163874502)

(86.40530424341024, -173.799102851863)

(-86.40543815455618, -171.799236785429)

(-54.99621927545844, -108.974093286877)

(-48.71542340888797, -96.4101132552267)

(70.69987875010902, 142.385714610033)

(45.5747939110765, 92.1278916459743)

(-73.84106144123533, -146.668489856598)

(1.9572827542206206, 4.55206306571846)

(11.081703758248404, -23.0775442284508)

(-61.27750871542658, -121.538567315839)

(98.9702215094204, -198.930390520815)

(-98.97032358289053, -196.930492607311)

(-89.54662022774141, 178.082011445089)

(-23.605198212141747, -46.1671768296396)

(-58.13681237345261, 115.256278640346)

(-0.2474124848851423, -0.123715373656181)

(-17.338079115853432, -33.6169256769223)

(14.20506617715089, 29.3423635380666)

(64.41805221617925, 129.820703137375)

(73.8408780976001, -148.668306470931)

(-2.123000906814568, 2.76354903624568)

(-51.85574834069936, 102.692030199991)


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=92.6877138973701x_{1} = 92.6877138973701
x2=67.5589341430727x_{2} = 67.5589341430727
x3=−67.5591531543674x_{3} = -67.5591531543674
x4=−80.1231711644351x_{4} = -80.1231711644351
x5=80.123015436615x_{5} = 80.123015436615
x6=−11.0897262388501x_{6} = -11.0897262388501
x7=29.8780368458978x_{7} = 29.8780368458978
x8=54.9958888407247x_{8} = 54.9958888407247
x9=−92.6878302742345x_{9} = -92.6878302742345
x10=4.89564432915531x_{10} = 4.89564432915531
x11=48.7150023424838x_{11} = 48.7150023424838
x12=42.4347877496486x_{12} = 42.4347877496486
x13=−36.1563536592178x_{13} = -36.1563536592178
x14=36.1555897201517x_{14} = 36.1555897201517
x15=−4.93419822854993x_{15} = -4.93419822854993
x16=61.2772425220152x_{16} = 61.2772425220152
x17=17.3347711916489x_{17} = 17.3347711916489
x18=−29.8791548121049x_{18} = -29.8791548121049
x19=23.6034090301611x_{19} = 23.6034090301611
x20=−42.4353425392198x_{20} = -42.4353425392198
x21=105.252809626976x_{21} = 105.252809626976
x22=86.4053042434102x_{22} = 86.4053042434102
x23=−86.4054381545562x_{23} = -86.4054381545562
x24=−54.9962192754584x_{24} = -54.9962192754584
x25=−48.715423408888x_{25} = -48.715423408888
x26=−73.8410614412353x_{26} = -73.8410614412353
x27=11.0817037582484x_{27} = 11.0817037582484
x28=−61.2775087154266x_{28} = -61.2775087154266
x29=98.9702215094204x_{29} = 98.9702215094204
x30=−98.9703235828905x_{30} = -98.9703235828905
x31=−23.6051982121417x_{31} = -23.6051982121417
x32=−0.247412484885142x_{32} = -0.247412484885142
x33=−17.3380791158534x_{33} = -17.3380791158534
x34=73.8408780976001x_{34} = 73.8408780976001
Puntos máximos de la función:
x34=39.2950316476879x_{34} = 39.2950316476879
x34=−7.98676475119172x_{34} = -7.98676475119172
x34=−33.0174658775265x_{34} = -33.0174658775265
x34=7.97148100902349x_{34} = 7.97148100902349
x34=76.9819255322054x_{34} = 76.9819255322054
x34=83.2641430354848x_{34} = 83.2641430354848
x34=−95.829065529839x_{34} = -95.829065529839
x34=58.1365166573738x_{34} = 58.1365166573738
x34=−39.2956785303244x_{34} = -39.2956785303244
x34=−83.2642872382528x_{34} = -83.2642872382528
x34=−26.7416265193495x_{34} = -26.7416265193495
x34=20.4680078422429x_{34} = 20.4680078422429
x34=−64.4182930958041x_{34} = -64.4182930958041
x34=95.8289566560771x_{34} = 95.8289566560771
x34=89.5464955446878x_{34} = 89.5464955446878
x34=51.8553766970605x_{34} = 51.8553766970605
x34=26.7402314854239x_{34} = 26.7402314854239
x34=−70.700078740623x_{34} = -70.700078740623
x34=−20.4703846071522x_{34} = -20.4703846071522
x34=−14.2099775813926x_{34} = -14.2099775813926
x34=33.0165500205799x_{34} = 33.0165500205799
x34=−76.9820942237331x_{34} = -76.9820942237331
x34=−45.5752749499286x_{34} = -45.5752749499286
x34=70.699878750109x_{34} = 70.699878750109
x34=45.5747939110765x_{34} = 45.5747939110765
x34=1.95728275422062x_{34} = 1.95728275422062
x34=−89.5466202277414x_{34} = -89.5466202277414
x34=−58.1368123734526x_{34} = -58.1368123734526
x34=14.2050661771509x_{34} = 14.2050661771509
x34=64.4180522161792x_{34} = 64.4180522161792
x34=−2.12300090681457x_{34} = -2.12300090681457
x34=−51.8557483406994x_{34} = -51.8557483406994
Decrece en los intervalos
[105.252809626976,∞)\left[105.252809626976, \infty\right)
Crece en los intervalos
(−∞,−98.9703235828905]\left(-\infty, -98.9703235828905\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
−(2x+1)sin⁡(x)+4cos⁡(x)=0- \left(2 x + 1\right) \sin{\left(x \right)} + 4 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−1.22363340679195x_{1} = -1.22363340679195
x2=6.55926589110157x_{2} = 6.55926589110157
x3=0.945096917005164x_{3} = 0.945096917005164
x4=44.0271833632886x_{4} = 44.0271833632886
x5=−91.128251546449x_{5} = -91.128251546449
x6=−15.8376298773678x_{6} = -15.8376298773678
x7=−59.7240176727685x_{7} = -59.7240176727685
x8=−78.5654302714376x_{8} = -78.5654302714376
x9=−44.0282120696665x_{9} = -44.0282120696665
x10=−37.7527476656581x_{10} = -37.7527476656581
x11=78.5651065552681x_{11} = 78.5651065552681
x12=−81.7060327275283x_{12} = -81.7060327275283
x13=25.2103744983198x_{13} = 25.2103744983198
x14=−22.0835478883776x_{14} = -22.0835478883776
x15=62.8634065553665x_{15} = 62.8634065553665
x16=−25.2134927005181x_{16} = -25.2134927005181
x17=−6.60000933977149x_{17} = -6.60000933977149
x18=−100.550952067693x_{18} = -100.550952067693
x19=100.550754365473x_{19} = 100.550754365473
x20=66.0035102644062x_{20} = 66.0035102644062
x21=−47.1667206869961x_{21} = -47.1667206869961
x22=−31.4803940350564x_{22} = -31.4803940350564
x23=−9.64019642987737x_{23} = -9.64019642987737
x24=−56.5843132552156x_{24} = -56.5843132552156
x25=34.6144143855739x_{25} = 34.6144143855739
x26=12.7165564923597x_{26} = 12.7165564923597
x27=−53.444832327677x_{27} = -53.444832327677
x28=31.4783874220183x_{28} = 31.4783874220183
x29=84.8464312618769x_{29} = 84.8464312618769
x30=−34.6160755605069x_{30} = -34.6160755605069
x31=−66.0039687440156x_{31} = -66.0039687440156
x32=−97.4100070356532x_{32} = -97.4100070356532
x33=91.1280108750695x_{33} = 91.1280108750695
x34=−69.1441658996248x_{34} = -69.1441658996248
x35=22.0794939571531x_{35} = 22.0794939571531
x36=−94.2691053608966x_{36} = -94.2691053608966
x37=9.61989414525743x_{37} = 9.61989414525743
x38=−3.70016832822322x_{38} = -3.70016832822322
x39=87.9871925938327x_{39} = 87.9871925938327
x40=47.1658239901862x_{40} = 47.1658239901862
x41=−40.8901810705869x_{41} = -40.8901810705869
x42=40.8889889691312x_{42} = 40.8889889691312
x43=59.7234578682196x_{43} = 59.7234578682196
x44=56.5836897166246x_{44} = 56.5836897166246
x45=53.444133531179x_{45} = 53.444133531179
x46=81.7057333981014x_{46} = 81.7057333981014
x47=69.1437480697611x_{47} = 69.1437480697611
x48=15.8298315748782x_{48} = 15.8298315748782
x49=18.9520130189604x_{49} = 18.9520130189604
x50=50.3048284778932x_{50} = 50.3048284778932
x51=75.4245595332952x_{51} = 75.4245595332952
x52=94.2688804495667x_{52} = 94.2688804495667
x53=28.3435626361769x_{53} = 28.3435626361769
x54=−87.9874507409867x_{54} = -87.9874507409867
x55=37.7513500111658x_{55} = 37.7513500111658
x56=−84.8467088588013x_{56} = -84.8467088588013
x57=−28.3460342726732x_{57} = -28.3460342726732
x58=3.59583707263255x_{58} = 3.59583707263255
x59=−72.2844850005113x_{59} = -72.2844850005113
x60=−75.4249107406798x_{60} = -75.4249107406798
x61=97.4097963860341x_{61} = 97.4097963860341
x62=−62.8639119133944x_{62} = -62.8639119133944
x63=−50.3056170075141x_{63} = -50.3056170075141
x64=72.2841026475956x_{64} = 72.2841026475956
x65=−12.7284877901053x_{65} = -12.7284877901053
x66=−18.9574918855266x_{66} = -18.9574918855266

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
[97.4097963860341,∞)\left[97.4097963860341, \infty\right)
Convexa en los intervalos
(−∞,−100.550952067693]\left(-\infty, -100.550952067693\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((2x+1)sin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(2 x + 1\right) \sin{\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→∞((2x+1)sin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(2 x + 1\right) \sin{\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 (2*x + 1)*sin(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((2x+1)sin⁡(x)x)=⟨−2,2⟩\lim_{x \to -\infty}\left(\frac{\left(2 x + 1\right) \sin{\left(x \right)}}{x}\right) = \left\langle -2, 2\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−2,2⟩xy = \left\langle -2, 2\right\rangle x
lim⁡x→∞((2x+1)sin⁡(x)x)=⟨−2,2⟩\lim_{x \to \infty}\left(\frac{\left(2 x + 1\right) \sin{\left(x \right)}}{x}\right) = \left\langle -2, 2\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−2,2⟩xy = \left\langle -2, 2\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:
(2x+1)sin⁡(x)=−(1−2x)sin⁡(x)\left(2 x + 1\right) \sin{\left(x \right)} = - \left(1 - 2 x\right) \sin{\left(x \right)}
- No
(2x+1)sin⁡(x)=(1−2x)sin⁡(x)\left(2 x + 1\right) \sin{\left(x \right)} = \left(1 - 2 x\right) \sin{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор