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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = (1 + 2*x)*sin(x) + cos(x)
f(x)=(2x+1)sin⁡(x)+cos⁡(x)f{\left(x \right)} = \left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)} 
f = (2*x + 1)*sin(x) + cos(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)+cos⁡(x)=0\left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−21.96786215672x_{1} = -21.96786215672
x2=−87.9588773902619x_{2} = -87.9588773902619
x3=−69.1077507016628x_{3} = -69.1077507016628
x4=62.8239573301117x_{4} = 62.8239573301117
x5=15.6770651495554x_{5} = 15.6770651495554
x6=21.9688992657133x_{6} = 21.9688992657133
x7=40.8286069292666x_{7} = 40.8286069292666
x8=2.99968291443692x_{8} = 2.99968291443692
x9=75.3916354401261x_{9} = 75.3916354401261
x10=−62.8238306304873x_{10} = -62.8238306304873
x11=−65.9658082992049x_{11} = -65.9658082992049
x12=37.6860187937327x_{12} = 37.6860187937327
x13=−40.8283068925649x_{13} = -40.8283068925649
x14=−59.6818120776324x_{14} = -59.6818120776324
x15=−100.525966254483x_{15} = -100.525966254483
x16=59.681952470794x_{16} = 59.681952470794
x17=9.37418407881317x_{17} = 9.37418407881317
x18=−84.8170717192227x_{18} = -84.8170717192227
x19=−6.19562307165851x_{19} = -6.19562307165851
x20=−50.2554336419907x_{20} = -50.2554336419907
x21=−53.3976231719776x_{21} = -53.3976231719776
x22=−75.3915474644952x_{22} = -75.3915474644952
x23=2799.15887575532x_{23} = 2799.15887575532
x24=50.2556316525002x_{24} = 50.2556316525002
x25=−25.1124290834791x_{25} = -25.1124290834791
x26=84.8171412269817x_{26} = 84.8171412269817
x27=91.1007285364445x_{27} = 91.1007285364445
x28=−47.1131636315434x_{28} = -47.1131636315434
x29=31.4002539628314x_{29} = 31.4002539628314
x30=94.2425021942145x_{30} = 94.2425021942145
x31=−94.2424458951605x_{31} = -94.2424458951605
x32=28.2569485320036x_{32} = 28.2569485320036
x33=12.5280105958623x_{33} = 12.5280105958623
x34=78.5334899921473x_{34} = 78.5334899921473
x35=43.9710543555825x_{35} = 43.9710543555825
x36=−31.3997465854878x_{36} = -31.3997465854878
x37=81.6753245168475x_{37} = 81.6753245168475
x38=−56.5397457624532x_{38} = -56.5397457624532
x39=−34.5428328661305x_{39} = -34.5428328661305
x40=100.526015735061x_{40} = 100.526015735061
x41=25.1132225406242x_{41} = 25.1132225406242
x42=65.9659232154374x_{42} = 65.9659232154374
x43=−97.3842115075001x_{43} = -97.3842115075001
x44=−43.9707956825554x_{44} = -43.9707956825554
x45=−37.6856666122629x_{45} = -37.6856666122629
x46=−12.5248138680222x_{46} = -12.5248138680222
x47=56.5399021956931x_{47} = 56.5399021956931
x48=−9.36845799714637x_{48} = -9.36845799714637
x49=−78.5334089154837x_{49} = -78.5334089154837
x50=−15.6750263115657x_{50} = -15.6750263115657
x51=53.3977985603904x_{51} = 53.3977985603904
x52=6.20879379579529x_{52} = 6.20879379579529
x53=87.9589420208932x_{53} = 87.9589420208932
x54=18.8236867141542x_{54} = 18.8236867141542
x55=−28.2563219162948x_{55} = -28.2563219162948
x56=72.2497582657079x_{56} = 72.2497582657079
x57=−18.8222735027545x_{57} = -18.8222735027545
x58=−91.1006682870401x_{58} = -91.1006682870401
x59=34.5432520754261x_{59} = 34.5432520754261
x60=47.1133889419474x_{60} = 47.1133889419474
x61=97.3842642323756x_{61} = 97.3842642323756
x62=−72.2496624714699x_{62} = -72.2496624714699
x63=−2.93942648460973x_{63} = -2.93942648460973
x64=−81.6752495582901x_{64} = -81.6752495582901
x65=69.1078554051879x_{65} = 69.1078554051879
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 (1 + 2*x)*sin(x) + cos(x).
(0⋅2+1)sin⁡(0)+cos⁡(0)\left(0 \cdot 2 + 1\right) \sin{\left(0 \right)} + \cos{\left(0 \right)}
Resultado:
f(0)=1f{\left(0 \right)} = 1
Punto:
(0, 1)
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)+sin⁡(x)=0\left(2 x + 1\right) \cos{\left(x \right)} + \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−45.5641883065108x_{1} = -45.5641883065108
x2=−42.4234267640088x_{2} = -42.4234267640088
x3=11.0388789632915x_{3} = 11.0388789632915
x4=−83.2582469405715x_{4} = -83.2582469405715
x5=51.8458303529263x_{5} = 51.8458303529263
x6=−58.1281401904923x_{6} = -58.1281401904923
x7=86.3995516798409x_{7} = 86.3995516798409
x8=−54.9870476730441x_{8} = -54.9870476730441
x9=−92.682407256163x_{9} = -92.682407256163
x10=−11.042963775064x_{10} = -11.042963775064
x11=−70.6929578069925x_{11} = -70.6929578069925
x12=80.1168147670621x_{12} = 80.1168147670621
x13=−0.3291899722468x_{13} = -0.3291899722468
x14=215.201414785852x_{14} = 215.201414785852
x15=42.4231490225752x_{15} = 42.4231490225752
x16=98.9651954297421x_{16} = 98.9651954297421
x17=76.9754735786459x_{17} = 76.9754735786459
x18=−98.965246478201x_{18} = -98.965246478201
x19=83.258174815787x_{19} = 83.258174815787
x20=14.1712340520224x_{20} = 14.1712340520224
x21=23.5827037080218x_{21} = 23.5827037080218
x22=−95.8238211649932x_{22} = -95.8238211649932
x23=−51.8460163302446x_{23} = -51.8460163302446
x24=−17.3084976836792x_{24} = -17.3084976836792
x25=−48.7050581142003x_{25} = -48.7050581142003
x26=−4.82742115185184x_{26} = -4.82742115185184
x27=−86.399618655593x_{27} = -86.399618655593
x28=64.4103521777991x_{28} = 64.4103521777991
x29=39.2824758561339x_{29} = 39.2824758561339
x30=95.8237667147742x_{30} = 95.8237667147742
x31=33.0016463943584x_{31} = 33.0016463943584
x32=−76.9755579564344x_{32} = -76.9755579564344
x33=61.2691512237165x_{33} = 61.2691512237165
x34=−14.1737171579923x_{34} = -14.1737171579923
x35=20.4442206488192x_{35} = 20.4442206488192
x36=36.1419602276141x_{36} = 36.1419602276141
x37=92.6823490524907x_{37} = 92.6823490524907
x38=−36.1423428546997x_{38} = -36.1423428546997
x39=−80.1168926582631x_{39} = -80.1168926582631
x40=−67.5516988465835x_{40} = -67.5516988465835
x41=17.3068313300672x_{41} = 17.3068313300672
x42=7.91334123766475x_{42} = 7.91334123766475
x43=−64.4104726829187x_{43} = -64.4104726829187
x44=54.9868823327609x_{44} = 54.9868823327609
x45=−61.2692844001807x_{45} = -61.2692844001807
x46=48.7048473813719x_{46} = 48.7048473813719
x47=−89.5410059585745x_{47} = -89.5410059585745
x48=−1.91128518636087x_{48} = -1.91128518636087
x49=−33.0021052681971x_{49} = -33.0021052681971
x50=−26.7226027651204x_{50} = -26.7226027651204
x51=70.6928577667219x_{51} = 70.6928577667219
x52=−73.8342453507376x_{52} = -73.8342453507376
x53=73.8341536410894x_{53} = 73.8341536410894
x54=45.5639475265121x_{54} = 45.5639475265121
x55=26.7219030526837x_{55} = 26.7219030526837
x56=−23.5836019131825x_{56} = -23.5836019131825
x57=−20.4454154165576x_{57} = -20.4454154165576
x58=58.127992234016x_{58} = 58.127992234016
x59=29.8615968926246x_{59} = 29.8615968926246
x60=−29.8621572849407x_{60} = -29.8621572849407
x61=67.551589286951x_{61} = 67.551589286951
x62=−7.92125402596329x_{62} = -7.92125402596329
x63=−39.2827997688231x_{63} = -39.2827997688231
x64=89.5409435995543x_{64} = 89.5409435995543
x65=1.78611723063107x_{65} = 1.78611723063107
x66=4.80633851753999x_{66} = 4.80633851753999
Signos de extremos en los puntos:
(-45.564188306510765, 90.1117348809766)

(-42.423426764008845, -83.828965253271)

(11.038878963291548, -23.0128313644785)

(-83.25824694057147, 165.507431533177)

(51.845830352926285, 104.677333679589)

(-58.12814019049232, 115.243266477271)

(86.39955167984093, -173.790472871928)

(-54.987047673044096, -108.960331283004)

(-92.68240725616296, -184.356678609269)

(-11.042963775064027, -21.0148832254847)

(-70.69295780699252, 140.375231097683)

(80.11681476706205, -161.224326472804)

(-0.3291899722468004, 0.835866746387795)

(215.20141478585202, 431.399352553948)

(42.4231490225752, -85.828826339141)

(98.96519542974214, -198.922850644623)

(76.97547357864586, 154.941266909541)

(-98.96524647820095, -196.922876170318)

(83.25817481578697, 167.507395467859)

(14.171234052022397, 29.2913822636188)

(23.58270370802177, -48.1342725614297)

(-95.82382116499323, 190.639774538346)

(-51.84601633024458, 102.677426687711)

(-17.30849768367923, -33.5723980957882)

(-48.705058114200305, -96.3945586714855)

(-4.827421151851844, -8.48286460185973)

(-86.39961865559299, -171.790506362328)

(64.41035217779908, 129.809150358171)

(39.282475856133935, 79.5461009272561)

(95.82376671477424, 192.639747311568)

(33.00164639435843, 66.9809087375767)

(-76.9755579564344, 152.94130910244)

(61.26915122371646, -123.526160928242)

(-14.173717157992298, 27.2926273004515)

(20.444220648819186, 41.8526437960035)

(36.14196022761406, -73.2634543408552)

(92.68234905249074, -186.356649505527)

(-36.14234285469967, -71.2636457368069)

(-80.11689265826308, -159.224365421818)

(-67.55169884658352, -134.092212657047)

(17.306831330067244, -35.5715633523643)

(7.913341237664746, 16.7377214945627)

(-64.41047268291865, 127.809210618901)

(54.986882332760906, -110.960248597481)

(-61.26928440018071, -121.526227526453)

(48.704847381371906, -98.3944532800821)

(-89.54100595857454, 178.073588986649)

(-1.911285186360867, 2.32658298380193)

(-33.002105268197106, 64.9811382930371)

(-26.722602765120406, 52.4166103144978)

(70.69285776672187, 142.375181071917)

(-73.83424535073762, -146.658263833259)

(73.83415364108944, -148.658217973703)

(45.563947526512116, 92.1116144583521)

(26.721903052683686, 54.4162601825328)

(-23.58360191318248, -46.134722118556)

(-20.445415416557612, 39.8532419845582)

(58.127992234015984, 117.243192486716)

(29.86159689262455, -60.6984954343149)

(-29.86215728494068, -58.6987758072991)

(67.55158928695097, -136.092157870478)

(-7.921254025963295, 14.7417136140648)

(-39.28279976882314, 77.5462629426524)

(89.5409435995543, 180.073557804951)

(1.7861172306310664, 4.25299094115468)

(4.806338517539989, -10.4720636055512)


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=−42.4234267640088x_{1} = -42.4234267640088
x2=11.0388789632915x_{2} = 11.0388789632915
x3=86.3995516798409x_{3} = 86.3995516798409
x4=−54.9870476730441x_{4} = -54.9870476730441
x5=−92.682407256163x_{5} = -92.682407256163
x6=−11.042963775064x_{6} = -11.042963775064
x7=80.1168147670621x_{7} = 80.1168147670621
x8=−0.3291899722468x_{8} = -0.3291899722468
x9=42.4231490225752x_{9} = 42.4231490225752
x10=98.9651954297421x_{10} = 98.9651954297421
x11=−98.965246478201x_{11} = -98.965246478201
x12=23.5827037080218x_{12} = 23.5827037080218
x13=−17.3084976836792x_{13} = -17.3084976836792
x14=−48.7050581142003x_{14} = -48.7050581142003
x15=−4.82742115185184x_{15} = -4.82742115185184
x16=−86.399618655593x_{16} = -86.399618655593
x17=61.2691512237165x_{17} = 61.2691512237165
x18=36.1419602276141x_{18} = 36.1419602276141
x19=92.6823490524907x_{19} = 92.6823490524907
x20=−36.1423428546997x_{20} = -36.1423428546997
x21=−80.1168926582631x_{21} = -80.1168926582631
x22=−67.5516988465835x_{22} = -67.5516988465835
x23=17.3068313300672x_{23} = 17.3068313300672
x24=54.9868823327609x_{24} = 54.9868823327609
x25=−61.2692844001807x_{25} = -61.2692844001807
x26=48.7048473813719x_{26} = 48.7048473813719
x27=−73.8342453507376x_{27} = -73.8342453507376
x28=73.8341536410894x_{28} = 73.8341536410894
x29=−23.5836019131825x_{29} = -23.5836019131825
x30=29.8615968926246x_{30} = 29.8615968926246
x31=−29.8621572849407x_{31} = -29.8621572849407
x32=67.551589286951x_{32} = 67.551589286951
x33=4.80633851753999x_{33} = 4.80633851753999
Puntos máximos de la función:
x33=−45.5641883065108x_{33} = -45.5641883065108
x33=−83.2582469405715x_{33} = -83.2582469405715
x33=51.8458303529263x_{33} = 51.8458303529263
x33=−58.1281401904923x_{33} = -58.1281401904923
x33=−70.6929578069925x_{33} = -70.6929578069925
x33=215.201414785852x_{33} = 215.201414785852
x33=76.9754735786459x_{33} = 76.9754735786459
x33=83.258174815787x_{33} = 83.258174815787
x33=14.1712340520224x_{33} = 14.1712340520224
x33=−95.8238211649932x_{33} = -95.8238211649932
x33=−51.8460163302446x_{33} = -51.8460163302446
x33=64.4103521777991x_{33} = 64.4103521777991
x33=39.2824758561339x_{33} = 39.2824758561339
x33=95.8237667147742x_{33} = 95.8237667147742
x33=33.0016463943584x_{33} = 33.0016463943584
x33=−76.9755579564344x_{33} = -76.9755579564344
x33=−14.1737171579923x_{33} = -14.1737171579923
x33=20.4442206488192x_{33} = 20.4442206488192
x33=7.91334123766475x_{33} = 7.91334123766475
x33=−64.4104726829187x_{33} = -64.4104726829187
x33=−89.5410059585745x_{33} = -89.5410059585745
x33=−1.91128518636087x_{33} = -1.91128518636087
x33=−33.0021052681971x_{33} = -33.0021052681971
x33=−26.7226027651204x_{33} = -26.7226027651204
x33=70.6928577667219x_{33} = 70.6928577667219
x33=45.5639475265121x_{33} = 45.5639475265121
x33=26.7219030526837x_{33} = 26.7219030526837
x33=−20.4454154165576x_{33} = -20.4454154165576
x33=58.127992234016x_{33} = 58.127992234016
x33=−7.92125402596329x_{33} = -7.92125402596329
x33=−39.2827997688231x_{33} = -39.2827997688231
x33=89.5409435995543x_{33} = 89.5409435995543
x33=1.78611723063107x_{33} = 1.78611723063107
Decrece en los intervalos
[98.9651954297421,∞)\left[98.9651954297421, \infty\right)
Crece en los intervalos
(−∞,−98.965246478201]\left(-\infty, -98.965246478201\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)+3cos⁡(x)=0- \left(2 x + 1\right) \sin{\left(x \right)} + 3 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=22.057547413684x_{1} = 22.057547413684
x2=44.0159801710147x_{2} = 44.0159801710147
x3=−56.575411079585x_{3} = -56.575411079585
x4=81.6996552199143x_{4} = 81.6996552199143
x5=−22.0606079763284x_{5} = -22.0606079763284
x6=62.8555245642201x_{6} = 62.8555245642201
x7=−87.9817390560024x_{7} = -87.9817390560024
x8=72.2772389543869x_{8} = 72.2772389543869
x9=59.7151659353044x_{9} = 59.7151659353044
x10=28.3263227657534x_{10} = 28.3263227657534
x11=−62.8559038941585x_{11} = -62.8559038941585
x12=31.4628216529508x_{12} = 31.4628216529508
x13=−12.6888185562704x_{13} = -12.6888185562704
x14=−72.2775258973187x_{14} = -72.2775258973187
x15=−91.1227375800941x_{15} = -91.1227375800941
x16=−84.8407847619536x_{16} = -84.8407847619536
x17=138.240887857568x_{17} = 138.240887857568
x18=−9.58834981179337x_{18} = -9.58834981179337
x19=3.5003357315193x_{19} = 3.5003357315193
x20=34.6002279682041x_{20} = 34.6002279682041
x21=−97.4048501265707x_{21} = -97.4048501265707
x22=−1.15761970579369x_{22} = -1.15761970579369
x23=65.9959996483222x_{23} = 65.9959996483222
x24=84.8405764703161x_{24} = 84.8405764703161
x25=12.6796944367434x_{25} = 12.6796944367434
x26=9.57261023280052x_{26} = 9.57261023280052
x27=−75.4182428370941x_{27} = -75.4182428370941
x28=15.7997308561529x_{28} = 15.7997308561529
x29=53.4348792604985x_{29} = 53.4348792604985
x30=87.9815453643975x_{30} = 87.9815453643975
x31=0.841223312100858x_{31} = 0.841223312100858
x32=−6.52710550993845x_{32} = -6.52710550993845
x33=−78.5590302014255x_{33} = -78.5590302014255
x34=25.1910610858234x_{34} = 25.1910610858234
x35=78.5587872865396x_{35} = 78.5587872865396
x36=−18.9307626147866x_{36} = -18.9307626147866
x37=75.4179792811716x_{37} = 75.4179792811716
x38=40.8769407042176x_{38} = 40.8769407042176
x39=91.1225570059484x_{39} = 91.1225570059484
x40=94.2636071472689x_{40} = 94.2636071472689
x41=−37.7393700308595x_{41} = -37.7393700308595
x42=−69.1368890381147x_{42} = -69.1368890381147
x43=−31.4643315303269x_{43} = -31.4643315303269
x44=−47.1560289193651x_{44} = -47.1560289193651
x45=−94.2637758924315x_{45} = -94.2637758924315
x46=−53.4354039534434x_{46} = -53.4354039534434
x47=50.2950043410024x_{47} = 50.2950043410024
x48=−3.59312505695837x_{48} = -3.59312505695837
x49=−44.0167529919137x_{49} = -44.0167529919137
x50=−50.2955964966371x_{50} = -50.2955964966371
x51=56.5749429514818x_{51} = 56.5749429514818
x52=47.1553554158828x_{52} = 47.1553554158828
x53=6.49444145318603x_{53} = 6.49444145318603
x54=−40.8778365144443x_{54} = -40.8778365144443
x55=−100.545956901206x_{55} = -100.545956901206
x56=18.9266166712118x_{56} = 18.9266166712118
x57=69.1365754528522x_{57} = 69.1365754528522
x58=−15.8056543017813x_{58} = -15.8056543017813
x59=−65.9963437643379x_{59} = -65.9963437643379
x60=100.545808576895x_{60} = 100.545808576895
x61=−25.1934116262445x_{61} = -25.1934116262445
x62=−59.7155861708734x_{62} = -59.7155861708734
x63=97.4046920852646x_{63} = 97.4046920852646
x64=−81.6998798262163x_{64} = -81.6998798262163
x65=37.7383194057537x_{65} = 37.7383194057537
x66=−28.3281839577061x_{66} = -28.3281839577061
x67=−34.6014772183955x_{67} = -34.6014772183955

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
[97.4046920852646,∞)\left[97.4046920852646, \infty\right)
Convexa en los intervalos
(−∞,−100.545956901206]\left(-\infty, -100.545956901206\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)+cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(2 x + 1\right) \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→∞((2x+1)sin⁡(x)+cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(2 x + 1\right) \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 (1 + 2*x)*sin(x) + cos(x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞((2x+1)sin⁡(x)+cos⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{\left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞((2x+1)sin⁡(x)+cos⁡(x)x)y = x \lim_{x \to \infty}\left(\frac{\left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)}}{x}\right)
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)+cos⁡(x)=−(1−2x)sin⁡(x)+cos⁡(x)\left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)} = - \left(1 - 2 x\right) \sin{\left(x \right)} + \cos{\left(x \right)}
- No
(2x+1)sin⁡(x)+cos⁡(x)=(1−2x)sin⁡(x)−cos⁡(x)\left(2 x + 1\right) \sin{\left(x \right)} + \cos{\left(x \right)} = \left(1 - 2 x\right) \sin{\left(x \right)} - \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор