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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

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

Solución numérica
x1=7.85398163397448x_{1} = 7.85398163397448
x2=−73.8274273593601x_{2} = -73.8274273593601
x3=−54.9778714378214x_{3} = -54.9778714378214
x4=64.3715822869017x_{4} = 64.3715822869017
x5=39.2189234266452x_{5} = 39.2189234266452
x6=−92.6553987604331x_{6} = -92.6553987604331
x7=89.5130484454873x_{7} = 89.5130484454873
x8=−10.8111042087213x_{8} = -10.8111042087213
x9=−4.71238898038469x_{9} = -4.71238898038469
x10=14.1371669411541x_{10} = 14.1371669411541
x11=45.5091533451563x_{11} = 45.5091533451563
x12=20.3220161353369x_{12} = 20.3220161353369
x13=58.1194640914112x_{13} = 58.1194640914112
x14=58.0850352160434x_{14} = 58.0850352160434
x15=−23.4768059032848x_{15} = -23.4768059032848
x16=70.6858347057703x_{16} = 70.6858347057703
x17=−36.1283155162826x_{17} = -36.1283155162826
x18=51.7976718062027x_{18} = 51.7976718062027
x19=26.6284652377851x_{19} = 26.6284652377851
x20=95.7976993646524x_{20} = 95.7976993646524
x21=−36.0728864084812x_{21} = -36.0728864084812
x22=−29.7779917432681x_{22} = -29.7779917432681
x23=7.59205618191083x_{23} = 7.59205618191083
x24=−92.6769832808989x_{24} = -92.6769832808989
x25=−86.3937979737193x_{25} = -86.3937979737193
x26=−98.9399549958912x_{26} = -98.9399549958912
x27=83.2281761528687x_{27} = 83.2281761528687
x28=−10.9955742875643x_{28} = -10.9955742875643
x29=39.2699081698724x_{29} = 39.2699081698724
x30=−67.5146210051587x_{30} = -67.5146210051587
x31=102.08216980829x_{31} = 102.08216980829
x32=−61.261056745001x_{32} = -61.261056745001
x33=−67.5442420521806x_{33} = -67.5442420521806
x34=−86.3706429922226x_{34} = -86.3706429922226
x35=26.7035375555132x_{35} = 26.7035375555132
x36=−48.6946861306418x_{36} = -48.6946861306418
x37=51.8362787842316x_{37} = 51.8362787842316
x38=−80.0856406984281x_{38} = -80.0856406984281
x39=76.9430282181184x_{39} = 76.9430282181184
x40=−98.9601685880785x_{40} = -98.9601685880785
x41=−42.4115008234622x_{41} = -42.4115008234622
x42=95.8185759344887x_{42} = 95.8185759344887
x43=1.5707963267949x_{43} = 1.5707963267949
x44=45.553093477052x_{44} = 45.553093477052
x45=−17.2787595947439x_{45} = -17.2787595947439
x46=−42.3643000278463x_{46} = -42.3643000278463
x47=−54.9414730837878x_{47} = -54.9414730837878
x48=76.9690200129499x_{48} = 76.9690200129499
x49=32.9259992567895x_{49} = 32.9259992567895
x50=70.6575310493539x_{50} = 70.6575310493539
x51=20.4203522483337x_{51} = 20.4203522483337
x52=−80.1106126665397x_{52} = -80.1106126665397
x53=−4.2502319840436x_{53} = -4.2502319840436
x54=32.9867228626928x_{54} = 32.9867228626928
x55=64.4026493985908x_{55} = 64.4026493985908
x56=−23.5619449019235x_{56} = -23.5619449019235
x57=−73.8003288675086x_{57} = -73.8003288675086
x58=−48.6535849776189x_{58} = -48.6535849776189
x59=89.5353906273091x_{59} = 89.5353906273091
x60=−61.2283950657729x_{60} = -61.2283950657729
x61=83.2522053201295x_{61} = 83.2522053201295
x62=−29.845130209103x_{62} = -29.845130209103
x63=−17.1623570970183x_{63} = -17.1623570970183
x64=13.9944961126907x_{64} = 13.9944961126907
x65=133.502707088111x_{65} = 133.502707088111
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) - x.
−0+(0sin⁡(0)+cos⁡(0))- 0 + \left(0 \sin{\left(0 \right)} + \cos{\left(0 \right)}\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
xcos⁡(x)−1=0x \cos{\left(x \right)} - 1 = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−2.07393280909122x_{1} = -2.07393280909122
x2=32.9563750616135x_{2} = 32.9563750616135
x3=20.3712437074438x_{3} = 20.3712437074438
x4=−64.4181735917203x_{4} = -64.4181735917203
x5=−33.0170149091969x_{5} = -33.0170149091969
x6=4.91718592528713x_{6} = 4.91718592528713
x7=−70.699979453112x_{7} = -70.699979453112
x8=−83.2642155700859x_{8} = -83.2642155700859
x9=7.72415319239641x_{9} = 7.72415319239641
x10=−10.9037335277384x_{10} = -10.9037335277384
x11=−54.959675275262x_{11} = -54.959675275262
x12=−26.740942117298x_{12} = -26.740942117298
x13=11.0859017287718x_{13} = 11.0859017287718
x14=98.9702728040995x_{14} = 98.9702728040995
x15=14.0660135689384x_{15} = 14.0660135689384
x16=95.8081382182729x_{16} = 95.8081382182729
x17=−67.5294331532335x_{17} = -67.5294331532335
x18=−14.2076100006438x_{18} = -14.2076100006438
x19=−80.0981276558536x_{19} = -80.0981276558536
x20=−29.8115799030901x_{20} = -29.8115799030901
x21=89.5242202334874x_{21} = 89.5242202334874
x22=−58.1366657885594x_{22} = -58.1366657885594
x23=−23.5194140147849x_{23} = -23.5194140147849
x24=−7.97963107097301x_{24} = -7.97963107097301
x25=−86.3822212589452x_{25} = -86.3822212589452
x26=−36.1006116108761x_{26} = -36.1006116108761
x27=−95.829011377113x_{27} = -95.829011377113
x28=−20.4692255293053x_{28} = -20.4692255293053
x29=−42.3879070002498x_{29} = -42.3879070002498
x30=61.2773767058956x_{30} = 61.2773767058956
x31=−45.5750370742992x_{31} = -45.5750370742992
x32=67.5590444598741x_{32} = 67.5590444598741
x33=17.336473487102x_{33} = 17.336473487102
x34=−114.676852122197x_{34} = -114.676852122197
x35=23.6043227065406x_{35} = 23.6043227065406
x36=29.8786052250774x_{36} = 29.8786052250774
x37=−17.2206571155732x_{37} = -17.2206571155732
x38=83.240191603726x_{38} = 83.240191603726
x39=86.405371586641x_{39} = 86.405371586641
x40=58.1022522048044x_{40} = 58.1022522048044
x41=92.6877723998433x_{41} = 92.6877723998433
x42=39.2444240846477x_{42} = 39.2444240846477
x43=54.9960555621608x_{43} = 54.9960555621608
x44=−51.8555643132686x_{44} = -51.8555643132686
x45=45.5311287148944x_{45} = 45.5311287148944
x46=−76.9820104261667x_{46} = -76.9820104261667
x47=−92.6661916492115x_{47} = -92.6661916492115
x48=−61.2447280834131x_{48} = -61.2447280834131
x49=36.1559769880743x_{49} = 36.1559769880743
x50=−4.48766960334109x_{50} = -4.48766960334109
x51=−48.6741398947227x_{51} = -48.6741398947227
x52=70.671684294851x_{52} = 70.671684294851
x53=80.1230937867295x_{53} = 80.1230937867295
x54=51.8169788924771x_{54} = 51.8169788924771
x55=−39.2953592151719x_{55} = -39.2953592151719
x56=73.8409703906111x_{56} = 73.8409703906111
x57=−73.8138793572668x_{57} = -73.8138793572668
x58=26.6660278619112x_{58} = 26.6660278619112
x59=−98.9500623082067x_{59} = -98.9500623082067
x60=−89.5465582344838x_{60} = -89.5465582344838
x61=64.3871177170664x_{61} = 64.3871177170664
x62=42.4350684201498x_{62} = 42.4350684201498
x63=48.7152150401823x_{63} = 48.7152150401823
x64=76.9560252131026x_{64} = 76.9560252131026
Signos de extremos en los puntos:
(-2.073932809091215, 3.40867683863142)

(32.95637506161347, 0.0151680777319427)

(20.371243707443842, 0.0245295981859854)

(-64.41817359172032, 128.813061361402)

(-33.017014909196874, 65.9885952228472)

(4.917185925287132, -9.52824562032736)

(-70.69997945311201, 141.378742138954)

(-83.26421557008594, 166.510415981788)

(7.724153192396411, 0.0644584754526054)

(-10.903733527738439, -0.0457590213602597)

(-54.959675275261986, -0.00909682613061591)

(-26.740942117297966, 53.4257839325997)

(11.085901728771786, -22.0364043437832)

(98.97027280409945, -197.925389413115)

(14.066013568938363, 0.0355016446467076)

(95.80813821827292, 0.00521862120285732)

(-67.52943315323353, -0.00740377288414606)

(-14.20761000064383, 28.3095990846546)

(-80.09812765585362, -0.00624209990532165)

(-29.811579903090074, -0.0167672854758187)

(89.52422023348744, 0.00558490653321542)

(-58.13666578855936, 116.247529667622)

(-23.519414014784864, -0.0212494164164099)

(-7.979631070973006, 15.7710355605792)

(-86.3822212589452, -0.00578803415562845)

(-36.100611610876136, -0.0138475229953983)

(-95.82901137711305, 191.642369732338)

(-20.46922552930527, 40.8651557259926)

(-42.3879070002498, -0.0117941753995794)

(61.27737670589561, -122.530274013769)

(-45.57503707429922, 91.1171600734531)

(67.55904445987407, -135.095885713621)

(17.336473487101994, -34.5864001575149)

(-114.67685212219666, 229.340623928028)

(23.60432270654059, -47.1450882176196)

(29.87860522507741, -59.7070026145832)

(-17.220657115573236, -0.0290103781662836)

(83.240191603726, 0.00600649696690425)

(86.40537158664104, -172.79338294768)

(58.10225220480441, 0.00860488101699275)

(92.68777239984328, -185.359361278257)

(39.2444240846477, 0.0127385946678444)

(54.99605556216085, -109.964835689388)

(-51.855564313268616, 103.682201229561)

(45.53112871489442, 0.0109801734091377)

(-76.9820104261667, 153.944535506522)

(-92.66619164921153, -0.00539555401387304)

(-61.24472808341312, -0.00816342379199142)

(36.15597698807427, -72.2704644139298)

(-4.487669603341088, -0.109997879424804)

(-48.67413989472275, -0.0102713109855017)

(70.671684294851, 0.0070746151713621)

(80.12309378672954, -160.227466136207)

(51.816978892477124, 0.0096484481933814)

(-39.29535921517187, 78.5525439230185)

(73.84097039061113, -147.661626544837)

(-73.81387935726681, -0.00677348298323466)

(26.666027861911218, 0.0187438522602434)

(-98.9500623082067, -0.00505292488966802)

(-89.54655823448383, 179.0763652323)

(64.38711771706639, 0.00776506019175827)

(42.43506842014976, -84.8347870814508)

(48.71521504018234, -97.3996377974613)

(76.95602521310259, 0.00649694276592072)


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=4.91718592528713x_{1} = 4.91718592528713
x2=−10.9037335277384x_{2} = -10.9037335277384
x3=−54.959675275262x_{3} = -54.959675275262
x4=11.0859017287718x_{4} = 11.0859017287718
x5=98.9702728040995x_{5} = 98.9702728040995
x6=−67.5294331532335x_{6} = -67.5294331532335
x7=−80.0981276558536x_{7} = -80.0981276558536
x8=−29.8115799030901x_{8} = -29.8115799030901
x9=−23.5194140147849x_{9} = -23.5194140147849
x10=−86.3822212589452x_{10} = -86.3822212589452
x11=−36.1006116108761x_{11} = -36.1006116108761
x12=−42.3879070002498x_{12} = -42.3879070002498
x13=61.2773767058956x_{13} = 61.2773767058956
x14=67.5590444598741x_{14} = 67.5590444598741
x15=17.336473487102x_{15} = 17.336473487102
x16=23.6043227065406x_{16} = 23.6043227065406
x17=29.8786052250774x_{17} = 29.8786052250774
x18=−17.2206571155732x_{18} = -17.2206571155732
x19=86.405371586641x_{19} = 86.405371586641
x20=92.6877723998433x_{20} = 92.6877723998433
x21=54.9960555621608x_{21} = 54.9960555621608
x22=−92.6661916492115x_{22} = -92.6661916492115
x23=−61.2447280834131x_{23} = -61.2447280834131
x24=36.1559769880743x_{24} = 36.1559769880743
x25=−4.48766960334109x_{25} = -4.48766960334109
x26=−48.6741398947227x_{26} = -48.6741398947227
x27=80.1230937867295x_{27} = 80.1230937867295
x28=73.8409703906111x_{28} = 73.8409703906111
x29=−73.8138793572668x_{29} = -73.8138793572668
x30=−98.9500623082067x_{30} = -98.9500623082067
x31=42.4350684201498x_{31} = 42.4350684201498
x32=48.7152150401823x_{32} = 48.7152150401823
Puntos máximos de la función:
x32=−2.07393280909122x_{32} = -2.07393280909122
x32=32.9563750616135x_{32} = 32.9563750616135
x32=20.3712437074438x_{32} = 20.3712437074438
x32=−64.4181735917203x_{32} = -64.4181735917203
x32=−33.0170149091969x_{32} = -33.0170149091969
x32=−70.699979453112x_{32} = -70.699979453112
x32=−83.2642155700859x_{32} = -83.2642155700859
x32=7.72415319239641x_{32} = 7.72415319239641
x32=−26.740942117298x_{32} = -26.740942117298
x32=14.0660135689384x_{32} = 14.0660135689384
x32=95.8081382182729x_{32} = 95.8081382182729
x32=−14.2076100006438x_{32} = -14.2076100006438
x32=89.5242202334874x_{32} = 89.5242202334874
x32=−58.1366657885594x_{32} = -58.1366657885594
x32=−7.97963107097301x_{32} = -7.97963107097301
x32=−95.829011377113x_{32} = -95.829011377113
x32=−20.4692255293053x_{32} = -20.4692255293053
x32=−45.5750370742992x_{32} = -45.5750370742992
x32=−114.676852122197x_{32} = -114.676852122197
x32=83.240191603726x_{32} = 83.240191603726
x32=58.1022522048044x_{32} = 58.1022522048044
x32=39.2444240846477x_{32} = 39.2444240846477
x32=−51.8555643132686x_{32} = -51.8555643132686
x32=45.5311287148944x_{32} = 45.5311287148944
x32=−76.9820104261667x_{32} = -76.9820104261667
x32=70.671684294851x_{32} = 70.671684294851
x32=51.8169788924771x_{32} = 51.8169788924771
x32=−39.2953592151719x_{32} = -39.2953592151719
x32=26.6660278619112x_{32} = 26.6660278619112
x32=−89.5465582344838x_{32} = -89.5465582344838
x32=64.3871177170664x_{32} = 64.3871177170664
x32=76.9560252131026x_{32} = 76.9560252131026
Decrece en los intervalos
[98.9702728040995,∞)\left[98.9702728040995, \infty\right)
Crece en los intervalos
(−∞,−98.9500623082067]\left(-\infty, -98.9500623082067\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)=0- x \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=87.9759605524932x_{1} = 87.9759605524932
x2=34.5864242152889x_{2} = 34.5864242152889
x3=62.8477631944545x_{3} = 62.8477631944545
x4=−69.1295029738953x_{4} = -69.1295029738953
x5=50.2853663377737x_{5} = 50.2853663377737
x6=18.90240995686x_{6} = 18.90240995686
x7=56.5663442798215x_{7} = 56.5663442798215
x8=6.43729817917195x_{8} = 6.43729817917195
x9=−62.8477631944545x_{9} = -62.8477631944545
x10=37.7256128277765x_{10} = 37.7256128277765
x11=−9.52933440536196x_{11} = -9.52933440536196
x12=15.7712848748159x_{12} = 15.7712848748159
x13=59.7070073053355x_{13} = 59.7070073053355
x14=12.6452872238566x_{14} = 12.6452872238566
x15=100.540910786842x_{15} = 100.540910786842
x16=78.5525459842429x_{16} = 78.5525459842429
x17=31.4477146375462x_{17} = 31.4477146375462
x18=−72.270467060309x_{18} = -72.270467060309
x19=−15.7712848748159x_{19} = -15.7712848748159
x20=44.0050179208308x_{20} = 44.0050179208308
x21=−94.2583883450399x_{21} = -94.2583883450399
x22=−0.86033358901938x_{22} = -0.86033358901938
x23=−34.5864242152889x_{23} = -34.5864242152889
x24=−31.4477146375462x_{24} = -31.4477146375462
x25=84.8347887180423x_{25} = 84.8347887180423
x26=−75.4114834888481x_{26} = -75.4114834888481
x27=−28.309642854452x_{27} = -28.309642854452
x28=−59.7070073053355x_{28} = -59.7070073053355
x29=−81.6936492356017x_{29} = -81.6936492356017
x30=28.309642854452x_{30} = 28.309642854452
x31=−22.0364967279386x_{31} = -22.0364967279386
x32=−25.1724463266467x_{32} = -25.1724463266467
x33=81.6936492356017x_{33} = 81.6936492356017
x34=65.9885986984904x_{34} = 65.9885986984904
x35=−65.9885986984904x_{35} = -65.9885986984904
x36=−84.8347887180423x_{36} = -84.8347887180423
x37=−78.5525459842429x_{37} = -78.5525459842429
x38=3.42561845948173x_{38} = 3.42561845948173
x39=−50.2853663377737x_{39} = -50.2853663377737
x40=9.52933440536196x_{40} = 9.52933440536196
x41=91.1171613944647x_{41} = 91.1171613944647
x42=−100.540910786842x_{42} = -100.540910786842
x43=−47.145097736761x_{43} = -47.145097736761
x44=−147.661626855354x_{44} = -147.661626855354
x45=75.4114834888481x_{45} = 75.4114834888481
x46=94.2583883450399x_{46} = 94.2583883450399
x47=−87.9759605524932x_{47} = -87.9759605524932
x48=47.145097736761x_{48} = 47.145097736761
x49=−116.247530303932x_{49} = -116.247530303932
x50=−91.1171613944647x_{50} = -91.1171613944647
x51=−12.6452872238566x_{51} = -12.6452872238566
x52=25.1724463266467x_{52} = 25.1724463266467
x53=72.270467060309x_{53} = 72.270467060309
x54=40.8651703304881x_{54} = 40.8651703304881
x55=−40.8651703304881x_{55} = -40.8651703304881
x56=−44.0050179208308x_{56} = -44.0050179208308
x57=0.86033358901938x_{57} = 0.86033358901938
x58=69.1295029738953x_{58} = 69.1295029738953
x59=−3.42561845948173x_{59} = -3.42561845948173
x60=−97.3996388790738x_{60} = -97.3996388790738
x61=−56.5663442798215x_{61} = -56.5663442798215
x62=97.3996388790738x_{62} = 97.3996388790738
x63=−6.43729817917195x_{63} = -6.43729817917195
x64=−53.4257904773947x_{64} = -53.4257904773947
x65=53.4257904773947x_{65} = 53.4257904773947
x66=22.0364967279386x_{66} = 22.0364967279386
x67=−37.7256128277765x_{67} = -37.7256128277765
x68=−18.90240995686x_{68} = -18.90240995686

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
[97.3996388790738,∞)\left[97.3996388790738, \infty\right)
Convexa en los intervalos
(−∞,−100.540910786842]\left(-\infty, -100.540910786842\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(−x+(xsin⁡(x)+cos⁡(x)))=⟨0,∞⟩\lim_{x \to -\infty}\left(- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right)\right) = \left\langle 0, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨0,∞⟩y = \left\langle 0, \infty\right\rangle
lim⁡x→∞(−x+(xsin⁡(x)+cos⁡(x)))=⟨−∞,0⟩\lim_{x \to \infty}\left(- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right)\right) = \left\langle -\infty, 0\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−∞,0⟩y = \left\langle -\infty, 0\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función x*sin(x) + cos(x) - 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→−∞(−x+(xsin⁡(x)+cos⁡(x))x)y = x \lim_{x \to -\infty}\left(\frac{- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{x}\right)
lim⁡x→∞(−x+(xsin⁡(x)+cos⁡(x))x)=⟨−∞,0⟩\lim_{x \to \infty}\left(\frac{- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{x}\right) = \left\langle -\infty, 0\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,0⟩xy = \left\langle -\infty, 0\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:
−x+(xsin⁡(x)+cos⁡(x))=xsin⁡(x)+x+cos⁡(x)- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = x \sin{\left(x \right)} + x + \cos{\left(x \right)}
- No
−x+(xsin⁡(x)+cos⁡(x))=−xsin⁡(x)−x−cos⁡(x)- x + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - x \sin{\left(x \right)} - x - \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор