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Trazado el gráfico de la función/ x×cos(x)

Gráfico de la función y = x×cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = x*cos(x)
f(x)=xcos⁡(x)f{\left(x \right)} = x \cos{\left(x \right)} 
f = x*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-2020
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:
xcos⁡(x)=0x \cos{\left(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}
Solución numérica
x1=48.6946861306418x_{1} = 48.6946861306418
x2=92.6769832808989x_{2} = 92.6769832808989
x3=86.3937979737193x_{3} = 86.3937979737193
x4=−7.85398163397448x_{4} = -7.85398163397448
x5=−86.3937979737193x_{5} = -86.3937979737193
x6=1.5707963267949x_{6} = 1.5707963267949
x7=−64.4026493985908x_{7} = -64.4026493985908
x8=−58.1194640914112x_{8} = -58.1194640914112
x9=−83.2522053201295x_{9} = -83.2522053201295
x10=−54.9778714378214x_{10} = -54.9778714378214
x11=54.9778714378214x_{11} = 54.9778714378214
x12=89.5353906273091x_{12} = 89.5353906273091
x13=−20.4203522483337x_{13} = -20.4203522483337
x14=32.9867228626928x_{14} = 32.9867228626928
x15=−17.2787595947439x_{15} = -17.2787595947439
x16=23.5619449019235x_{16} = 23.5619449019235
x17=−45.553093477052x_{17} = -45.553093477052
x18=64.4026493985908x_{18} = 64.4026493985908
x19=45.553093477052x_{19} = 45.553093477052
x20=83.2522053201295x_{20} = 83.2522053201295
x21=−29.845130209103x_{21} = -29.845130209103
x22=−51.8362787842316x_{22} = -51.8362787842316
x23=80.1106126665397x_{23} = 80.1106126665397
x24=−39.2699081698724x_{24} = -39.2699081698724
x25=−92.6769832808989x_{25} = -92.6769832808989
x26=4.71238898038469x_{26} = 4.71238898038469
x27=70.6858347057703x_{27} = 70.6858347057703
x28=36.1283155162826x_{28} = 36.1283155162826
x29=−70.6858347057703x_{29} = -70.6858347057703
x30=−48.6946861306418x_{30} = -48.6946861306418
x31=42.4115008234622x_{31} = 42.4115008234622
x32=−42.4115008234622x_{32} = -42.4115008234622
x33=−67.5442420521806x_{33} = -67.5442420521806
x34=10.9955742875643x_{34} = 10.9955742875643
x35=98.9601685880785x_{35} = 98.9601685880785
x36=−23.5619449019235x_{36} = -23.5619449019235
x37=20.4203522483337x_{37} = 20.4203522483337
x38=−61.261056745001x_{38} = -61.261056745001
x39=−10.9955742875643x_{39} = -10.9955742875643
x40=17.2787595947439x_{40} = 17.2787595947439
x41=−95.8185759344887x_{41} = -95.8185759344887
x42=−36.1283155162826x_{42} = -36.1283155162826
x43=61.261056745001x_{43} = 61.261056745001
x44=114.668131856027x_{44} = 114.668131856027
x45=73.8274273593601x_{45} = 73.8274273593601
x46=14.1371669411541x_{46} = 14.1371669411541
x47=−26.7035375555132x_{47} = -26.7035375555132
x48=51.8362787842316x_{48} = 51.8362787842316
x49=−89.5353906273091x_{49} = -89.5353906273091
x50=39.2699081698724x_{50} = 39.2699081698724
x51=−32.9867228626928x_{51} = -32.9867228626928
x52=−14.1371669411541x_{52} = -14.1371669411541
x53=−4.71238898038469x_{53} = -4.71238898038469
x54=−76.9690200129499x_{54} = -76.9690200129499
x55=95.8185759344887x_{55} = 95.8185759344887
x56=−114.668131856027x_{56} = -114.668131856027
x57=76.9690200129499x_{57} = 76.9690200129499
x58=58.1194640914112x_{58} = 58.1194640914112
x59=−80.1106126665397x_{59} = -80.1106126665397
x60=−73.8274273593601x_{60} = -73.8274273593601
x61=7.85398163397448x_{61} = 7.85398163397448
x62=−1.5707963267949x_{62} = -1.5707963267949
x63=29.845130209103x_{63} = 29.845130209103
x64=0x_{64} = 0
x65=67.5442420521806x_{65} = 67.5442420521806
x66=26.7035375555132x_{66} = 26.7035375555132
x67=−98.9601685880785x_{67} = -98.9601685880785
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*cos(x).
0cos⁡(0)0 \cos{\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
−xsin⁡(x)+cos⁡(x)=0- x \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=59.7070073053355x_{1} = 59.7070073053355
x2=84.8347887180423x_{2} = 84.8347887180423
x3=−78.5525459842429x_{3} = -78.5525459842429
x4=6.43729817917195x_{4} = 6.43729817917195
x5=−47.145097736761x_{5} = -47.145097736761
x6=−69.1295029738953x_{6} = -69.1295029738953
x7=−9.52933440536196x_{7} = -9.52933440536196
x8=40.8651703304881x_{8} = 40.8651703304881
x9=22.0364967279386x_{9} = 22.0364967279386
x10=18.90240995686x_{10} = 18.90240995686
x11=−40.8651703304881x_{11} = -40.8651703304881
x12=0.86033358901938x_{12} = 0.86033358901938
x13=28.309642854452x_{13} = 28.309642854452
x14=25.1724463266467x_{14} = 25.1724463266467
x15=65.9885986984904x_{15} = 65.9885986984904
x16=−147.661626855354x_{16} = -147.661626855354
x17=−100.540910786842x_{17} = -100.540910786842
x18=−0.86033358901938x_{18} = -0.86033358901938
x19=44.0050179208308x_{19} = 44.0050179208308
x20=12.6452872238566x_{20} = 12.6452872238566
x21=3.42561845948173x_{21} = 3.42561845948173
x22=97.3996388790738x_{22} = 97.3996388790738
x23=−15.7712848748159x_{23} = -15.7712848748159
x24=72.270467060309x_{24} = 72.270467060309
x25=−84.8347887180423x_{25} = -84.8347887180423
x26=9.52933440536196x_{26} = 9.52933440536196
x27=−44.0050179208308x_{27} = -44.0050179208308
x28=−75.4114834888481x_{28} = -75.4114834888481
x29=−65.9885986984904x_{29} = -65.9885986984904
x30=−56.5663442798215x_{30} = -56.5663442798215
x31=53.4257904773947x_{31} = 53.4257904773947
x32=−53.4257904773947x_{32} = -53.4257904773947
x33=87.9759605524932x_{33} = 87.9759605524932
x34=69.1295029738953x_{34} = 69.1295029738953
x35=47.145097736761x_{35} = 47.145097736761
x36=−6.43729817917195x_{36} = -6.43729817917195
x37=−97.3996388790738x_{37} = -97.3996388790738
x38=−18.90240995686x_{38} = -18.90240995686
x39=78.5525459842429x_{39} = 78.5525459842429
x40=−25.1724463266467x_{40} = -25.1724463266467
x41=15.7712848748159x_{41} = 15.7712848748159
x42=−91.1171613944647x_{42} = -91.1171613944647
x43=−28.309642854452x_{43} = -28.309642854452
x44=−81.6936492356017x_{44} = -81.6936492356017
x45=−3.42561845948173x_{45} = -3.42561845948173
x46=−12.6452872238566x_{46} = -12.6452872238566
x47=−59.7070073053355x_{47} = -59.7070073053355
x48=91.1171613944647x_{48} = 91.1171613944647
x49=31.4477146375462x_{49} = 31.4477146375462
x50=−72.270467060309x_{50} = -72.270467060309
x51=81.6936492356017x_{51} = 81.6936492356017
x52=−116.247530303932x_{52} = -116.247530303932
x53=−94.2583883450399x_{53} = -94.2583883450399
x54=−50.2853663377737x_{54} = -50.2853663377737
x55=−31.4477146375462x_{55} = -31.4477146375462
x56=−37.7256128277765x_{56} = -37.7256128277765
x57=−87.9759605524932x_{57} = -87.9759605524932
x58=34.5864242152889x_{58} = 34.5864242152889
x59=94.2583883450399x_{59} = 94.2583883450399
x60=62.8477631944545x_{60} = 62.8477631944545
x61=−34.5864242152889x_{61} = -34.5864242152889
x62=−62.8477631944545x_{62} = -62.8477631944545
x63=37.7256128277765x_{63} = 37.7256128277765
x64=−22.0364967279386x_{64} = -22.0364967279386
x65=50.2853663377737x_{65} = 50.2853663377737
x66=75.4114834888481x_{66} = 75.4114834888481
x67=56.5663442798215x_{67} = 56.5663442798215
x68=100.540910786842x_{68} = 100.540910786842
Signos de extremos en los puntos:
(59.70700730533546, -59.6986348402658)

(84.83478871804229, -84.8288955236568)

(-78.55254598424293, 78.5461815917343)

(6.437298179171947, 6.36100394483385)

(-47.14509773676103, 47.1344957575419)

(-69.12950297389526, -69.1222713069218)

(-9.529334405361963, 9.47729425947979)

(40.86517033048807, -40.8529404645174)

(22.036496727938566, -22.0138420791585)

(18.902409956860023, 18.876013697969)

(-40.86517033048807, 40.8529404645174)

(0.8603335890193797, 0.561096338191045)

(28.30964285445201, -28.2919975390943)

(25.172446326646664, 25.1526068178715)

(65.98859869849039, -65.9810229367917)

(-147.66162685535437, 147.658240851742)

(-100.54091078684232, -100.535938055826)

(-0.8603335890193797, -0.561096338191045)

(44.005017920830845, 43.9936599791065)

(12.645287223856643, 12.6059312978927)

(3.4256184594817283, -3.2883713955909)

(97.39963887907376, -97.3945057956234)

(-15.771284874815882, 15.7396769621337)

(72.27046706030896, -72.2635495982494)

(-84.83478871804229, 84.8288955236568)

(9.529334405361963, -9.47729425947979)

(-44.005017920830845, -43.9936599791065)

(-75.41148348884815, -75.4048540732019)

(-65.98859869849039, 65.9810229367917)

(-56.56634427982152, -56.5575071728762)

(53.42579047739466, -53.4164341598961)

(-53.42579047739466, 53.4164341598961)

(87.97596055249322, 87.9702777324248)

(69.12950297389526, 69.1222713069218)

(47.14509773676103, -47.1344957575419)

(-6.437298179171947, -6.36100394483385)

(-97.39963887907376, 97.3945057956234)

(-18.902409956860023, -18.876013697969)

(78.55254598424293, -78.5461815917343)

(-25.172446326646664, -25.1526068178715)

(15.771284874815882, -15.7396769621337)

(-91.11716139446474, 91.1116744496469)

(-28.30964285445201, 28.2919975390943)

(-81.69364923560168, -81.6875294965246)

(-3.4256184594817283, 3.2883713955909)

(-12.645287223856643, -12.6059312978927)

(-59.70700730533546, 59.6986348402658)

(91.11716139446474, -91.1116744496469)

(31.447714637546234, 31.4318272785346)

(-72.27046706030896, 72.2635495982494)

(81.69364923560168, 81.6875294965246)

(-116.2475303039321, 116.243229375987)

(-94.25838834503986, -94.2530842251087)

(-50.28536633777365, -50.2754260353972)

(-31.447714637546234, -31.4318272785346)

(-37.7256128277765, -37.71236621281)

(-87.97596055249322, -87.9702777324248)

(34.58642421528892, -34.5719767335884)

(94.25838834503986, 94.2530842251087)

(62.84776319445445, 62.8398089721545)

(-34.58642421528892, 34.5719767335884)

(-62.84776319445445, -62.8398089721545)

(37.7256128277765, 37.71236621281)

(-22.036496727938566, 22.0138420791585)

(50.28536633777365, 50.2754260353972)

(75.41148348884815, 75.4048540732019)

(56.56634427982152, 56.5575071728762)

(100.54091078684232, 100.535938055826)


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=59.7070073053355x_{1} = 59.7070073053355
x2=84.8347887180423x_{2} = 84.8347887180423
x3=−69.1295029738953x_{3} = -69.1295029738953
x4=40.8651703304881x_{4} = 40.8651703304881
x5=22.0364967279386x_{5} = 22.0364967279386
x6=28.309642854452x_{6} = 28.309642854452
x7=65.9885986984904x_{7} = 65.9885986984904
x8=−100.540910786842x_{8} = -100.540910786842
x9=−0.86033358901938x_{9} = -0.86033358901938
x10=3.42561845948173x_{10} = 3.42561845948173
x11=97.3996388790738x_{11} = 97.3996388790738
x12=72.270467060309x_{12} = 72.270467060309
x13=9.52933440536196x_{13} = 9.52933440536196
x14=−44.0050179208308x_{14} = -44.0050179208308
x15=−75.4114834888481x_{15} = -75.4114834888481
x16=−56.5663442798215x_{16} = -56.5663442798215
x17=53.4257904773947x_{17} = 53.4257904773947
x18=47.145097736761x_{18} = 47.145097736761
x19=−6.43729817917195x_{19} = -6.43729817917195
x20=−18.90240995686x_{20} = -18.90240995686
x21=78.5525459842429x_{21} = 78.5525459842429
x22=−25.1724463266467x_{22} = -25.1724463266467
x23=15.7712848748159x_{23} = 15.7712848748159
x24=−81.6936492356017x_{24} = -81.6936492356017
x25=−12.6452872238566x_{25} = -12.6452872238566
x26=91.1171613944647x_{26} = 91.1171613944647
x27=−94.2583883450399x_{27} = -94.2583883450399
x28=−50.2853663377737x_{28} = -50.2853663377737
x29=−31.4477146375462x_{29} = -31.4477146375462
x30=−37.7256128277765x_{30} = -37.7256128277765
x31=−87.9759605524932x_{31} = -87.9759605524932
x32=34.5864242152889x_{32} = 34.5864242152889
x33=−62.8477631944545x_{33} = -62.8477631944545
Puntos máximos de la función:
x33=−78.5525459842429x_{33} = -78.5525459842429
x33=6.43729817917195x_{33} = 6.43729817917195
x33=−47.145097736761x_{33} = -47.145097736761
x33=−9.52933440536196x_{33} = -9.52933440536196
x33=18.90240995686x_{33} = 18.90240995686
x33=−40.8651703304881x_{33} = -40.8651703304881
x33=0.86033358901938x_{33} = 0.86033358901938
x33=25.1724463266467x_{33} = 25.1724463266467
x33=−147.661626855354x_{33} = -147.661626855354
x33=44.0050179208308x_{33} = 44.0050179208308
x33=12.6452872238566x_{33} = 12.6452872238566
x33=−15.7712848748159x_{33} = -15.7712848748159
x33=−84.8347887180423x_{33} = -84.8347887180423
x33=−65.9885986984904x_{33} = -65.9885986984904
x33=−53.4257904773947x_{33} = -53.4257904773947
x33=87.9759605524932x_{33} = 87.9759605524932
x33=69.1295029738953x_{33} = 69.1295029738953
x33=−97.3996388790738x_{33} = -97.3996388790738
x33=−91.1171613944647x_{33} = -91.1171613944647
x33=−28.309642854452x_{33} = -28.309642854452
x33=−3.42561845948173x_{33} = -3.42561845948173
x33=−59.7070073053355x_{33} = -59.7070073053355
x33=31.4477146375462x_{33} = 31.4477146375462
x33=−72.270467060309x_{33} = -72.270467060309
x33=81.6936492356017x_{33} = 81.6936492356017
x33=−116.247530303932x_{33} = -116.247530303932
x33=94.2583883450399x_{33} = 94.2583883450399
x33=62.8477631944545x_{33} = 62.8477631944545
x33=−34.5864242152889x_{33} = -34.5864242152889
x33=37.7256128277765x_{33} = 37.7256128277765
x33=−22.0364967279386x_{33} = -22.0364967279386
x33=50.2853663377737x_{33} = 50.2853663377737
x33=75.4114834888481x_{33} = 75.4114834888481
x33=56.5663442798215x_{33} = 56.5663442798215
x33=100.540910786842x_{33} = 100.540910786842
Decrece en los intervalos
[97.3996388790738,∞)\left[97.3996388790738, \infty\right)
Crece en los intervalos
(−∞,−100.540910786842]\left(-\infty, -100.540910786842\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
−(xcos⁡(x)+2sin⁡(x))=0- (x \cos{\left(x \right)} + 2 \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=33.0471686947054x_{1} = 33.0471686947054
x2=−76.9949898891676x_{2} = -76.9949898891676
x3=−98.9803718651523x_{3} = -98.9803718651523
x4=5.08698509410227x_{4} = 5.08698509410227
x5=−64.4336791037316x_{5} = -64.4336791037316
x6=92.6985552433969x_{6} = 92.6985552433969
x7=42.458570771699x_{7} = 42.458570771699
x8=45.5969279840735x_{8} = 45.5969279840735
x9=51.8748140534268x_{9} = 51.8748140534268
x10=−95.839441141233x_{10} = -95.839441141233
x11=64.4336791037316x_{11} = 64.4336791037316
x12=48.7357007949054x_{12} = 48.7357007949054
x13=−48.7357007949054x_{13} = -48.7357007949054
x14=−29.9118938695518x_{14} = -29.9118938695518
x15=−17.3932439645948x_{15} = -17.3932439645948
x16=−80.1355651940744x_{16} = -80.1355651940744
x17=−5.08698509410227x_{17} = -5.08698509410227
x18=−33.0471686947054x_{18} = -33.0471686947054
x19=58.153842078645x_{19} = 58.153842078645
x20=−8.09616360322292x_{20} = -8.09616360322292
x21=70.7141100665485x_{21} = 70.7141100665485
x22=61.2936749662429x_{22} = 61.2936749662429
x23=29.9118938695518x_{23} = 29.9118938695518
x24=86.4169374541167x_{24} = 86.4169374541167
x25=23.6463238196036x_{25} = 23.6463238196036
x26=−23.6463238196036x_{26} = -23.6463238196036
x27=−58.153842078645x_{27} = -58.153842078645
x28=20.5175229099417x_{28} = 20.5175229099417
x29=36.1835330907526x_{29} = 36.1835330907526
x30=−89.5577188827244x_{30} = -89.5577188827244
x31=14.2763529183365x_{31} = 14.2763529183365
x32=−39.3207281322521x_{32} = -39.3207281322521
x33=11.17270586833x_{33} = 11.17270586833
x34=17.3932439645948x_{34} = 17.3932439645948
x35=98.9803718651523x_{35} = 98.9803718651523
x36=80.1355651940744x_{36} = 80.1355651940744
x37=−2.2889297281034x_{37} = -2.2889297281034
x38=−67.573830670859x_{38} = -67.573830670859
x39=2.2889297281034x_{39} = 2.2889297281034
x40=−36.1835330907526x_{40} = -36.1835330907526
x41=−14.2763529183365x_{41} = -14.2763529183365
x42=−73.8545010149048x_{42} = -73.8545010149048
x43=−42.458570771699x_{43} = -42.458570771699
x44=55.0142096788381x_{44} = 55.0142096788381
x45=89.5577188827244x_{45} = 89.5577188827244
x46=−92.6985552433969x_{46} = -92.6985552433969
x47=26.7780870755585x_{47} = 26.7780870755585
x48=−26.7780870755585x_{48} = -26.7780870755585
x49=−61.2936749662429x_{49} = -61.2936749662429
x50=8.09616360322292x_{50} = 8.09616360322292
x51=−51.8748140534268x_{51} = -51.8748140534268
x52=−83.2762171649775x_{52} = -83.2762171649775
x53=95.839441141233x_{53} = 95.839441141233
x54=−45.5969279840735x_{54} = -45.5969279840735
x55=73.8545010149048x_{55} = 73.8545010149048
x56=−70.7141100665485x_{56} = -70.7141100665485
x57=−20.5175229099417x_{57} = -20.5175229099417
x58=67.573830670859x_{58} = 67.573830670859
x59=39.3207281322521x_{59} = 39.3207281322521
x60=76.9949898891676x_{60} = 76.9949898891676
x61=83.2762171649775x_{61} = 83.2762171649775
x62=−55.0142096788381x_{62} = -55.0142096788381
x63=0x_{63} = 0
x64=−86.4169374541167x_{64} = -86.4169374541167
x65=−11.17270586833x_{65} = -11.17270586833

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
[95.839441141233,∞)\left[95.839441141233, \infty\right)
Convexa en los intervalos
(−∞,−95.839441141233]\left(-\infty, -95.839441141233\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xcos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \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→∞(xcos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \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 x*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞cos⁡(x)=⟨−1,1⟩\lim_{x \to -\infty} \cos{\left(x \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞cos⁡(x)=⟨−1,1⟩\lim_{x \to \infty} \cos{\left(x \right)} = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\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:
xcos⁡(x)=−xcos⁡(x)x \cos{\left(x \right)} = - x \cos{\left(x \right)}
- No
xcos⁡(x)=xcos⁡(x)x \cos{\left(x \right)} = x \cos{\left(x \right)}
- Sí
es decir, función
es
impar
    © Sr Examen – Калькулятор