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

Gráfico de la función y = cos(x)*2*x

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cos(x)*2*x
f(x)=x2cos⁡(x)f{\left(x \right)} = x 2 \cos{\left(x \right)} 
f = x*(2*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:
x2cos⁡(x)=0x 2 \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=−1.5707963267949x_{1} = -1.5707963267949
x2=−64.4026493985908x_{2} = -64.4026493985908
x3=76.9690200129499x_{3} = 76.9690200129499
x4=−23.5619449019235x_{4} = -23.5619449019235
x5=−58.1194640914112x_{5} = -58.1194640914112
x6=61.261056745001x_{6} = 61.261056745001
x7=80.1106126665397x_{7} = 80.1106126665397
x8=114.668131856027x_{8} = 114.668131856027
x9=−29.845130209103x_{9} = -29.845130209103
x10=−48.6946861306418x_{10} = -48.6946861306418
x11=−114.668131856027x_{11} = -114.668131856027
x12=−4.71238898038469x_{12} = -4.71238898038469
x13=−86.3937979737193x_{13} = -86.3937979737193
x14=−36.1283155162826x_{14} = -36.1283155162826
x15=−98.9601685880785x_{15} = -98.9601685880785
x16=1.5707963267949x_{16} = 1.5707963267949
x17=−39.2699081698724x_{17} = -39.2699081698724
x18=73.8274273593601x_{18} = 73.8274273593601
x19=−92.6769832808989x_{19} = -92.6769832808989
x20=42.4115008234622x_{20} = 42.4115008234622
x21=67.5442420521806x_{21} = 67.5442420521806
x22=−32.9867228626928x_{22} = -32.9867228626928
x23=14.1371669411541x_{23} = 14.1371669411541
x24=4.71238898038469x_{24} = 4.71238898038469
x25=32.9867228626928x_{25} = 32.9867228626928
x26=−10.9955742875643x_{26} = -10.9955742875643
x27=0x_{27} = 0
x28=36.1283155162826x_{28} = 36.1283155162826
x29=70.6858347057703x_{29} = 70.6858347057703
x30=20.4203522483337x_{30} = 20.4203522483337
x31=−70.6858347057703x_{31} = -70.6858347057703
x32=−26.7035375555132x_{32} = -26.7035375555132
x33=10.9955742875643x_{33} = 10.9955742875643
x34=23.5619449019235x_{34} = 23.5619449019235
x35=45.553093477052x_{35} = 45.553093477052
x36=83.2522053201295x_{36} = 83.2522053201295
x37=−67.5442420521806x_{37} = -67.5442420521806
x38=−89.5353906273091x_{38} = -89.5353906273091
x39=−54.9778714378214x_{39} = -54.9778714378214
x40=95.8185759344887x_{40} = 95.8185759344887
x41=−17.2787595947439x_{41} = -17.2787595947439
x42=26.7035375555132x_{42} = 26.7035375555132
x43=17.2787595947439x_{43} = 17.2787595947439
x44=−42.4115008234622x_{44} = -42.4115008234622
x45=54.9778714378214x_{45} = 54.9778714378214
x46=−7.85398163397448x_{46} = -7.85398163397448
x47=48.6946861306418x_{47} = 48.6946861306418
x48=−51.8362787842316x_{48} = -51.8362787842316
x49=89.5353906273091x_{49} = 89.5353906273091
x50=92.6769832808989x_{50} = 92.6769832808989
x51=58.1194640914112x_{51} = 58.1194640914112
x52=−80.1106126665397x_{52} = -80.1106126665397
x53=−73.8274273593601x_{53} = -73.8274273593601
x54=86.3937979737193x_{54} = 86.3937979737193
x55=−76.9690200129499x_{55} = -76.9690200129499
x56=51.8362787842316x_{56} = 51.8362787842316
x57=39.2699081698724x_{57} = 39.2699081698724
x58=−20.4203522483337x_{58} = -20.4203522483337
x59=64.4026493985908x_{59} = 64.4026493985908
x60=−83.2522053201295x_{60} = -83.2522053201295
x61=98.9601685880785x_{61} = 98.9601685880785
x62=7.85398163397448x_{62} = 7.85398163397448
x63=−95.8185759344887x_{63} = -95.8185759344887
x64=−14.1371669411541x_{64} = -14.1371669411541
x65=29.845130209103x_{65} = 29.845130209103
x66=−45.553093477052x_{66} = -45.553093477052
x67=−61.261056745001x_{67} = -61.261056745001
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 (cos(x)*2)*x.
0⋅2cos⁡(0)0 \cdot 2 \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
−2xsin⁡(x)+2cos⁡(x)=0- 2 x \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=100.540910786842x_{1} = 100.540910786842
x2=−62.8477631944545x_{2} = -62.8477631944545
x3=−84.8347887180423x_{3} = -84.8347887180423
x4=−31.4477146375462x_{4} = -31.4477146375462
x5=−12.6452872238566x_{5} = -12.6452872238566
x6=37.7256128277765x_{6} = 37.7256128277765
x7=−9.52933440536196x_{7} = -9.52933440536196
x8=72.270467060309x_{8} = 72.270467060309
x9=12.6452872238566x_{9} = 12.6452872238566
x10=−53.4257904773947x_{10} = -53.4257904773947
x11=−147.661626855354x_{11} = -147.661626855354
x12=−34.5864242152889x_{12} = -34.5864242152889
x13=15.7712848748159x_{13} = 15.7712848748159
x14=75.4114834888481x_{14} = 75.4114834888481
x15=−37.7256128277765x_{15} = -37.7256128277765
x16=65.9885986984904x_{16} = 65.9885986984904
x17=−28.309642854452x_{17} = -28.309642854452
x18=97.3996388790738x_{18} = 97.3996388790738
x19=62.8477631944545x_{19} = 62.8477631944545
x20=6.43729817917195x_{20} = 6.43729817917195
x21=−44.0050179208308x_{21} = -44.0050179208308
x22=22.0364967279386x_{22} = 22.0364967279386
x23=−87.9759605524932x_{23} = -87.9759605524932
x24=59.7070073053355x_{24} = 59.7070073053355
x25=−97.3996388790738x_{25} = -97.3996388790738
x26=−0.86033358901938x_{26} = -0.86033358901938
x27=0.86033358901938x_{27} = 0.86033358901938
x28=−78.5525459842429x_{28} = -78.5525459842429
x29=−3.42561845948173x_{29} = -3.42561845948173
x30=−22.0364967279386x_{30} = -22.0364967279386
x31=−69.1295029738953x_{31} = -69.1295029738953
x32=18.90240995686x_{32} = 18.90240995686
x33=78.5525459842429x_{33} = 78.5525459842429
x34=31.4477146375462x_{34} = 31.4477146375462
x35=−18.90240995686x_{35} = -18.90240995686
x36=−116.247530303932x_{36} = -116.247530303932
x37=53.4257904773947x_{37} = 53.4257904773947
x38=−75.4114834888481x_{38} = -75.4114834888481
x39=−25.1724463266467x_{39} = -25.1724463266467
x40=−15.7712848748159x_{40} = -15.7712848748159
x41=−56.5663442798215x_{41} = -56.5663442798215
x42=81.6936492356017x_{42} = 81.6936492356017
x43=25.1724463266467x_{43} = 25.1724463266467
x44=56.5663442798215x_{44} = 56.5663442798215
x45=50.2853663377737x_{45} = 50.2853663377737
x46=44.0050179208308x_{46} = 44.0050179208308
x47=−6.43729817917195x_{47} = -6.43729817917195
x48=−65.9885986984904x_{48} = -65.9885986984904
x49=−94.2583883450399x_{49} = -94.2583883450399
x50=87.9759605524932x_{50} = 87.9759605524932
x51=−47.145097736761x_{51} = -47.145097736761
x52=3.42561845948173x_{52} = 3.42561845948173
x53=−91.1171613944647x_{53} = -91.1171613944647
x54=−100.540910786842x_{54} = -100.540910786842
x55=34.5864242152889x_{55} = 34.5864242152889
x56=40.8651703304881x_{56} = 40.8651703304881
x57=94.2583883450399x_{57} = 94.2583883450399
x58=−81.6936492356017x_{58} = -81.6936492356017
x59=−72.270467060309x_{59} = -72.270467060309
x60=−59.7070073053355x_{60} = -59.7070073053355
x61=9.52933440536196x_{61} = 9.52933440536196
x62=69.1295029738953x_{62} = 69.1295029738953
x63=28.309642854452x_{63} = 28.309642854452
x64=91.1171613944647x_{64} = 91.1171613944647
x65=47.145097736761x_{65} = 47.145097736761
x66=−40.8651703304881x_{66} = -40.8651703304881
x67=−50.2853663377737x_{67} = -50.2853663377737
x68=84.8347887180423x_{68} = 84.8347887180423
Signos de extremos en los puntos:
(100.54091078684232, 201.071876111652)

(-62.84776319445445, -125.679617944309)

(-84.83478871804229, 169.657791047314)

(-31.447714637546234, -62.8636545570692)

(-12.645287223856643, -25.2118625957854)

(37.7256128277765, 75.4247324256199)

(-9.529334405361963, 18.9545885189596)

(72.27046706030896, -144.527099196499)

(12.645287223856643, 25.2118625957854)

(-53.42579047739466, 106.832868319792)

(-147.66162685535437, 295.316481703484)

(-34.58642421528892, 69.1439534671769)

(15.771284874815882, -31.4793539242675)

(75.41148348884815, 150.809708146404)

(-37.7256128277765, -75.4247324256199)

(65.98859869849039, -131.962045873583)

(-28.30964285445201, 56.5839950781887)

(97.39963887907376, -194.789011591247)

(62.84776319445445, 125.679617944309)

(6.437298179171947, 12.7220078896677)

(-44.005017920830845, -87.9873199582129)

(22.036496727938566, -44.0276841583169)

(-87.97596055249322, -175.94055546485)

(59.70700730533546, -119.397269680532)

(-97.39963887907376, 194.789011591247)

(-0.8603335890193797, -1.12219267638209)

(0.8603335890193797, 1.12219267638209)

(-78.55254598424293, 157.092363183469)

(-3.4256184594817283, 6.57674279118179)

(-22.036496727938566, 44.0276841583169)

(-69.12950297389526, -138.244542613844)

(18.902409956860023, 37.752027395938)

(78.55254598424293, -157.092363183469)

(31.447714637546234, 62.8636545570692)

(-18.902409956860023, -37.752027395938)

(-116.2475303039321, 232.486458751974)

(53.42579047739466, -106.832868319792)

(-75.41148348884815, -150.809708146404)

(-25.172446326646664, -50.3052136357431)

(-15.771284874815882, 31.4793539242675)

(-56.56634427982152, -113.115014345752)

(81.69364923560168, 163.375058993049)

(25.172446326646664, 50.3052136357431)

(56.56634427982152, 113.115014345752)

(50.28536633777365, 100.550852070794)

(44.005017920830845, 87.9873199582129)

(-6.437298179171947, -12.7220078896677)

(-65.98859869849039, 131.962045873583)

(-94.25838834503986, -188.506168450217)

(87.97596055249322, 175.94055546485)

(-47.14509773676103, 94.2689915150839)

(3.4256184594817283, -6.57674279118179)

(-91.11716139446474, 182.223348899294)

(-100.54091078684232, -201.071876111652)

(34.58642421528892, -69.1439534671769)

(40.86517033048807, -81.7058809290348)

(94.25838834503986, 188.506168450217)

(-81.69364923560168, -163.375058993049)

(-72.27046706030896, 144.527099196499)

(-59.70700730533546, 119.397269680532)

(9.529334405361963, -18.9545885189596)

(69.12950297389526, 138.244542613844)

(28.30964285445201, -56.5839950781887)

(91.11716139446474, -182.223348899294)

(47.14509773676103, -94.2689915150839)

(-40.86517033048807, 81.7058809290348)

(-50.28536633777365, -100.550852070794)

(84.83478871804229, -169.657791047314)


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

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→−∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x 2 \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→∞(x2cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x 2 \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 (cos(x)*2)*x, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(2cos⁡(x))=⟨−2,2⟩\lim_{x \to -\infty}\left(2 \cos{\left(x \right)}\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→∞(2cos⁡(x))=⟨−2,2⟩\lim_{x \to \infty}\left(2 \cos{\left(x \right)}\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:
x2cos⁡(x)=−2xcos⁡(x)x 2 \cos{\left(x \right)} = - 2 x \cos{\left(x \right)}
- No
x2cos⁡(x)=2xcos⁡(x)x 2 \cos{\left(x \right)} = 2 x \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор