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Trazado el gráfico de la función/ xcosx

Gráfico de la función y = xcosx

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
20.000020.010020.001020.002020.003020.004020.005020.006020.007020.008020.00908.168.18
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=4.71238898038469x_{1} = 4.71238898038469
x2=114.668131856027x_{2} = 114.668131856027
x3=17.2787595947439x_{3} = 17.2787595947439
x4=−89.5353906273091x_{4} = -89.5353906273091
x5=64.4026493985908x_{5} = 64.4026493985908
x6=70.6858347057703x_{6} = 70.6858347057703
x7=36.1283155162826x_{7} = 36.1283155162826
x8=−98.9601685880785x_{8} = -98.9601685880785
x9=48.6946861306418x_{9} = 48.6946861306418
x10=−58.1194640914112x_{10} = -58.1194640914112
x11=7.85398163397448x_{11} = 7.85398163397448
x12=39.2699081698724x_{12} = 39.2699081698724
x13=−95.8185759344887x_{13} = -95.8185759344887
x14=−1.5707963267949x_{14} = -1.5707963267949
x15=−92.6769832808989x_{15} = -92.6769832808989
x16=−23.5619449019235x_{16} = -23.5619449019235
x17=23.5619449019235x_{17} = 23.5619449019235
x18=61.261056745001x_{18} = 61.261056745001
x19=29.845130209103x_{19} = 29.845130209103
x20=−32.9867228626928x_{20} = -32.9867228626928
x21=−51.8362787842316x_{21} = -51.8362787842316
x22=−80.1106126665397x_{22} = -80.1106126665397
x23=−83.2522053201295x_{23} = -83.2522053201295
x24=67.5442420521806x_{24} = 67.5442420521806
x25=98.9601685880785x_{25} = 98.9601685880785
x26=92.6769832808989x_{26} = 92.6769832808989
x27=−39.2699081698724x_{27} = -39.2699081698724
x28=86.3937979737193x_{28} = 86.3937979737193
x29=45.553093477052x_{29} = 45.553093477052
x30=−67.5442420521806x_{30} = -67.5442420521806
x31=51.8362787842316x_{31} = 51.8362787842316
x32=76.9690200129499x_{32} = 76.9690200129499
x33=−26.7035375555132x_{33} = -26.7035375555132
x34=−4.71238898038469x_{34} = -4.71238898038469
x35=95.8185759344887x_{35} = 95.8185759344887
x36=−86.3937979737193x_{36} = -86.3937979737193
x37=−10.9955742875643x_{37} = -10.9955742875643
x38=83.2522053201295x_{38} = 83.2522053201295
x39=−7.85398163397448x_{39} = -7.85398163397448
x40=−36.1283155162826x_{40} = -36.1283155162826
x41=−17.2787595947439x_{41} = -17.2787595947439
x42=−14.1371669411541x_{42} = -14.1371669411541
x43=20.4203522483337x_{43} = 20.4203522483337
x44=54.9778714378214x_{44} = 54.9778714378214
x45=−70.6858347057703x_{45} = -70.6858347057703
x46=−48.6946861306418x_{46} = -48.6946861306418
x47=−54.9778714378214x_{47} = -54.9778714378214
x48=−45.553093477052x_{48} = -45.553093477052
x49=14.1371669411541x_{49} = 14.1371669411541
x50=−73.8274273593601x_{50} = -73.8274273593601
x51=26.7035375555132x_{51} = 26.7035375555132
x52=89.5353906273091x_{52} = 89.5353906273091
x53=10.9955742875643x_{53} = 10.9955742875643
x54=80.1106126665397x_{54} = 80.1106126665397
x55=73.8274273593601x_{55} = 73.8274273593601
x56=−114.668131856027x_{56} = -114.668131856027
x57=−61.261056745001x_{57} = -61.261056745001
x58=58.1194640914112x_{58} = 58.1194640914112
x59=1.5707963267949x_{59} = 1.5707963267949
x60=−20.4203522483337x_{60} = -20.4203522483337
x61=−42.4115008234622x_{61} = -42.4115008234622
x62=32.9867228626928x_{62} = 32.9867228626928
x63=0x_{63} = 0
x64=42.4115008234622x_{64} = 42.4115008234622
x65=−76.9690200129499x_{65} = -76.9690200129499
x66=−64.4026493985908x_{66} = -64.4026493985908
x67=−29.845130209103x_{67} = -29.845130209103
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=40.8651703304881x_{1} = 40.8651703304881
x2=−78.5525459842429x_{2} = -78.5525459842429
x3=−53.4257904773947x_{3} = -53.4257904773947
x4=−50.2853663377737x_{4} = -50.2853663377737
x5=15.7712848748159x_{5} = 15.7712848748159
x6=−44.0050179208308x_{6} = -44.0050179208308
x7=87.9759605524932x_{7} = 87.9759605524932
x8=59.7070073053355x_{8} = 59.7070073053355
x9=−116.247530303932x_{9} = -116.247530303932
x10=−47.145097736761x_{10} = -47.145097736761
x11=53.4257904773947x_{11} = 53.4257904773947
x12=−22.0364967279386x_{12} = -22.0364967279386
x13=50.2853663377737x_{13} = 50.2853663377737
x14=69.1295029738953x_{14} = 69.1295029738953
x15=65.9885986984904x_{15} = 65.9885986984904
x16=0.86033358901938x_{16} = 0.86033358901938
x17=−0.86033358901938x_{17} = -0.86033358901938
x18=12.6452872238566x_{18} = 12.6452872238566
x19=−34.5864242152889x_{19} = -34.5864242152889
x20=25.1724463266467x_{20} = 25.1724463266467
x21=−28.309642854452x_{21} = -28.309642854452
x22=62.8477631944545x_{22} = 62.8477631944545
x23=−87.9759605524932x_{23} = -87.9759605524932
x24=−40.8651703304881x_{24} = -40.8651703304881
x25=−147.661626855354x_{25} = -147.661626855354
x26=44.0050179208308x_{26} = 44.0050179208308
x27=−59.7070073053355x_{27} = -59.7070073053355
x28=3.42561845948173x_{28} = 3.42561845948173
x29=56.5663442798215x_{29} = 56.5663442798215
x30=−81.6936492356017x_{30} = -81.6936492356017
x31=22.0364967279386x_{31} = 22.0364967279386
x32=−3.42561845948173x_{32} = -3.42561845948173
x33=9.52933440536196x_{33} = 9.52933440536196
x34=72.270467060309x_{34} = 72.270467060309
x35=81.6936492356017x_{35} = 81.6936492356017
x36=−75.4114834888481x_{36} = -75.4114834888481
x37=37.7256128277765x_{37} = 37.7256128277765
x38=75.4114834888481x_{38} = 75.4114834888481
x39=6.43729817917195x_{39} = 6.43729817917195
x40=−91.1171613944647x_{40} = -91.1171613944647
x41=−84.8347887180423x_{41} = -84.8347887180423
x42=−9.52933440536196x_{42} = -9.52933440536196
x43=−6.43729817917195x_{43} = -6.43729817917195
x44=−18.90240995686x_{44} = -18.90240995686
x45=−100.540910786842x_{45} = -100.540910786842
x46=−25.1724463266467x_{46} = -25.1724463266467
x47=18.90240995686x_{47} = 18.90240995686
x48=28.309642854452x_{48} = 28.309642854452
x49=−69.1295029738953x_{49} = -69.1295029738953
x50=84.8347887180423x_{50} = 84.8347887180423
x51=91.1171613944647x_{51} = 91.1171613944647
x52=−62.8477631944545x_{52} = -62.8477631944545
x53=34.5864242152889x_{53} = 34.5864242152889
x54=−94.2583883450399x_{54} = -94.2583883450399
x55=−56.5663442798215x_{55} = -56.5663442798215
x56=94.2583883450399x_{56} = 94.2583883450399
x57=47.145097736761x_{57} = 47.145097736761
x58=97.3996388790738x_{58} = 97.3996388790738
x59=31.4477146375462x_{59} = 31.4477146375462
x60=−31.4477146375462x_{60} = -31.4477146375462
x61=−37.7256128277765x_{61} = -37.7256128277765
x62=78.5525459842429x_{62} = 78.5525459842429
x63=−12.6452872238566x_{63} = -12.6452872238566
x64=−72.270467060309x_{64} = -72.270467060309
x65=−65.9885986984904x_{65} = -65.9885986984904
x66=−15.7712848748159x_{66} = -15.7712848748159
x67=−97.3996388790738x_{67} = -97.3996388790738
x68=100.540910786842x_{68} = 100.540910786842
Signos de extremos en los puntos:
(40.86517033048807, -40.8529404645174)

(-78.55254598424293, 78.5461815917343)

(-53.42579047739466, 53.4164341598961)

(-50.28536633777365, -50.2754260353972)

(15.771284874815882, -15.7396769621337)

(-44.005017920830845, -43.9936599791065)

(87.97596055249322, 87.9702777324248)

(59.70700730533546, -59.6986348402658)

(-116.2475303039321, 116.243229375987)

(-47.14509773676103, 47.1344957575419)

(53.42579047739466, -53.4164341598961)

(-22.036496727938566, 22.0138420791585)

(50.28536633777365, 50.2754260353972)

(69.12950297389526, 69.1222713069218)

(65.98859869849039, -65.9810229367917)

(0.8603335890193797, 0.561096338191045)

(-0.8603335890193797, -0.561096338191045)

(12.645287223856643, 12.6059312978927)

(-34.58642421528892, 34.5719767335884)

(25.172446326646664, 25.1526068178715)

(-28.30964285445201, 28.2919975390943)

(62.84776319445445, 62.8398089721545)

(-87.97596055249322, -87.9702777324248)

(-40.86517033048807, 40.8529404645174)

(-147.66162685535437, 147.658240851742)

(44.005017920830845, 43.9936599791065)

(-59.70700730533546, 59.6986348402658)

(3.4256184594817283, -3.2883713955909)

(56.56634427982152, 56.5575071728762)

(-81.69364923560168, -81.6875294965246)

(22.036496727938566, -22.0138420791585)

(-3.4256184594817283, 3.2883713955909)

(9.529334405361963, -9.47729425947979)

(72.27046706030896, -72.2635495982494)

(81.69364923560168, 81.6875294965246)

(-75.41148348884815, -75.4048540732019)

(37.7256128277765, 37.71236621281)

(75.41148348884815, 75.4048540732019)

(6.437298179171947, 6.36100394483385)

(-91.11716139446474, 91.1116744496469)

(-84.83478871804229, 84.8288955236568)

(-9.529334405361963, 9.47729425947979)

(-6.437298179171947, -6.36100394483385)

(-18.902409956860023, -18.876013697969)

(-100.54091078684232, -100.535938055826)

(-25.172446326646664, -25.1526068178715)

(18.902409956860023, 18.876013697969)

(28.30964285445201, -28.2919975390943)

(-69.12950297389526, -69.1222713069218)

(84.83478871804229, -84.8288955236568)

(91.11716139446474, -91.1116744496469)

(-62.84776319445445, -62.8398089721545)

(34.58642421528892, -34.5719767335884)

(-94.25838834503986, -94.2530842251087)

(-56.56634427982152, -56.5575071728762)

(94.25838834503986, 94.2530842251087)

(47.14509773676103, -47.1344957575419)

(97.39963887907376, -97.3945057956234)

(31.447714637546234, 31.4318272785346)

(-31.447714637546234, -31.4318272785346)

(-37.7256128277765, -37.71236621281)

(78.55254598424293, -78.5461815917343)

(-12.645287223856643, -12.6059312978927)

(-72.27046706030896, 72.2635495982494)

(-65.98859869849039, 65.9810229367917)

(-15.771284874815882, 15.7396769621337)

(-97.39963887907376, 97.3945057956234)

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

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