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x^5*cos(x)
Trazado el gráfico de la función/ x^5*cos(x)

Gráfico de la función y = x^5*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        5       
f(x) = x *cos(x)
f(x)=x5cos⁡(x)f{\left(x \right)} = x^{5} \cos{\left(x \right)} 
f = x^5*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-200000200000
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:
x5cos⁡(x)=0x^{5} \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=32.9867228626928x_{1} = 32.9867228626928
x2=73.8274273593601x_{2} = 73.8274273593601
x3=4.71238898038469x_{3} = 4.71238898038469
x4=39.2699081698724x_{4} = 39.2699081698724
x5=−0.00387691491721065x_{5} = -0.00387691491721065
x6=95.8185759344887x_{6} = 95.8185759344887
x7=45.553093477052x_{7} = 45.553093477052
x8=70.6858347057703x_{8} = 70.6858347057703
x9=−10.9955742875643x_{9} = -10.9955742875643
x10=−58.1194640914112x_{10} = -58.1194640914112
x11=−23.5619449019235x_{11} = -23.5619449019235
x12=26.7035375555132x_{12} = 26.7035375555132
x13=−26.7035375555132x_{13} = -26.7035375555132
x14=−89.5353906273091x_{14} = -89.5353906273091
x15=−17.2787595947439x_{15} = -17.2787595947439
x16=−42.4115008234622x_{16} = -42.4115008234622
x17=−61.261056745001x_{17} = -61.261056745001
x18=92.6769832808989x_{18} = 92.6769832808989
x19=−76.9690200129499x_{19} = -76.9690200129499
x20=−92.6769832808989x_{20} = -92.6769832808989
x21=−98.9601685880785x_{21} = -98.9601685880785
x22=61.261056745001x_{22} = 61.261056745001
x23=−54.9778714378214x_{23} = -54.9778714378214
x24=42.4115008234622x_{24} = 42.4115008234622
x25=−64.4026493985908x_{25} = -64.4026493985908
x26=67.5442420521806x_{26} = 67.5442420521806
x27=−7.85398163397448x_{27} = -7.85398163397448
x28=80.1106126665397x_{28} = 80.1106126665397
x29=−14.1371669411541x_{29} = -14.1371669411541
x30=14.1371669411541x_{30} = 14.1371669411541
x31=−1.5707963267949x_{31} = -1.5707963267949
x32=1.5707963267949x_{32} = 1.5707963267949
x33=29.845130209103x_{33} = 29.845130209103
x34=10.9955742875643x_{34} = 10.9955742875643
x35=17.2787595947439x_{35} = 17.2787595947439
x36=−51.8362787842316x_{36} = -51.8362787842316
x37=−29.845130209103x_{37} = -29.845130209103
x38=0x_{38} = 0
x39=−48.6946861306418x_{39} = -48.6946861306418
x40=−73.8274273593601x_{40} = -73.8274273593601
x41=23.5619449019235x_{41} = 23.5619449019235
x42=20.4203522483337x_{42} = 20.4203522483337
x43=−86.3937979737193x_{43} = -86.3937979737193
x44=54.9778714378214x_{44} = 54.9778714378214
x45=58.1194640914112x_{45} = 58.1194640914112
x46=51.8362787842316x_{46} = 51.8362787842316
x47=−67.5442420521806x_{47} = -67.5442420521806
x48=−4.71238898038469x_{48} = -4.71238898038469
x49=−45.553093477052x_{49} = -45.553093477052
x50=−70.6858347057703x_{50} = -70.6858347057703
x51=48.6946861306418x_{51} = 48.6946861306418
x52=−83.2522053201295x_{52} = -83.2522053201295
x53=−95.8185759344887x_{53} = -95.8185759344887
x54=89.5353906273091x_{54} = 89.5353906273091
x55=−39.2699081698724x_{55} = -39.2699081698724
x56=76.9690200129499x_{56} = 76.9690200129499
x57=−32.9867228626928x_{57} = -32.9867228626928
x58=−20.4203522483337x_{58} = -20.4203522483337
x59=−36.1283155162826x_{59} = -36.1283155162826
x60=7.85398163397448x_{60} = 7.85398163397448
x61=−80.1106126665397x_{61} = -80.1106126665397
x62=86.3937979737193x_{62} = 86.3937979737193
x63=98.9601685880785x_{63} = 98.9601685880785
x64=36.1283155162826x_{64} = 36.1283155162826
x65=64.4026493985908x_{65} = 64.4026493985908
x66=83.2522053201295x_{66} = 83.2522053201295
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^5*cos(x).
05cos⁡(0)0^{5} \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
−x5sin⁡(x)+5x4cos⁡(x)=0- x^{5} \sin{\left(x \right)} + 5 x^{4} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=62.9111635112525x_{1} = 62.9111635112525
x2=37.8305186388889x_{2} = 37.8305186388889
x3=97.4406405869711x_{3} = 97.4406405869711
x4=−69.1871806855712x_{4} = -69.1871806855712
x5=−75.4643834089706x_{5} = -75.4643834089706
x6=81.7425005689042x_{6} = 81.7425005689042
x7=−47.2293632804741x_{7} = -47.2293632804741
x8=50.3644346278355x_{8} = 50.3644346278355
x9=−56.6367214297364x_{9} = -56.6367214297364
x10=28.4483142882062x_{10} = 28.4483142882062
x11=6.90959579542153x_{11} = 6.90959579542153
x12=22.2125562085988x_{12} = 22.2125562085988
x13=91.1609800814091x_{13} = 91.1609800814091
x14=−97.4406405869711x_{14} = -97.4406405869711
x15=−40.9621674789216x_{15} = -40.9621674789216
x16=59.7737149408088x_{16} = 59.7737149408088
x17=−66.0490029831692x_{17} = -66.0490029831692
x18=72.3256529801404x_{18} = 72.3256529801404
x19=−4.03356779033998x_{19} = -4.03356779033998
x20=84.8818390729824x_{20} = 84.8818390729824
x21=−53.5002619192185x_{21} = -53.5002619192185
x22=−34.7006238709965x_{22} = -34.7006238709965
x23=31.5729854784403x_{23} = 31.5729854784403
x24=66.0490029831692x_{24} = 66.0490029831692
x25=44.0952059009573x_{25} = 44.0952059009573
x26=1.3138377164929x_{26} = 1.3138377164929
x27=94.30075185089x_{27} = 94.30075185089
x28=19.1055198623998x_{28} = 19.1055198623998
x29=69.1871806855712x_{29} = 69.1871806855712
x30=75.4643834089706x_{30} = 75.4643834089706
x31=9.89275256512429x_{31} = 9.89275256512429
x32=−81.7425005689042x_{32} = -81.7425005689042
x33=0x_{33} = 0
x34=−28.4483142882062x_{34} = -28.4483142882062
x35=−88.0213377290448x_{35} = -88.0213377290448
x36=47.2293632804741x_{36} = 47.2293632804741
x37=−62.9111635112525x_{37} = -62.9111635112525
x38=−25.3276477920726x_{38} = -25.3276477920726
x39=−12.9352212801115x_{39} = -12.9352212801115
x40=56.6367214297364x_{40} = 56.6367214297364
x41=−100.580635384527x_{41} = -100.580635384527
x42=−16.0106585966129x_{42} = -16.0106585966129
x43=−22.2125562085988x_{43} = -22.2125562085988
x44=4.03356779033998x_{44} = 4.03356779033998
x45=−72.3256529801404x_{45} = -72.3256529801404
x46=−9.89275256512429x_{46} = -9.89275256512429
x47=−31.5729854784403x_{47} = -31.5729854784403
x48=−59.7737149408088x_{48} = -59.7737149408088
x49=−6.90959579542153x_{49} = -6.90959579542153
x50=100.580635384527x_{50} = 100.580635384527
x51=103.720726651558x_{51} = 103.720726651558
x52=−94.30075185089x_{52} = -94.30075185089
x53=−44.0952059009573x_{53} = -44.0952059009573
x54=−50.3644346278355x_{54} = -50.3644346278355
x55=−91.1609800814091x_{55} = -91.1609800814091
x56=53.5002619192185x_{56} = 53.5002619192185
x57=34.7006238709965x_{57} = 34.7006238709965
x58=78.6033412791698x_{58} = 78.6033412791698
x59=16.0106585966129x_{59} = 16.0106585966129
x60=−84.8818390729824x_{60} = -84.8818390729824
x61=−37.8305186388889x_{61} = -37.8305186388889
x62=−1.3138377164929x_{62} = -1.3138377164929
x63=12.9352212801115x_{63} = 12.9352212801115
x64=40.9621674789216x_{64} = 40.9621674789216
x65=88.0213377290448x_{65} = 88.0213377290448
x66=−78.6033412791698x_{66} = -78.6033412791698
x67=−19.1055198623998x_{67} = -19.1055198623998
x68=25.3276477920726x_{68} = 25.3276477920726
Signos de extremos en los puntos:
(62.91116351125249, 982361343.674869)

(37.830518638888854, 76815876.763504)

(97.44064058697107, -8772626573.89269)

(-69.18718068557116, -1581237269.79774)

(-75.46438340897063, -2442074835.1523)

(81.74250056890423, 3642744051.26235)

(-47.2293632804741, 233690077.851263)

(50.36443462783552, 322470604.989764)

(-56.63672142973645, -580503316.767324)

(28.44831428820623, -18351703.6596154)

(6.909595795421526, 12759.1487492828)

(22.212556208598823, -5275452.6005768)

(91.16098008140906, -6286264691.69339)

(-97.44064058697107, 8772626573.89269)

(-40.96216747892155, 114473011.24935)

(59.77371494080883, -760391276.15604)

(-66.04900298316916, 1253402274.18613)

(72.32565298014042, -1974360702.22499)

(-4.033567790339982, 670.379412457278)

(84.88183907298242, -4398673622.91735)

(-53.500261919218524, 436406435.530439)

(-34.70062387099647, 49799410.9183366)

(31.572985478440316, 30988431.8368961)

(66.04900298316916, -1253402274.18613)

(44.09520590095732, 165646664.621845)

(1.3138377164928983, 0.994905864288247)

(94.30075185089002, 7446739532.87571)

(19.10551986239984, 2462687.0243185)

(69.18718068557116, 1581237269.79774)

(75.46438340897063, 2442074835.1523)

(9.892752565124287, -84564.1022728481)

(-81.74250056890423, -3642744051.26235)

(0, 0)

(-28.44831428820623, 18351703.6596154)

(-88.02133772904483, -5275216316.74103)

(47.2293632804741, -233690077.851263)

(-62.91116351125249, -982361343.674869)

(-25.327647792072558, -10225214.1985132)

(-12.935221280111474, -337777.725370395)

(56.63672142973645, 580503316.767324)

(-100.58063538452689, -10281013219.2145)

(-16.010658596612945, 1004242.32805887)

(-22.212556208598823, 5275452.6005768)

(4.033567790339982, -670.379412457278)

(-72.32565298014042, 1974360702.22499)

(-9.892752565124287, 84564.1022728481)

(-31.572985478440316, -30988431.8368961)

(-59.77371494080883, 760391276.15604)

(-6.909595795421526, -12759.1487492828)

(100.58063538452689, 10281013219.2145)

(103.72072665155811, -11990125266.5391)

(-94.30075185089002, -7446739532.87571)

(-44.09520590095732, -165646664.621845)

(-50.36443462783552, -322470604.989764)

(-91.16098008140906, 6286264691.69339)

(53.500261919218524, -436406435.530439)

(34.70062387099647, -49799410.9183366)

(78.60334127916975, -2994526546.59522)

(16.010658596612945, -1004242.32805887)

(-84.88183907298242, 4398673622.91735)

(-37.830518638888854, -76815876.763504)

(-1.3138377164928983, -0.994905864288247)

(12.935221280111474, 337777.725370395)

(40.96216747892155, -114473011.24935)

(88.02133772904483, 5275216316.74103)

(-78.60334127916975, 2994526546.59522)

(-19.10551986239984, -2462687.0243185)

(25.327647792072558, 10225214.1985132)


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=97.4406405869711x_{1} = 97.4406405869711
x2=−69.1871806855712x_{2} = -69.1871806855712
x3=−75.4643834089706x_{3} = -75.4643834089706
x4=−56.6367214297364x_{4} = -56.6367214297364
x5=28.4483142882062x_{5} = 28.4483142882062
x6=22.2125562085988x_{6} = 22.2125562085988
x7=91.1609800814091x_{7} = 91.1609800814091
x8=59.7737149408088x_{8} = 59.7737149408088
x9=72.3256529801404x_{9} = 72.3256529801404
x10=84.8818390729824x_{10} = 84.8818390729824
x11=66.0490029831692x_{11} = 66.0490029831692
x12=9.89275256512429x_{12} = 9.89275256512429
x13=−81.7425005689042x_{13} = -81.7425005689042
x14=−88.0213377290448x_{14} = -88.0213377290448
x15=47.2293632804741x_{15} = 47.2293632804741
x16=−62.9111635112525x_{16} = -62.9111635112525
x17=−25.3276477920726x_{17} = -25.3276477920726
x18=−12.9352212801115x_{18} = -12.9352212801115
x19=−100.580635384527x_{19} = -100.580635384527
x20=4.03356779033998x_{20} = 4.03356779033998
x21=−31.5729854784403x_{21} = -31.5729854784403
x22=−6.90959579542153x_{22} = -6.90959579542153
x23=103.720726651558x_{23} = 103.720726651558
x24=−94.30075185089x_{24} = -94.30075185089
x25=−44.0952059009573x_{25} = -44.0952059009573
x26=−50.3644346278355x_{26} = -50.3644346278355
x27=53.5002619192185x_{27} = 53.5002619192185
x28=34.7006238709965x_{28} = 34.7006238709965
x29=78.6033412791698x_{29} = 78.6033412791698
x30=16.0106585966129x_{30} = 16.0106585966129
x31=−37.8305186388889x_{31} = -37.8305186388889
x32=−1.3138377164929x_{32} = -1.3138377164929
x33=40.9621674789216x_{33} = 40.9621674789216
x34=−19.1055198623998x_{34} = -19.1055198623998
Puntos máximos de la función:
x34=62.9111635112525x_{34} = 62.9111635112525
x34=37.8305186388889x_{34} = 37.8305186388889
x34=81.7425005689042x_{34} = 81.7425005689042
x34=−47.2293632804741x_{34} = -47.2293632804741
x34=50.3644346278355x_{34} = 50.3644346278355
x34=6.90959579542153x_{34} = 6.90959579542153
x34=−97.4406405869711x_{34} = -97.4406405869711
x34=−40.9621674789216x_{34} = -40.9621674789216
x34=−66.0490029831692x_{34} = -66.0490029831692
x34=−4.03356779033998x_{34} = -4.03356779033998
x34=−53.5002619192185x_{34} = -53.5002619192185
x34=−34.7006238709965x_{34} = -34.7006238709965
x34=31.5729854784403x_{34} = 31.5729854784403
x34=44.0952059009573x_{34} = 44.0952059009573
x34=1.3138377164929x_{34} = 1.3138377164929
x34=94.30075185089x_{34} = 94.30075185089
x34=19.1055198623998x_{34} = 19.1055198623998
x34=69.1871806855712x_{34} = 69.1871806855712
x34=75.4643834089706x_{34} = 75.4643834089706
x34=−28.4483142882062x_{34} = -28.4483142882062
x34=56.6367214297364x_{34} = 56.6367214297364
x34=−16.0106585966129x_{34} = -16.0106585966129
x34=−22.2125562085988x_{34} = -22.2125562085988
x34=−72.3256529801404x_{34} = -72.3256529801404
x34=−9.89275256512429x_{34} = -9.89275256512429
x34=−59.7737149408088x_{34} = -59.7737149408088
x34=100.580635384527x_{34} = 100.580635384527
x34=−91.1609800814091x_{34} = -91.1609800814091
x34=−84.8818390729824x_{34} = -84.8818390729824
x34=12.9352212801115x_{34} = 12.9352212801115
x34=88.0213377290448x_{34} = 88.0213377290448
x34=−78.6033412791698x_{34} = -78.6033412791698
x34=25.3276477920726x_{34} = 25.3276477920726
Decrece en los intervalos
[103.720726651558,∞)\left[103.720726651558, \infty\right)
Crece en los intervalos
(−∞,−100.580635384527]\left(-\infty, -100.580635384527\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
x3(−x2cos⁡(x)−10xsin⁡(x)+20cos⁡(x))=0x^{3} \left(- x^{2} \cos{\left(x \right)} - 10 x \sin{\left(x \right)} + 20 \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−8.84273059058252x_{1} = -8.84273059058252
x2=33.2836493011193x_{2} = 33.2836493011193
x3=−64.5570590894316x_{3} = -64.5570590894316
x4=−73.962303624384x_{4} = -73.962303624384
x5=−17.8184044339812x_{5} = -17.8184044339812
x6=80.2349896313731x_{6} = 80.2349896313731
x7=23.9699278811445x_{7} = 23.9699278811445
x8=77.0984348522717x_{8} = 77.0984348522717
x9=−52.0275482445915x_{9} = -52.0275482445915
x10=−89.6467551796771x_{10} = -89.6467551796771
x11=92.7845934526386x_{11} = 92.7845934526386
x12=3.38800018896783x_{12} = 3.38800018896783
x13=45.7702052260758x_{13} = 45.7702052260758
x14=99.0609797661521x_{14} = 99.0609797661521
x15=−14.7774181424266x_{15} = -14.7774181424266
x16=61.4232906091751x_{16} = 61.4232906091751
x17=30.1718641797055x_{17} = 30.1718641797055
x18=−48.898066866027x_{18} = -48.898066866027
x19=−83.3719206875712x_{19} = -83.3719206875712
x20=−27.0665354028426x_{20} = -27.0665354028426
x21=−77.0984348522717x_{21} = -77.0984348522717
x22=−67.6915439151872x_{22} = -67.6915439151872
x23=−55.1583807713174x_{23} = -55.1583807713174
x24=39.5208198495105x_{24} = 39.5208198495105
x25=−20.8854471818157x_{25} = -20.8854471818157
x26=73.962303624384x_{26} = 73.962303624384
x27=55.1583807713174x_{27} = 55.1583807713174
x28=64.5570590894316x_{28} = 64.5570590894316
x29=−36.4003346188174x_{29} = -36.4003346188174
x30=86.5091875084809x_{30} = 86.5091875084809
x31=0x_{31} = 0
x32=95.9226759924468x_{32} = 95.9226759924468
x33=−33.2836493011193x_{33} = -33.2836493011193
x34=67.6915439151872x_{34} = 67.6915439151872
x35=6.01972397833195x_{35} = 6.01972397833195
x36=−45.7702052260758x_{36} = -45.7702052260758
x37=−99.0609797661521x_{37} = -99.0609797661521
x38=−3.38800018896783x_{38} = -3.38800018896783
x39=83.3719206875712x_{39} = 83.3719206875712
x40=−23.9699278811445x_{40} = -23.9699278811445
x41=−86.5091875084809x_{41} = -86.5091875084809
x42=20.8854471818157x_{42} = 20.8854471818157
x43=−39.5208198495105x_{43} = -39.5208198495105
x44=−1.05940066702192x_{44} = -1.05940066702192
x45=−42.6443071932623x_{45} = -42.6443071932623
x46=70.8266514488225x_{46} = 70.8266514488225
x47=−30.1718641797055x_{47} = -30.1718641797055
x48=14.7774181424266x_{48} = 14.7774181424266
x49=89.6467551796771x_{49} = 89.6467551796771
x50=42.6443071932623x_{50} = 42.6443071932623
x51=11.7770465493812x_{51} = 11.7770465493812
x52=−70.8266514488225x_{52} = -70.8266514488225
x53=−61.4232906091751x_{53} = -61.4232906091751
x54=27.0665354028426x_{54} = 27.0665354028426
x55=−58.2903517418568x_{55} = -58.2903517418568
x56=−92.7845934526386x_{56} = -92.7845934526386
x57=58.2903517418568x_{57} = 58.2903517418568
x58=48.898066866027x_{58} = 48.898066866027
x59=−6.01972397833195x_{59} = -6.01972397833195
x60=36.4003346188174x_{60} = 36.4003346188174
x61=−95.9226759924468x_{61} = -95.9226759924468
x62=−80.2349896313731x_{62} = -80.2349896313731
x63=1.05940066702192x_{63} = 1.05940066702192
x64=−11.7770465493812x_{64} = -11.7770465493812
x65=8.84273059058252x_{65} = 8.84273059058252
x66=52.0275482445915x_{66} = 52.0275482445915
x67=17.8184044339812x_{67} = 17.8184044339812

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
[95.9226759924468,∞)\left[95.9226759924468, \infty\right)
Convexa en los intervalos
(−∞,−95.9226759924468]\left(-\infty, -95.9226759924468\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x5cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{5} \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→∞(x5cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{5} \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^5*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(x4cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x^{4} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(x4cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x^{4} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\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:
x5cos⁡(x)=−x5cos⁡(x)x^{5} \cos{\left(x \right)} = - x^{5} \cos{\left(x \right)}
- No
x5cos⁡(x)=x5cos⁡(x)x^{5} \cos{\left(x \right)} = x^{5} \cos{\left(x \right)}
- Sí
es decir, función
es
impar
Gráfico
Gráfico de la función y = x^5*cos(x)
    © Sr Examen – Калькулятор