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y=(x^3+2x+1)cosx

  • ¿Cómo usar?

  • Gráfico de la función y =:
  • y=-x^3+3x-2 y=-x^3+3x-2
  • y=(x+1)^3 y=(x+1)^3
  • 2*x^2-6*x 2*x^2-6*x
  • y=2x y=2x

  • Expresiones idénticas

  • y=(x^ tres +2x+ uno)cosx
  • y es igual a (x al cubo más 2x más 1) coseno de x
  • y es igual a (x en el grado tres más 2x más uno) coseno de x
  • y=(x3+2x+1)cosx
  • y=x3+2x+1cosx
  • y=(x³+2x+1)cosx
  • y=(x en el grado 3+2x+1)cosx
  • y=x^3+2x+1cosx

  • Expresiones semejantes

  • y=(x^3+2x-1)cosx
  • y=(x^3-2x+1)cosx

  • Expresiones con funciones

  • cosx
  • cosx+cos3x
Trazado el gráfico de la función/ y=(x^3+2x+1)cosx

Gráfico de la función y = y=(x^3+2x+1)cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       / 3          \       
f(x) = \x  + 2*x + 1/*cos(x)
f(x)=((x3+2x)+1)cos⁡(x)f{\left(x \right)} = \left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)} 
f = (x^3 + 2*x + 1)*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-20002000
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:
((x3+2x)+1)cos⁡(x)=0\left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π2x_{1} = - \frac{\pi}{2}
x2=π2x_{2} = \frac{\pi}{2}
x3=−123(9+177)23+418369+1773x_{3} = \frac{- \sqrt[3]{12} \left(9 + \sqrt{177}\right)^{\frac{2}{3}} + 4 \sqrt[3]{18}}{6 \sqrt[3]{9 + \sqrt{177}}}
Solución numérica
x1=26.7035375555132x_{1} = 26.7035375555132
x2=64.4026493985908x_{2} = 64.4026493985908
x3=17.2787595947439x_{3} = 17.2787595947439
x4=80.1106126665397x_{4} = 80.1106126665397
x5=−48.6946861306418x_{5} = -48.6946861306418
x6=23.5619449019235x_{6} = 23.5619449019235
x7=−39.2699081698724x_{7} = -39.2699081698724
x8=−86.3937979737193x_{8} = -86.3937979737193
x9=−98.9601685880785x_{9} = -98.9601685880785
x10=36.1283155162826x_{10} = 36.1283155162826
x11=−51.8362787842316x_{11} = -51.8362787842316
x12=−45.553093477052x_{12} = -45.553093477052
x13=−73.8274273593601x_{13} = -73.8274273593601
x14=−10.9955742875643x_{14} = -10.9955742875643
x15=14.1371669411541x_{15} = 14.1371669411541
x16=−4.71238898038469x_{16} = -4.71238898038469
x17=−14.1371669411541x_{17} = -14.1371669411541
x18=−42.4115008234622x_{18} = -42.4115008234622
x19=−17.2787595947439x_{19} = -17.2787595947439
x20=51.8362787842316x_{20} = 51.8362787842316
x21=−29.845130209103x_{21} = -29.845130209103
x22=70.6858347057703x_{22} = 70.6858347057703
x23=−95.8185759344887x_{23} = -95.8185759344887
x24=92.6769832808989x_{24} = 92.6769832808989
x25=67.5442420521806x_{25} = 67.5442420521806
x26=61.261056745001x_{26} = 61.261056745001
x27=−76.9690200129499x_{27} = -76.9690200129499
x28=10.9955742875643x_{28} = 10.9955742875643
x29=−70.6858347057703x_{29} = -70.6858347057703
x30=58.1194640914112x_{30} = 58.1194640914112
x31=−83.2522053201295x_{31} = -83.2522053201295
x32=−7.85398163397448x_{32} = -7.85398163397448
x33=39.2699081698724x_{33} = 39.2699081698724
x34=54.9778714378214x_{34} = 54.9778714378214
x35=73.8274273593601x_{35} = 73.8274273593601
x36=−80.1106126665397x_{36} = -80.1106126665397
x37=−26.7035375555132x_{37} = -26.7035375555132
x38=7.85398163397448x_{38} = 7.85398163397448
x39=29.845130209103x_{39} = 29.845130209103
x40=−58.1194640914112x_{40} = -58.1194640914112
x41=48.6946861306418x_{41} = 48.6946861306418
x42=76.9690200129499x_{42} = 76.9690200129499
x43=−67.5442420521806x_{43} = -67.5442420521806
x44=83.2522053201295x_{44} = 83.2522053201295
x45=95.8185759344887x_{45} = 95.8185759344887
x46=20.4203522483337x_{46} = 20.4203522483337
x47=32.9867228626928x_{47} = 32.9867228626928
x48=42.4115008234622x_{48} = 42.4115008234622
x49=89.5353906273091x_{49} = 89.5353906273091
x50=86.3937979737193x_{50} = 86.3937979737193
x51=−54.9778714378214x_{51} = -54.9778714378214
x52=−92.6769832808989x_{52} = -92.6769832808989
x53=−36.1283155162826x_{53} = -36.1283155162826
x54=−1.5707963267949x_{54} = -1.5707963267949
x55=−0.453397651516404x_{55} = -0.453397651516404
x56=−23.5619449019235x_{56} = -23.5619449019235
x57=−64.4026493985908x_{57} = -64.4026493985908
x58=4.71238898038469x_{58} = 4.71238898038469
x59=−20.4203522483337x_{59} = -20.4203522483337
x60=1.5707963267949x_{60} = 1.5707963267949
x61=45.553093477052x_{61} = 45.553093477052
x62=98.9601685880785x_{62} = 98.9601685880785
x63=−32.9867228626928x_{63} = -32.9867228626928
x64=−61.261056745001x_{64} = -61.261056745001
x65=−89.5353906273091x_{65} = -89.5353906273091
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^3 + 2*x + 1)*cos(x).
((03+0⋅2)+1)cos⁡(0)\left(\left(0^{3} + 0 \cdot 2\right) + 1\right) \cos{\left(0 \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
(3x2+2)cos⁡(x)−((x3+2x)+1)sin⁡(x)=0\left(3 x^{2} + 2\right) \cos{\left(x \right)} - \left(\left(x^{3} + 2 x\right) + 1\right) \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=53.4631033513221x_{1} = 53.4631033513221
x2=−50.3249937367556x_{2} = -50.3249937367556
x3=−1.13487603616033x_{3} = -1.13487603616033
x4=−6.69495081302555x_{4} = -6.69495081302555
x5=−78.5779682954009x_{5} = -78.5779682954009
x6=84.8583333750259x_{6} = 84.8583333750259
x7=−56.601598561603x_{7} = -56.601598561603
x8=−12.7949922812582x_{8} = -12.7949922812582
x9=44.0502488673189x_{9} = 44.0502488673189
x10=−31.5107226870357x_{10} = -31.5107226870357
x11=31.5107166938176x_{11} = 31.5107166938176
x12=56.6015979798179x_{12} = 56.6015979798179
x13=−34.6438060042567x_{13} = -34.6438060042567
x14=78.5779681384113x_{14} = 78.5779681384113
x15=−47.1873434421594x_{15} = -47.1873434421594
x16=−84.8583334904907x_{16} = -84.8583334904907
x17=12.7947876198271x_{17} = 12.7947876198271
x18=0.898156030964093x_{18} = 0.898156030964093
x19=81.7180967035527x_{19} = 81.7180967035527
x20=−28.3794848194894x_{20} = -28.3794848194894
x21=22.1255432072045x_{21} = 22.1255432072045
x22=−9.72052765208499x_{22} = -9.72052765208499
x23=−91.1390865621644x_{23} = -91.1390865621644
x24=100.560784813579x_{24} = 100.560784813579
x25=25.2507438158889x_{25} = 25.2507438158889
x26=−25.2507582279964x_{26} = -25.2507582279964
x27=66.0188420348377x_{27} = 66.0188420348377
x28=−81.7180968377928x_{28} = -81.7180968377928
x29=−69.1583779590621x_{29} = -69.1583779590621
x30=6.69272909877312x_{30} = 6.69272909877312
x31=15.8935249248021x_{31} = 15.8935249248021
x32=−87.9986667163813x_{32} = -87.9986667163813
x33=19.0055253593543x_{33} = 19.0055253593543
x34=−62.8795113618607x_{34} = -62.8795113618607
x35=50.324992806945x_{35} = 50.324992806945
x36=59.7404165912071x_{36} = 59.7404165912071
x37=−97.4201526944972x_{37} = -97.4201526944972
x38=87.9986666165222x_{38} = 87.9986666165222
x39=47.1873422402597x_{39} = 47.1873422402597
x40=37.7782811749652x_{40} = 37.7782811749652
x41=−66.0188423495794x_{41} = -66.0188423495794
x42=−22.1255674828128x_{42} = -22.1255674828128
x43=−15.8936135659735x_{43} = -15.8936135659735
x44=−75.4379613119007x_{44} = -75.4379613119007
x45=34.6438018914911x_{45} = 34.6438018914911
x46=−19.0055694712868x_{46} = -19.0055694712868
x47=9.71994970640422x_{47} = 9.71994970640422
x48=28.3794757425549x_{48} = 28.3794757425549
x49=97.4201526279921x_{49} = 97.4201526279921
x50=−100.560784872163x_{50} = -100.560784872163
x51=91.139086475362x_{51} = 91.139086475362
x52=−3.77921314352456x_{52} = -3.77921314352456
x53=−40.9138413659871x_{53} = -40.9138413659871
x54=40.9138392441632x_{54} = 40.9138392441632
x55=−53.4631040818061x_{55} = -53.4631040818061
x56=−37.7782840893048x_{56} = -37.7782840893048
x57=94.2795843199939x_{57} = 94.2795843199939
x58=75.4379611271343x_{58} = 75.4379611271343
x59=72.2980914407818x_{59} = 72.2980914407818
x60=−72.2980916597453x_{60} = -72.2980916597453
x61=−59.7404170602539x_{61} = -59.7404170602539
x62=−44.050250448344x_{62} = -44.050250448344
x63=62.879510979535x_{63} = 62.879510979535
x64=69.1583776976161x_{64} = 69.1583776976161
x65=3.76515208768669x_{65} = 3.76515208768669
x66=−94.2795843958049x_{66} = -94.2795843958049
Signos de extremos en los puntos:
(53.463103351322076, -152681.737018446)

(-50.32499373675559, -127327.176801498)

(-1.1348760361603267, -1.15332302046989)

(-6.694950813025552, -286.355549537686)

(-78.57796829540091, 484982.415873428)

(84.85833337502594, -610848.738307089)

(-56.601598561603005, -181194.942101814)

(-12.794992281258168, -2064.13720953261)

(44.050248867318935, 85367.8092463204)

(-31.51072268703568, -31209.0718909136)

(31.510716693817596, 31211.0629118981)

(56.60159797981787, 181196.93930083)

(-34.64380600425673, 41492.6058057626)

(78.57796813841132, -484984.414418039)

(-47.18734344215936, 104951.21405826)

(-84.8583334904907, 610846.739555295)

(12.794787619827124, 2066.08521531336)

(0.8981560309640927, 2.19367136980121)

(81.71809670355275, 545498.087019984)

(-28.379484819489416, 22785.9070005137)

(22.12554320720447, -10778.5038294632)

(-9.720527652084987, 896.243233040788)

(-91.13908656216441, 756803.128856264)

(100.56078481357947, 1016667.99468457)

(25.250743815888907, 16039.0569476009)

(-25.250758227996435, -16037.0708577578)

(66.01884203483772, -287578.756303204)

(-81.71809683779281, -545496.088365826)

(-69.15837795906207, -330602.893352491)

(6.69272909877312, 288.189269756003)

(15.893524924802108, -3978.07185710068)

(-87.99866671638132, -681220.407151219)

(19.005525359354255, 6820.19193213889)

(-62.879511361860686, -248457.413361075)

(50.324992806944955, 127329.173261006)

(59.74041659120713, -213060.818033725)

(-97.42015269449716, 924339.885377188)

(87.9986666165222, 681222.405990405)

(47.18734224025965, -104953.210033323)

(37.778281174965194, 53824.5419412293)

(-66.01884234957944, 287576.758363689)

(-22.12556748281282, 10776.5218674633)

(-15.893613565973487, 3976.10620789341)

(-75.43796131190066, -429119.684360617)

(34.64380189149112, -41494.598365321)

(-19.00556947128676, -6818.21621618191)

(9.719949706404224, -898.156569294279)

(28.379475742554913, -22787.8959549306)

(97.42015262799207, -924341.88442983)

(-100.56078487216341, -1016665.99557373)

(91.13908647536205, -756805.12777398)

(-3.77921314352456, 48.6406361019671)

(-40.91384136598713, 68384.9380284104)

(40.913839244163185, -68386.9326819477)

(-53.46310408180612, 152679.74015683)

(-37.77828408930481, -53822.5482059698)

(94.27958431999394, 837782.941356021)

(75.43796112713433, 429121.682781753)

(72.29809144078176, -377723.854381354)

(-72.29809165974525, 377721.856100082)

(-59.740417060253925, 213058.820548863)

(-44.05025044834403, -85365.8138620871)

(62.87951097953499, 248459.41109021)

(69.15837769761613, 330604.891474477)

(3.76515208768669, -50.2560107380802)

(-94.2795843958049, -837780.942367477)


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=53.4631033513221x_{1} = 53.4631033513221
x2=−50.3249937367556x_{2} = -50.3249937367556
x3=−1.13487603616033x_{3} = -1.13487603616033
x4=−6.69495081302555x_{4} = -6.69495081302555
x5=84.8583333750259x_{5} = 84.8583333750259
x6=−56.601598561603x_{6} = -56.601598561603
x7=−12.7949922812582x_{7} = -12.7949922812582
x8=−31.5107226870357x_{8} = -31.5107226870357
x9=78.5779681384113x_{9} = 78.5779681384113
x10=22.1255432072045x_{10} = 22.1255432072045
x11=−25.2507582279964x_{11} = -25.2507582279964
x12=66.0188420348377x_{12} = 66.0188420348377
x13=−81.7180968377928x_{13} = -81.7180968377928
x14=−69.1583779590621x_{14} = -69.1583779590621
x15=15.8935249248021x_{15} = 15.8935249248021
x16=−87.9986667163813x_{16} = -87.9986667163813
x17=−62.8795113618607x_{17} = -62.8795113618607
x18=59.7404165912071x_{18} = 59.7404165912071
x19=47.1873422402597x_{19} = 47.1873422402597
x20=−75.4379613119007x_{20} = -75.4379613119007
x21=34.6438018914911x_{21} = 34.6438018914911
x22=−19.0055694712868x_{22} = -19.0055694712868
x23=9.71994970640422x_{23} = 9.71994970640422
x24=28.3794757425549x_{24} = 28.3794757425549
x25=97.4201526279921x_{25} = 97.4201526279921
x26=−100.560784872163x_{26} = -100.560784872163
x27=91.139086475362x_{27} = 91.139086475362
x28=40.9138392441632x_{28} = 40.9138392441632
x29=−37.7782840893048x_{29} = -37.7782840893048
x30=72.2980914407818x_{30} = 72.2980914407818
x31=−44.050250448344x_{31} = -44.050250448344
x32=3.76515208768669x_{32} = 3.76515208768669
x33=−94.2795843958049x_{33} = -94.2795843958049
Puntos máximos de la función:
x33=−78.5779682954009x_{33} = -78.5779682954009
x33=44.0502488673189x_{33} = 44.0502488673189
x33=31.5107166938176x_{33} = 31.5107166938176
x33=56.6015979798179x_{33} = 56.6015979798179
x33=−34.6438060042567x_{33} = -34.6438060042567
x33=−47.1873434421594x_{33} = -47.1873434421594
x33=−84.8583334904907x_{33} = -84.8583334904907
x33=12.7947876198271x_{33} = 12.7947876198271
x33=0.898156030964093x_{33} = 0.898156030964093
x33=81.7180967035527x_{33} = 81.7180967035527
x33=−28.3794848194894x_{33} = -28.3794848194894
x33=−9.72052765208499x_{33} = -9.72052765208499
x33=−91.1390865621644x_{33} = -91.1390865621644
x33=100.560784813579x_{33} = 100.560784813579
x33=25.2507438158889x_{33} = 25.2507438158889
x33=6.69272909877312x_{33} = 6.69272909877312
x33=19.0055253593543x_{33} = 19.0055253593543
x33=50.324992806945x_{33} = 50.324992806945
x33=−97.4201526944972x_{33} = -97.4201526944972
x33=87.9986666165222x_{33} = 87.9986666165222
x33=37.7782811749652x_{33} = 37.7782811749652
x33=−66.0188423495794x_{33} = -66.0188423495794
x33=−22.1255674828128x_{33} = -22.1255674828128
x33=−15.8936135659735x_{33} = -15.8936135659735
x33=−3.77921314352456x_{33} = -3.77921314352456
x33=−40.9138413659871x_{33} = -40.9138413659871
x33=−53.4631040818061x_{33} = -53.4631040818061
x33=94.2795843199939x_{33} = 94.2795843199939
x33=75.4379611271343x_{33} = 75.4379611271343
x33=−72.2980916597453x_{33} = -72.2980916597453
x33=−59.7404170602539x_{33} = -59.7404170602539
x33=62.879510979535x_{33} = 62.879510979535
x33=69.1583776976161x_{33} = 69.1583776976161
Decrece en los intervalos
[97.4201526279921,∞)\left[97.4201526279921, \infty\right)
Crece en los intervalos
(−∞,−100.560784872163]\left(-\infty, -100.560784872163\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
6xcos⁡(x)−2(3x2+2)sin⁡(x)−(x3+2x+1)cos⁡(x)=06 x \cos{\left(x \right)} - 2 \left(3 x^{2} + 2\right) \sin{\left(x \right)} - \left(x^{3} + 2 x + 1\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−20.7053721719038x_{1} = -20.7053721719038
x2=−55.0865297063908x_{2} = -55.0865297063908
x3=51.9514583212332x_{3} = 51.9514583212332
x4=17.6116978832396x_{4} = 17.6116978832396
x5=20.7053116151775x_{5} = 20.7053116151775
x6=−86.4631238914497x_{6} = -86.4631238914497
x7=86.4631236776905x_{7} = 86.4631236776905
x8=42.5519367794676x_{8} = 42.5519367794676
x9=67.6328143374953x_{9} = 67.6328143374953
x10=−0.481110544016919x_{10} = -0.481110544016919
x11=61.3586523297075x_{11} = 61.3586523297075
x12=8.49934607662776x_{12} = 8.49934607662776
x13=−99.0207167818494x_{13} = -99.0207167818494
x14=−2.92292294722943x_{14} = -2.92292294722943
x15=2.89473759655266x_{15} = 2.89473759655266
x16=−14.5366474961493x_{16} = -14.5366474961493
x17=−67.6328149068678x_{17} = -67.6328149068678
x18=14.5364157171433x_{18} = 14.5364157171433
x19=−51.9514599484851x_{19} = -51.9514599484851
x20=−95.881103671322x_{20} = -95.881103671322
x21=−23.8107735818565x_{21} = -23.8107735818565
x22=−80.185354298459x_{22} = -80.185354298459
x23=−61.3586531688726x_{23} = -61.3586531688726
x24=−5.61186459433389x_{24} = -5.61186459433389
x25=−39.4214008298055x_{25} = -39.4214008298055
x26=70.7704918003409x_{26} = 70.7704918003409
x27=−73.9085003321614x_{27} = -73.9085003321614
x28=−58.2222959557336x_{28} = -58.2222959557336
x29=−77.0467989687362x_{29} = -77.0467989687362
x30=30.0432390144102x_{30} = 30.0432390144102
x31=−30.0432532181997x_{31} = -30.0432532181997
x32=−92.7416241664239x_{32} = -92.7416241664239
x33=11.4913222459787x_{33} = 11.4913222459787
x34=73.9084999324372x_{34} = 73.9084999324372
x35=−33.1664435752451x_{35} = -33.1664435752451
x36=5.60618997590852x_{36} = 5.60618997590852
x37=58.2222949216126x_{37} = 58.2222949216126
x38=36.2927244101684x_{38} = 36.2927244101684
x39=33.1664339503951x_{39} = 33.1664339503951
x40=45.6839710069479x_{40} = 45.6839710069479
x41=39.4213959654803x_{41} = 39.4213959654803
x42=80.1853540096874x_{42} = 80.1853540096874
x43=−70.770492275556x_{43} = -70.770492275556
x44=92.7416240048385x_{44} = 92.7416240048385
x45=−8.50090333790813x_{45} = -8.50090333790813
x46=102.16045112111x_{46} = 102.16045112111
x47=−83.324137496708x_{47} = -83.324137496708
x48=−26.9241875926441x_{48} = -26.9241875926441
x49=−17.611810427649x_{49} = -17.611810427649
x50=−45.6839737186162x_{50} = -45.6839737186162
x51=−42.5519403734117x_{51} = -42.5519403734117
x52=−36.2927311559135x_{52} = -36.2927311559135
x53=26.9241657640557x_{53} = 26.9241657640557
x54=−11.4918697344793x_{54} = -11.4918697344793
x55=48.8172166930811x_{55} = 48.8172166930811
x56=64.4955153586767x_{56} = 64.4955153586767
x57=23.810738330328x_{57} = 23.810738330328
x58=55.0865284173953x_{58} = 55.0865284173953
x59=−89.6022922426408x_{59} = -89.6022922426408
x60=−48.8172187768559x_{60} = -48.8172187768559
x61=83.324137248956x_{61} = 83.324137248956
x62=77.0467986301026x_{62} = 77.0467986301026
x63=89.6022920572429x_{63} = 89.6022920572429
x64=95.8811035298479x_{64} = 95.8811035298479
x65=−64.495516046687x_{65} = -64.495516046687
x66=99.0207166574545x_{66} = 99.0207166574545

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
[102.16045112111,∞)\left[102.16045112111, \infty\right)
Convexa en los intervalos
(−∞,−95.881103671322]\left(-\infty, -95.881103671322\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(((x3+2x)+1)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(\left(x^{3} + 2 x\right) + 1\right) \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→∞(((x3+2x)+1)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(\left(x^{3} + 2 x\right) + 1\right) \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^3 + 2*x + 1)*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(((x3+2x)+1)cos⁡(x)x)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{\left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)}}{x}\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→∞(((x3+2x)+1)cos⁡(x)x)=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{\left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)}}{x}\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:
((x3+2x)+1)cos⁡(x)=(−x3−2x+1)cos⁡(x)\left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)} = \left(- x^{3} - 2 x + 1\right) \cos{\left(x \right)}
- No
((x3+2x)+1)cos⁡(x)=−(−x3−2x+1)cos⁡(x)\left(\left(x^{3} + 2 x\right) + 1\right) \cos{\left(x \right)} = - \left(- x^{3} - 2 x + 1\right) \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = y=(x^3+2x+1)cosx
    © Sr Examen – Калькулятор