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(2*x+1)*cos(x)
Trazado el gráfico de la función/ (2*x+1)*cos(x)

Gráfico de la función y = (2*x+1)*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = (2*x + 1)*cos(x)
f(x)=(2x+1)cos⁡(x)f{\left(x \right)} = \left(2 x + 1\right) \cos{\left(x \right)} 
f = (2*x + 1)*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:
(2x+1)cos⁡(x)=0\left(2 x + 1\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−12x_{1} = - \frac{1}{2}
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Solución numérica
x1=−29.845130209103x_{1} = -29.845130209103
x2=−67.5442420521806x_{2} = -67.5442420521806
x3=−70.6858347057703x_{3} = -70.6858347057703
x4=64.4026493985908x_{4} = 64.4026493985908
x5=−36.1283155162826x_{5} = -36.1283155162826
x6=−92.6769832808989x_{6} = -92.6769832808989
x7=−61.261056745001x_{7} = -61.261056745001
x8=246.615023306799x_{8} = 246.615023306799
x9=−76.9690200129499x_{9} = -76.9690200129499
x10=−98.9601685880785x_{10} = -98.9601685880785
x11=−95.8185759344887x_{11} = -95.8185759344887
x12=29.845130209103x_{12} = 29.845130209103
x13=80.1106126665397x_{13} = 80.1106126665397
x14=−64.4026493985908x_{14} = -64.4026493985908
x15=36.1283155162826x_{15} = 36.1283155162826
x16=73.8274273593601x_{16} = 73.8274273593601
x17=32.9867228626928x_{17} = 32.9867228626928
x18=−4.71238898038469x_{18} = -4.71238898038469
x19=−39.2699081698724x_{19} = -39.2699081698724
x20=26.7035375555132x_{20} = 26.7035375555132
x21=−7.85398163397448x_{21} = -7.85398163397448
x22=95.8185759344887x_{22} = 95.8185759344887
x23=−17.2787595947439x_{23} = -17.2787595947439
x24=−10.9955742875643x_{24} = -10.9955742875643
x25=98.9601685880785x_{25} = 98.9601685880785
x26=−86.3937979737193x_{26} = -86.3937979737193
x27=92.6769832808989x_{27} = 92.6769832808989
x28=−48.6946861306418x_{28} = -48.6946861306418
x29=54.9778714378214x_{29} = 54.9778714378214
x30=45.553093477052x_{30} = 45.553093477052
x31=23.5619449019235x_{31} = 23.5619449019235
x32=76.9690200129499x_{32} = 76.9690200129499
x33=−89.5353906273091x_{33} = -89.5353906273091
x34=4.71238898038469x_{34} = 4.71238898038469
x35=−26.7035375555132x_{35} = -26.7035375555132
x36=−80.1106126665397x_{36} = -80.1106126665397
x37=7.85398163397448x_{37} = 7.85398163397448
x38=14.1371669411541x_{38} = 14.1371669411541
x39=86.3937979737193x_{39} = 86.3937979737193
x40=−45.553093477052x_{40} = -45.553093477052
x41=−83.2522053201295x_{41} = -83.2522053201295
x42=70.6858347057703x_{42} = 70.6858347057703
x43=−0.5x_{43} = -0.5
x44=83.2522053201295x_{44} = 83.2522053201295
x45=48.6946861306418x_{45} = 48.6946861306418
x46=−20.4203522483337x_{46} = -20.4203522483337
x47=51.8362787842316x_{47} = 51.8362787842316
x48=10.9955742875643x_{48} = 10.9955742875643
x49=20.4203522483337x_{49} = 20.4203522483337
x50=1.5707963267949x_{50} = 1.5707963267949
x51=89.5353906273091x_{51} = 89.5353906273091
x52=17.2787595947439x_{52} = 17.2787595947439
x53=58.1194640914112x_{53} = 58.1194640914112
x54=61.261056745001x_{54} = 61.261056745001
x55=−32.9867228626928x_{55} = -32.9867228626928
x56=−51.8362787842316x_{56} = -51.8362787842316
x57=−14.1371669411541x_{57} = -14.1371669411541
x58=−58.1194640914112x_{58} = -58.1194640914112
x59=−42.4115008234622x_{59} = -42.4115008234622
x60=−54.9778714378214x_{60} = -54.9778714378214
x61=−1.5707963267949x_{61} = -1.5707963267949
x62=42.4115008234622x_{62} = 42.4115008234622
x63=39.2699081698724x_{63} = 39.2699081698724
x64=67.5442420521806x_{64} = 67.5442420521806
x65=−23.5619449019235x_{65} = -23.5619449019235
x66=−114.668131856027x_{66} = -114.668131856027
x67=−73.8274273593601x_{67} = -73.8274273593601
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 (2*x + 1)*cos(x).
(0⋅2+1)cos⁡(0)\left(0 \cdot 2 + 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
−(2x+1)sin⁡(x)+2cos⁡(x)=0- \left(2 x + 1\right) \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−12.64850014121x_{1} = -12.64850014121
x2=−25.1732487838808x_{2} = -25.1732487838808
x3=−18.9038390299029x_{3} = -18.9038390299029
x4=53.425617048068x_{4} = 53.425617048068
x5=3.39302627455498x_{5} = 3.39302627455498
x6=56.5661894822938x_{6} = 56.5661894822938
x7=37.7252665845726x_{7} = 37.7252665845726
x8=9.52420750805087x_{8} = 9.52420750805087
x9=−75.4115719657448x_{9} = -75.4115719657448
x10=50.2851707005576x_{10} = 50.2851707005576
x11=−37.7259683523547x_{11} = -37.7259683523547
x12=−6.44970449955024x_{12} = -6.44970449955024
x13=12.6423143748731x_{13} = 12.6423143748731
x14=−3.46670616835097x_{14} = -3.46670616835097
x15=72.2703720240308x_{15} = 72.2703720240308
x16=−15.7733434995656x_{16} = -15.7733434995656
x17=62.8476376690475x_{17} = 62.8476376690475
x18=0.696269839120548x_{18} = 0.696269839120548
x19=−69.1296083184295x_{19} = -69.1296083184295
x20=84.8347196701717x_{20} = 84.8347196701717
x21=−84.8348585843051x_{21} = -84.8348585843051
x22=−50.2855658998982x_{22} = -50.2855658998982
x23=−28.3102763278749x_{23} = -28.3102763278749
x24=69.1293991413482x_{24} = 69.1293991413482
x25=25.1716749823811x_{25} = 25.1716749823811
x26=59.7068682917958x_{26} = 59.7068682917958
x27=65.9884847898322x_{27} = 65.9884847898322
x28=−87.9760255062228x_{28} = -87.9760255062228
x29=−125.671695000226x_{29} = -125.671695000226
x30=−59.7071486648078x_{30} = -59.7071486648078
x31=−78.5526275073207x_{31} = -78.5526275073207
x32=81.6935747942071x_{32} = 81.6935747942071
x33=47.1448753388288x_{33} = 47.1448753388288
x34=28.3090312886332x_{34} = 28.3090312886332
x35=−47.1453248960698x_{35} = -47.1453248960698
x36=22.0354939271259x_{36} = 22.0354939271259
x37=−94.2584449091977x_{37} = -94.2584449091977
x38=−53.4259671800873x_{38} = -53.4259671800873
x39=34.5860128618665x_{39} = 34.5860128618665
x40=−22.0375457987899x_{40} = -22.0375457987899
x41=40.8648748890387x_{41} = 40.8648748890387
x42=−40.865473077863x_{42} = -40.865473077863
x43=100.540861577829x_{43} = 100.540861577829
x44=−81.6937245934194x_{44} = -81.6937245934194
x45=−9.53500986666914x_{45} = -9.53500986666914
x46=6.4265662907479x_{46} = 6.4265662907479
x47=31.4472179490066x_{47} = 31.4472179490066
x48=−31.4482273260185x_{48} = -31.4482273260185
x49=−97.3996918452035x_{49} = -97.3996918452035
x50=94.2583323776119x_{50} = 94.2583323776119
x51=−100.540960487598x_{51} = -100.540960487598
x52=−65.988714345308x_{52} = -65.988714345308
x53=−72.2705634199913x_{53} = -72.2705634199913
x54=−34.5868476060207x_{54} = -34.5868476060207
x55=97.3995864537986x_{55} = 97.3995864537986
x56=44.0047628751252x_{56} = 44.0047628751252
x57=−44.0052788198049x_{57} = -44.0052788198049
x58=−56.5665018357101x_{58} = -56.5665018357101
x59=−128.813092076407x_{59} = -128.813092076407
x60=18.9010539397122x_{60} = 18.9010539397122
x61=−1.0601748825407x_{61} = -1.0601748825407
x62=91.1171015134381x_{62} = 91.1171015134381
x63=−62.8478907316314x_{63} = -62.8478907316314
x64=78.552465491919x_{64} = 78.552465491919
x65=−91.1172219360647x_{65} = -91.1172219360647
x66=87.9758963326206x_{66} = 87.9758963326206
x67=75.4113961768682x_{67} = 75.4113961768682
x68=15.7693513037718x_{68} = 15.7693513037718
Signos de extremos en los puntos:
(-12.648500141210008, -24.2151015515211)

(-25.17324878388082, -49.3060177064026)

(-18.903839029902947, -36.7534615948653)

(53.425617048068, -107.832694815235)

(3.3930262745549844, -7.54123369500216)

(56.56618948229382, 114.114859488293)

(37.72526658457259, 76.4243858824178)

(9.524207508050871, -19.9493949645634)

(-75.41157196574477, -149.809796642876)

(50.28517070055758, 101.550656337842)

(-37.725968352354734, -74.4250882665036)

(-6.449704499550243, -11.7348126404397)

(12.642314374873074, 26.208867469117)

(-3.466706168350972, 5.62258741075848)

(72.27037202403078, -145.527004137635)

(-15.773343499565579, 30.4814232045169)

(62.84763766904753, 126.679492379497)

(0.6962698391205479, 1.83565189459708)

(-69.12960831842948, -137.24464798613)

(84.83471967017165, -170.657721987522)

(-84.83485858430505, 168.657860925782)

(-50.2855658998982, -99.5510517325365)

(-28.31027632787489, 55.5846295565941)

(69.12939914134816, 139.244438754336)

(25.171674982381056, 51.304440800867)

(59.70686829179576, -120.397130618661)

(65.98848478983224, -132.961931932477)

(-87.97602550622281, -174.940620429129)

(-125.67169500022553, -250.33540135626)

(-59.70714866480777, 118.39741108998)

(-78.55262750732065, 156.092444723165)

(81.6935747942071, 164.374984537798)

(47.14487533882878, -95.2687689934234)

(28.309031288633168, -57.5833825757534)

(-47.14532489606982, 93.2692188034772)

(22.035493927125895, -45.0266788364878)

(-94.2584449091977, -187.506225022375)

(-53.425967180087326, 105.833045100583)

(34.586012861866465, -70.1435416902434)

(-22.03754579878994, 43.0287359885494)

(40.86487488903865, -82.7055852691928)

(-40.865473077862994, 80.7061839057418)

(100.54086157782926, 202.071826896584)

(-81.69372459341942, -162.375134365067)

(-9.535009866669144, 17.9603457903642)

(6.426566290747898, 13.7109792784596)

(31.447217949006586, 63.8631572509322)

(-31.448227326018454, -61.8641679035984)

(-97.3996918452035, 193.789064564391)

(94.25833237761192, 189.506112474957)

(-100.54096048759759, -200.071925818584)

(-65.988714345308, 130.962161553847)

(-72.27056341999133, 143.5271955794)

(-34.58684760602069, 68.1443773065834)

(97.39958645379863, -195.7889591591)

(44.004762875125245, 88.9870647497717)

(-44.00527881980492, -86.9875810274806)

(-56.56650183571013, -112.115171963728)

(-128.81309207640712, 256.618391070808)

(18.90105393971224, 38.7506667645283)

(-1.0601748825407007, -0.547536793420254)

(91.11710151343806, -183.223289009301)

(-62.84789073163143, -124.679745522165)

(78.55246549191897, -158.092282674943)

(-91.11722193606472, 181.223409450059)

(87.97589633262062, 176.940491234665)

(75.41139617686817, 151.809620815361)

(15.76935130377178, -32.4774109562335)


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=−12.64850014121x_{1} = -12.64850014121
x2=−25.1732487838808x_{2} = -25.1732487838808
x3=−18.9038390299029x_{3} = -18.9038390299029
x4=53.425617048068x_{4} = 53.425617048068
x5=3.39302627455498x_{5} = 3.39302627455498
x6=9.52420750805087x_{6} = 9.52420750805087
x7=−75.4115719657448x_{7} = -75.4115719657448
x8=−37.7259683523547x_{8} = -37.7259683523547
x9=−6.44970449955024x_{9} = -6.44970449955024
x10=72.2703720240308x_{10} = 72.2703720240308
x11=−69.1296083184295x_{11} = -69.1296083184295
x12=84.8347196701717x_{12} = 84.8347196701717
x13=−50.2855658998982x_{13} = -50.2855658998982
x14=59.7068682917958x_{14} = 59.7068682917958
x15=65.9884847898322x_{15} = 65.9884847898322
x16=−87.9760255062228x_{16} = -87.9760255062228
x17=−125.671695000226x_{17} = -125.671695000226
x18=47.1448753388288x_{18} = 47.1448753388288
x19=28.3090312886332x_{19} = 28.3090312886332
x20=22.0354939271259x_{20} = 22.0354939271259
x21=−94.2584449091977x_{21} = -94.2584449091977
x22=34.5860128618665x_{22} = 34.5860128618665
x23=40.8648748890387x_{23} = 40.8648748890387
x24=−81.6937245934194x_{24} = -81.6937245934194
x25=−31.4482273260185x_{25} = -31.4482273260185
x26=−100.540960487598x_{26} = -100.540960487598
x27=97.3995864537986x_{27} = 97.3995864537986
x28=−44.0052788198049x_{28} = -44.0052788198049
x29=−56.5665018357101x_{29} = -56.5665018357101
x30=−1.0601748825407x_{30} = -1.0601748825407
x31=91.1171015134381x_{31} = 91.1171015134381
x32=−62.8478907316314x_{32} = -62.8478907316314
x33=78.552465491919x_{33} = 78.552465491919
x34=15.7693513037718x_{34} = 15.7693513037718
Puntos máximos de la función:
x34=56.5661894822938x_{34} = 56.5661894822938
x34=37.7252665845726x_{34} = 37.7252665845726
x34=50.2851707005576x_{34} = 50.2851707005576
x34=12.6423143748731x_{34} = 12.6423143748731
x34=−3.46670616835097x_{34} = -3.46670616835097
x34=−15.7733434995656x_{34} = -15.7733434995656
x34=62.8476376690475x_{34} = 62.8476376690475
x34=0.696269839120548x_{34} = 0.696269839120548
x34=−84.8348585843051x_{34} = -84.8348585843051
x34=−28.3102763278749x_{34} = -28.3102763278749
x34=69.1293991413482x_{34} = 69.1293991413482
x34=25.1716749823811x_{34} = 25.1716749823811
x34=−59.7071486648078x_{34} = -59.7071486648078
x34=−78.5526275073207x_{34} = -78.5526275073207
x34=81.6935747942071x_{34} = 81.6935747942071
x34=−47.1453248960698x_{34} = -47.1453248960698
x34=−53.4259671800873x_{34} = -53.4259671800873
x34=−22.0375457987899x_{34} = -22.0375457987899
x34=−40.865473077863x_{34} = -40.865473077863
x34=100.540861577829x_{34} = 100.540861577829
x34=−9.53500986666914x_{34} = -9.53500986666914
x34=6.4265662907479x_{34} = 6.4265662907479
x34=31.4472179490066x_{34} = 31.4472179490066
x34=−97.3996918452035x_{34} = -97.3996918452035
x34=94.2583323776119x_{34} = 94.2583323776119
x34=−65.988714345308x_{34} = -65.988714345308
x34=−72.2705634199913x_{34} = -72.2705634199913
x34=−34.5868476060207x_{34} = -34.5868476060207
x34=44.0047628751252x_{34} = 44.0047628751252
x34=−128.813092076407x_{34} = -128.813092076407
x34=18.9010539397122x_{34} = 18.9010539397122
x34=−91.1172219360647x_{34} = -91.1172219360647
x34=87.9758963326206x_{34} = 87.9758963326206
x34=75.4113961768682x_{34} = 75.4113961768682
Decrece en los intervalos
[97.3995864537986,∞)\left[97.3995864537986, \infty\right)
Crece en los intervalos
(−∞,−125.671695000226]\left(-\infty, -125.671695000226\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
−((2x+1)cos⁡(x)+4sin⁡(x))=0- (\left(2 x + 1\right) \cos{\left(x \right)} + 4 \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−92.6986721657607x_{1} = -92.6986721657607
x2=2.20709108184684x_{2} = 2.20709108184684
x3=89.5575949877563x_{3} = 89.5575949877563
x4=98.9802703690406x_{4} = 98.9802703690406
x5=−76.9951595030424x_{5} = -76.9951595030424
x6=8.08291734224172x_{6} = 8.08291734224172
x7=48.7352850837268x_{7} = 48.7352850837268
x8=92.6984395744237x_{8} = 92.6984395744237
x9=83.2760739509161x_{9} = 83.2760739509161
x10=70.713911725806x_{10} = 70.713911725806
x11=−58.1541398031508x_{11} = -58.1541398031508
x12=−80.1357217460823x_{12} = -80.1357217460823
x13=−33.04809323157x_{13} = -33.04809323157
x14=5.05781499394109x_{14} = 5.05781499394109
x15=−55.0145424492814x_{15} = -55.0145424492814
x16=−26.7794960916493x_{16} = -26.7794960916493
x17=−67.5740510103712x_{17} = -67.5740510103712
x18=−29.9130227930797x_{18} = -29.9130227930797
x19=26.77672915311x_{19} = 26.77672915311
x20=−17.39657854932x_{20} = -17.39657854932
x21=−5.12086411057475x_{21} = -5.12086411057475
x22=42.4580243046486x_{22} = 42.4580243046486
x23=−73.8546853951763x_{23} = -73.8546853951763
x24=95.8393329056745x_{24} = 95.8393329056745
x25=55.0138828870594x_{25} = 55.0138828870594
x26=11.1653710575518x_{26} = 11.1653710575518
x27=−0.165645446198141x_{27} = -0.165645446198141
x28=67.5736135624991x_{28} = 67.5736135624991
x29=61.2934113605903x_{29} = 61.2934113605903
x30=86.4168044238104x_{30} = 86.4168044238104
x31=33.0462715195808x_{31} = 33.0462715195808
x32=−45.5974128787206x_{32} = -45.5974128787206
x33=64.4334404345819x_{33} = 64.4334404345819
x34=51.8744467999248x_{34} = 51.8744467999248
x35=−83.2763621071686x_{35} = -83.2763621071686
x36=39.3200919008673x_{36} = 39.3200919008673
x37=−2.38562216316639x_{37} = -2.38562216316639
x38=−48.7361250951756x_{38} = -48.7361250951756
x39=20.5152355295825x_{39} = 20.5152355295825
x40=14.2717422464289x_{40} = 14.2717422464289
x41=−61.2939428986749x_{41} = -61.2939428986749
x42=−95.8395505110637x_{42} = -95.8395505110637
x43=17.3900910590423x_{43} = 17.3900910590423
x44=−8.11095118927483x_{44} = -8.11095118927483
x45=−86.4170720311158x_{45} = -86.4170720311158
x46=−64.4339214987184x_{46} = -64.4339214987184
x47=−11.1806845006899x_{47} = -11.1806845006899
x48=−14.2812851466031x_{48} = -14.2812851466031
x49=29.9108017432811x_{49} = 29.9108017432811
x50=80.1354105811416x_{50} = 80.1354105811416
x51=−98.9804743910415x_{51} = -98.9804743910415
x52=45.5964535685511x_{52} = 45.5964535685511
x53=23.6445905112205x_{53} = 23.6445905112205
x54=−89.5578441674745x_{54} = -89.5578441674745
x55=−70.7143112275452x_{55} = -70.7143112275452
x56=73.8543191107716x_{56} = 73.8543191107716
x57=−20.5199223723935x_{57} = -20.5199223723935
x58=−23.6481309326897x_{58} = -23.6481309326897
x59=−39.3213806671139x_{59} = -39.3213806671139
x60=−51.8751884340414x_{60} = -51.8751884340414
x61=36.182783079284x_{61} = 36.182783079284
x62=−36.1843039911433x_{62} = -36.1843039911433
x63=−42.4591302044701x_{63} = -42.4591302044701
x64=58.1535494182186x_{64} = 58.1535494182186
x65=76.9948224610694x_{65} = 76.9948224610694

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
[95.8393329056745,∞)\left[95.8393329056745, \infty\right)
Convexa en los intervalos
(−∞,−95.8395505110637]\left(-\infty, -95.8395505110637\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((2x+1)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(2 x + 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→∞((2x+1)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(2 x + 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 (2*x + 1)*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((2x+1)cos⁡(x)x)=⟨−2,2⟩\lim_{x \to -\infty}\left(\frac{\left(2 x + 1\right) \cos{\left(x \right)}}{x}\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→∞((2x+1)cos⁡(x)x)=⟨−2,2⟩\lim_{x \to \infty}\left(\frac{\left(2 x + 1\right) \cos{\left(x \right)}}{x}\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:
(2x+1)cos⁡(x)=(1−2x)cos⁡(x)\left(2 x + 1\right) \cos{\left(x \right)} = \left(1 - 2 x\right) \cos{\left(x \right)}
- No
(2x+1)cos⁡(x)=−(1−2x)cos⁡(x)\left(2 x + 1\right) \cos{\left(x \right)} = - \left(1 - 2 x\right) \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = (2*x+1)*cos(x)
    © Sr Examen – Калькулятор