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Trazado el gráfico de la función/ cosx/(x+1)

Gráfico de la función y = cosx/(x+1)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       cos(x)
f(x) = ------
       x + 1
f(x)=cos⁡(x)x+1f{\left(x \right)} = \frac{\cos{\left(x \right)}}{x + 1} 
f = cos(x)/(x + 1)
Gráfico de la función
0.02.00.20.40.60.81.01.21.41.61.82-1
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=−1x_{1} = -1
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:
cos⁡(x)x+1=0\frac{\cos{\left(x \right)}}{x + 1} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=π2x_{1} = \frac{\pi}{2}
x2=3π2x_{2} = \frac{3 \pi}{2}
Solución numérica
x1=1.5707963267949x_{1} = 1.5707963267949
x2=39.2699081698724x_{2} = 39.2699081698724
x3=−39.2699081698724x_{3} = -39.2699081698724
x4=14.1371669411541x_{4} = 14.1371669411541
x5=−70.6858347057703x_{5} = -70.6858347057703
x6=32.9867228626928x_{6} = 32.9867228626928
x7=61.261056745001x_{7} = 61.261056745001
x8=36.1283155162826x_{8} = 36.1283155162826
x9=−61.261056745001x_{9} = -61.261056745001
x10=−36.1283155162826x_{10} = -36.1283155162826
x11=−48.6946861306418x_{11} = -48.6946861306418
x12=7.85398163397448x_{12} = 7.85398163397448
x13=70.6858347057703x_{13} = 70.6858347057703
x14=−80.1106126665397x_{14} = -80.1106126665397
x15=42.4115008234622x_{15} = 42.4115008234622
x16=51.8362787842316x_{16} = 51.8362787842316
x17=−98.9601685880785x_{17} = -98.9601685880785
x18=80.1106126665397x_{18} = 80.1106126665397
x19=−64.4026493985908x_{19} = -64.4026493985908
x20=−29.845130209103x_{20} = -29.845130209103
x21=98.9601685880785x_{21} = 98.9601685880785
x22=−256.039801267568x_{22} = -256.039801267568
x23=83.2522053201295x_{23} = 83.2522053201295
x24=−89.5353906273091x_{24} = -89.5353906273091
x25=−86.3937979737193x_{25} = -86.3937979737193
x26=−10.9955742875643x_{26} = -10.9955742875643
x27=17.2787595947439x_{27} = 17.2787595947439
x28=−26.7035375555132x_{28} = -26.7035375555132
x29=−54.9778714378214x_{29} = -54.9778714378214
x30=−92.6769832808989x_{30} = -92.6769832808989
x31=89.5353906273091x_{31} = 89.5353906273091
x32=58.1194640914112x_{32} = 58.1194640914112
x33=4.71238898038469x_{33} = 4.71238898038469
x34=20.4203522483337x_{34} = 20.4203522483337
x35=73.8274273593601x_{35} = 73.8274273593601
x36=−67.5442420521806x_{36} = -67.5442420521806
x37=45.553093477052x_{37} = 45.553093477052
x38=−58.1194640914112x_{38} = -58.1194640914112
x39=−51.8362787842316x_{39} = -51.8362787842316
x40=−83.2522053201295x_{40} = -83.2522053201295
x41=−76.9690200129499x_{41} = -76.9690200129499
x42=−14.1371669411541x_{42} = -14.1371669411541
x43=−73.8274273593601x_{43} = -73.8274273593601
x44=92.6769832808989x_{44} = 92.6769832808989
x45=−20.4203522483337x_{45} = -20.4203522483337
x46=64.4026493985908x_{46} = 64.4026493985908
x47=95.8185759344887x_{47} = 95.8185759344887
x48=67.5442420521806x_{48} = 67.5442420521806
x49=54.9778714378214x_{49} = 54.9778714378214
x50=48.6946861306418x_{50} = 48.6946861306418
x51=−4.71238898038469x_{51} = -4.71238898038469
x52=76.9690200129499x_{52} = 76.9690200129499
x53=−45.553093477052x_{53} = -45.553093477052
x54=−7.85398163397448x_{54} = -7.85398163397448
x55=−161.792021659874x_{55} = -161.792021659874
x56=−95.8185759344887x_{56} = -95.8185759344887
x57=29.845130209103x_{57} = 29.845130209103
x58=−17.2787595947439x_{58} = -17.2787595947439
x59=−32.9867228626928x_{59} = -32.9867228626928
x60=26.7035375555132x_{60} = 26.7035375555132
x61=−1.5707963267949x_{61} = -1.5707963267949
x62=10.9955742875643x_{62} = 10.9955742875643
x63=−127.234502470387x_{63} = -127.234502470387
x64=230.90706003885x_{64} = 230.90706003885
x65=86.3937979737193x_{65} = 86.3937979737193
x66=23.5619449019235x_{66} = 23.5619449019235
x67=−23.5619449019235x_{67} = -23.5619449019235
x68=−42.4115008234622x_{68} = -42.4115008234622
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)/(x + 1).
cos⁡(0)1\frac{\cos{\left(0 \right)}}{1}
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
−sin⁡(x)x+1−cos⁡(x)(x+1)2=0- \frac{\sin{\left(x \right)}}{x + 1} - \frac{\cos{\left(x \right)}}{\left(x + 1\right)^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=9.32825706323943x_{1} = 9.32825706323943
x2=43.9600588531378x_{2} = 43.9600588531378
x3=−94.2370546693974x_{3} = -94.2370546693974
x4=2.88996969767843x_{4} = 2.88996969767843
x5=72.242978694986x_{5} = 72.242978694986
x6=18.7990914357831x_{6} = 18.7990914357831
x7=69.1007741687956x_{7} = 69.1007741687956
x8=−31.3830252979972x_{8} = -31.3830252979972
x9=−25.0912562079058x_{9} = -25.0912562079058
x10=−91.0950880256329x_{10} = -91.0950880256329
x11=−28.2376364595748x_{11} = -28.2376364595748
x12=−637.741738184573x_{12} = -637.741738184573
x13=−53.3879890840753x_{13} = -53.3879890840753
x14=40.8167952172419x_{14} = 40.8167952172419
x15=1313.18496827279x_{15} = 1313.18496827279
x16=−81.6690132946536x_{16} = -81.6690132946536
x17=15.6479679638982x_{17} = 15.6479679638982
x18=−72.24259540785x_{18} = -72.24259540785
x19=−2.57625015820118x_{19} = -2.57625015820118
x20=6.14411351301787x_{20} = 6.14411351301787
x21=−12.4794779911025x_{21} = -12.4794779911025
x22=94.2372799036618x_{22} = 94.2372799036618
x23=84.8113487041494x_{23} = 84.8113487041494
x24=81.6693131963402x_{24} = 81.6693131963402
x25=56.5312876685112x_{25} = 56.5312876685112
x26=−47.1022022669651x_{26} = -47.1022022669651
x27=100.521115065812x_{27} = 100.521115065812
x28=−100.520917114109x_{28} = -100.520917114109
x29=−62.815677356778x_{29} = -62.815677356778
x30=37.673259943911x_{30} = 37.673259943911
x31=−97.378996929011x_{31} = -97.378996929011
x32=47.1031041186137x_{32} = 47.1031041186137
x33=65.9585122146304x_{33} = 65.9585122146304
x34=78.5272426949571x_{34} = 78.5272426949571
x35=−87.9530943542027x_{35} = -87.9530943542027
x36=−15.6397620877646x_{36} = -15.6397620877646
x37=53.388691007263x_{37} = 53.388691007263
x38=−21.9434371567881x_{38} = -21.9434371567881
x39=−59.6732185170696x_{39} = -59.6732185170696
x40=12.492390025579x_{40} = 12.492390025579
x41=172.781841669816x_{41} = 172.781841669816
x42=50.2459712046114x_{42} = 50.2459712046114
x43=31.38505790634x_{43} = 31.38505790634
x44=−75.3847808857452x_{44} = -75.3847808857452
x45=34.5293808983144x_{45} = 34.5293808983144
x46=−37.6718497263809x_{46} = -37.6718497263809
x47=−34.527701946778x_{47} = -34.527701946778
x48=75.3851328811964x_{48} = 75.3851328811964
x49=−6.08916120309943x_{49} = -6.08916120309943
x50=−43.9590233567938x_{50} = -43.9590233567938
x51=59.6737803264459x_{51} = 59.6737803264459
x52=−69.1003552230555x_{52} = -69.1003552230555
x53=−40.8155939881502x_{53} = -40.8155939881502
x54=28.2401476526276x_{54} = 28.2401476526276
x55=−9.30494468339504x_{55} = -9.30494468339504
x56=−78.5269183093816x_{56} = -78.5269183093816
x57=21.9475985837942x_{57} = 21.9475985837942
x58=−18.7934144113698x_{58} = -18.7934144113698
x59=−56.5306616416093x_{59} = -56.5306616416093
x60=91.0953290668266x_{60} = 91.0953290668266
x61=87.9533529268738x_{61} = 87.9533529268738
x62=197.915309953386x_{62} = 197.915309953386
x63=−84.8110706151124x_{63} = -84.8110706151124
x64=25.0944376288815x_{64} = 25.0944376288815
x65=62.8161843480611x_{65} = 62.8161843480611
x66=−50.2451786914948x_{66} = -50.2451786914948
x67=−65.9580523911179x_{67} = -65.9580523911179
x68=97.379207861883x_{68} = 97.379207861883
Signos de extremos en los puntos:
(9.328257063239425, -0.0963710979823201)

(43.960058853137774, 0.022236464203186)

(-94.23705466939735, -0.010724732692878)

(2.8899696976784344, -0.248976134877405)

(72.242978694986, -0.0136519134817116)

(18.79909143578314, 0.0504430691319447)

(69.10077416879557, 0.0142637264671467)

(-31.38302529799723, -0.0328953023371544)

(-25.091256207905772, -0.0414731225016059)

(-91.09508802563293, 0.0110987005999837)

(-28.237636459574798, 0.0366891865463047)

(-637.7417381845734, 0.00157049350907233)

(-53.387989084075315, 0.0190848682073296)

(40.81679521724192, -0.023907001519389)

(1313.1849682727866, 0.000760927673528925)

(-81.66901329465364, -0.0123953812433342)

(15.647967963898166, -0.0599593189797558)

(-72.24259540785, 0.0140351638863266)

(-2.5762501582011796, 0.535705052303484)

(6.1441135130178655, 0.138623930394573)

(-12.479477991102517, -0.0867833198945747)

(94.23727990366179, 0.0104995111118831)

(84.81134870414938, -0.0116526790492257)

(81.66931319634023, 0.0120955020439642)

(56.53128766851124, 0.0173792211238612)

(-47.10220226696507, 0.0216858368023364)

(100.52111506581193, 0.00984968979094353)

(-100.52091711410945, -0.0100476316966419)

(-62.815677356778, -0.0161750096209984)

(37.673259943911006, 0.0258490197028825)

(-97.37899692901101, 0.0103751461271118)

(47.10310411861372, -0.0207841885412821)

(65.95851221463039, -0.0149329557083856)

(78.52724269495707, -0.0125733134820883)

(-87.95309435420273, -0.0114996928375307)

(-15.63976208776456, 0.0681483206400774)

(53.388691007263, -0.0183830682189117)

(-21.94343715678808, 0.0476933188520339)

(-59.673218517069586, 0.0170410762454831)

(12.492390025578958, 0.0739131230459364)

(172.781841669816, -0.0057542458670116)

(50.24597120461141, 0.0195100148956696)

(31.385057906339963, 0.0308637274812354)

(-75.38478088574516, -0.0134423955413013)

(34.5293808983144, -0.0281345781753277)

(-37.67184972638089, -0.0272587398500595)

(-34.52770194677802, 0.0298128246468963)

(75.38513288119637, 0.0130904310684593)

(-6.089161203099427, -0.192809042427521)

(-43.95902335679378, -0.0232716924030311)

(59.67378032644585, -0.0164793457895915)

(-69.1003552230555, -0.0146826283229769)

(-40.81559398815024, 0.0251078697468112)

(28.240147652627645, -0.0341795711715136)

(-9.304944683395044, 0.119546681963348)

(-78.5269183093816, 0.0128976727485698)

(21.947598583794207, -0.0435362264748061)

(-18.793414411369753, -0.0561120230339157)

(-56.53066164160934, -0.0180051500304447)

(91.09532906682657, -0.0108576739325778)

(87.9533529268738, 0.0112411368826843)

(197.91530995338616, -0.00502720159537522)

(-84.81107061511238, 0.0119307487512748)

(25.094437628881476, 0.0382942342355763)

(62.81618434806106, 0.0156680826074814)

(-50.245178691494786, -0.0203023709567303)

(-65.9580523911179, 0.0153927263543733)

(97.37920786188297, -0.0101642243790071)


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=9.32825706323943x_{1} = 9.32825706323943
x2=−94.2370546693974x_{2} = -94.2370546693974
x3=2.88996969767843x_{3} = 2.88996969767843
x4=72.242978694986x_{4} = 72.242978694986
x5=−31.3830252979972x_{5} = -31.3830252979972
x6=−25.0912562079058x_{6} = -25.0912562079058
x7=40.8167952172419x_{7} = 40.8167952172419
x8=−81.6690132946536x_{8} = -81.6690132946536
x9=15.6479679638982x_{9} = 15.6479679638982
x10=−12.4794779911025x_{10} = -12.4794779911025
x11=84.8113487041494x_{11} = 84.8113487041494
x12=−100.520917114109x_{12} = -100.520917114109
x13=−62.815677356778x_{13} = -62.815677356778
x14=47.1031041186137x_{14} = 47.1031041186137
x15=65.9585122146304x_{15} = 65.9585122146304
x16=78.5272426949571x_{16} = 78.5272426949571
x17=−87.9530943542027x_{17} = -87.9530943542027
x18=53.388691007263x_{18} = 53.388691007263
x19=172.781841669816x_{19} = 172.781841669816
x20=−75.3847808857452x_{20} = -75.3847808857452
x21=34.5293808983144x_{21} = 34.5293808983144
x22=−37.6718497263809x_{22} = -37.6718497263809
x23=−6.08916120309943x_{23} = -6.08916120309943
x24=−43.9590233567938x_{24} = -43.9590233567938
x25=59.6737803264459x_{25} = 59.6737803264459
x26=−69.1003552230555x_{26} = -69.1003552230555
x27=28.2401476526276x_{27} = 28.2401476526276
x28=21.9475985837942x_{28} = 21.9475985837942
x29=−18.7934144113698x_{29} = -18.7934144113698
x30=−56.5306616416093x_{30} = -56.5306616416093
x31=91.0953290668266x_{31} = 91.0953290668266
x32=197.915309953386x_{32} = 197.915309953386
x33=−50.2451786914948x_{33} = -50.2451786914948
x34=97.379207861883x_{34} = 97.379207861883
Puntos máximos de la función:
x34=43.9600588531378x_{34} = 43.9600588531378
x34=18.7990914357831x_{34} = 18.7990914357831
x34=69.1007741687956x_{34} = 69.1007741687956
x34=−91.0950880256329x_{34} = -91.0950880256329
x34=−28.2376364595748x_{34} = -28.2376364595748
x34=−637.741738184573x_{34} = -637.741738184573
x34=−53.3879890840753x_{34} = -53.3879890840753
x34=1313.18496827279x_{34} = 1313.18496827279
x34=−72.24259540785x_{34} = -72.24259540785
x34=−2.57625015820118x_{34} = -2.57625015820118
x34=6.14411351301787x_{34} = 6.14411351301787
x34=94.2372799036618x_{34} = 94.2372799036618
x34=81.6693131963402x_{34} = 81.6693131963402
x34=56.5312876685112x_{34} = 56.5312876685112
x34=−47.1022022669651x_{34} = -47.1022022669651
x34=100.521115065812x_{34} = 100.521115065812
x34=37.673259943911x_{34} = 37.673259943911
x34=−97.378996929011x_{34} = -97.378996929011
x34=−15.6397620877646x_{34} = -15.6397620877646
x34=−21.9434371567881x_{34} = -21.9434371567881
x34=−59.6732185170696x_{34} = -59.6732185170696
x34=12.492390025579x_{34} = 12.492390025579
x34=50.2459712046114x_{34} = 50.2459712046114
x34=31.38505790634x_{34} = 31.38505790634
x34=−34.527701946778x_{34} = -34.527701946778
x34=75.3851328811964x_{34} = 75.3851328811964
x34=−40.8155939881502x_{34} = -40.8155939881502
x34=−9.30494468339504x_{34} = -9.30494468339504
x34=−78.5269183093816x_{34} = -78.5269183093816
x34=87.9533529268738x_{34} = 87.9533529268738
x34=−84.8110706151124x_{34} = -84.8110706151124
x34=25.0944376288815x_{34} = 25.0944376288815
x34=62.8161843480611x_{34} = 62.8161843480611
x34=−65.9580523911179x_{34} = -65.9580523911179
Decrece en los intervalos
[197.915309953386,∞)\left[197.915309953386, \infty\right)
Crece en los intervalos
(−∞,−100.520917114109]\left(-\infty, -100.520917114109\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
−cos⁡(x)+2sin⁡(x)x+1+2cos⁡(x)(x+1)2x+1=0\frac{- \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x + 1} + \frac{2 \cos{\left(x \right)}}{\left(x + 1\right)^{2}}}{x + 1} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=23.4801553706306x_{1} = 23.4801553706306
x2=95.797912862081x_{2} = 95.797912862081
x3=86.3709050594723x_{3} = 86.3709050594723
x4=−54.9407852505616x_{4} = -54.9407852505616
x5=4.32863617605124x_{5} = 4.32863617605124
x6=−86.3703684986956x_{6} = -86.3703684986956
x7=83.228458145445x_{7} = 83.228458145445
x8=42.3653647291314x_{8} = 42.3653647291314
x9=−26.6254109350763x_{9} = -26.6254109350763
x10=32.9277399444348x_{10} = 32.9277399444348
x11=−58.0844210975337x_{11} = -58.0844210975337
x12=64.3720505127272x_{12} = 64.3720505127272
x13=−10.7898786754269x_{13} = -10.7898786754269
x14=26.6310922236611x_{14} = 26.6310922236611
x15=36.0743437126941x_{15} = 36.0743437126941
x16=92.6556268279389x_{16} = 92.6556268279389
x17=89.5132926274963x_{17} = 89.5132926274963
x18=−89.5127931011103x_{18} = -89.5127931011103
x19=−80.0853208283276x_{19} = -80.0853208283276
x20=45.5100787997204x_{20} = 45.5100787997204
x21=98.9401552763972x_{21} = 98.9401552763972
x22=−45.5081427660817x_{22} = -45.5081427660817
x23=51.7983897861238x_{23} = 51.7983897861238
x24=−95.7974767616183x_{24} = -95.7974767616183
x25=70.657920700132x_{25} = 70.657920700132
x26=−64.3710840254309x_{26} = -64.3710840254309
x27=10.825651157762x_{27} = 10.825651157762
x28=−67.5141687409854x_{28} = -67.5141687409854
x29=−32.9240332040206x_{29} = -32.9240332040206
x30=−39.2175523279643x_{30} = -39.2175523279643
x31=−29.7755709323142x_{31} = -29.7755709323142
x32=136.64474976163x_{32} = 136.64474976163
x33=29.7801075137773x_{33} = 29.7801075137773
x34=−76.9426813176863x_{34} = -76.9426813176863
x35=−98.9397464504172x_{35} = -98.9397464504172
x36=−17.1546413657741x_{36} = -17.1546413657741
x37=39.22016138731x_{37} = 39.22016138731
x38=−73.7999513585394x_{38} = -73.7999513585394
x39=−48.6527034788051x_{39} = -48.6527034788051
x40=48.654396838104x_{40} = 48.654396838104
x41=61.2289118119026x_{41} = 61.2289118119026
x42=−4.00507341668955x_{42} = -4.00507341668955
x43=−42.3631297553676x_{43} = -42.3631297553676
x44=−83.2278802717944x_{44} = -83.2278802717944
x45=−36.0712578833702x_{45} = -36.0712578833702
x46=17.1684571899007x_{46} = 17.1684571899007
x47=14.0034717913284x_{47} = 14.0034717913284
x48=−70.6571186927646x_{48} = -70.6571186927646
x49=−13.9825085391948x_{49} = -13.9825085391948
x50=76.9433575383977x_{50} = 76.9433575383977
x51=−7.54372449628009x_{51} = -7.54372449628009
x52=102.082358062481x_{52} = 102.082358062481
x53=80.0859449790141x_{53} = 80.0859449790141
x54=−61.2278434114583x_{54} = -61.2278434114583
x55=58.0856084395179x_{55} = 58.0856084395179
x56=7.61991323310644x_{56} = 7.61991323310644
x57=20.3264348242219x_{57} = 20.3264348242219
x58=−20.3166301288662x_{58} = -20.3166301288662
x59=67.5150472396589x_{59} = 67.5150472396589
x60=54.9421125829153x_{60} = 54.9421125829153
x61=−92.6551606286758x_{61} = -92.6551606286758
x62=−23.4728313498836x_{62} = -23.4728313498836
x63=73.80068645168x_{63} = 73.80068645168
x64=−51.7968961320869x_{64} = -51.7968961320869
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=−1x_{1} = -1

lim⁡x→−1−(−cos⁡(x)+2sin⁡(x)x+1+2cos⁡(x)(x+1)2x+1)=−∞\lim_{x \to -1^-}\left(\frac{- \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x + 1} + \frac{2 \cos{\left(x \right)}}{\left(x + 1\right)^{2}}}{x + 1}\right) = -\infty
lim⁡x→−1+(−cos⁡(x)+2sin⁡(x)x+1+2cos⁡(x)(x+1)2x+1)=∞\lim_{x \to -1^+}\left(\frac{- \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x + 1} + \frac{2 \cos{\left(x \right)}}{\left(x + 1\right)^{2}}}{x + 1}\right) = \infty
- los límites no son iguales, signo
x1=−1x_{1} = -1
- es el punto de flexión

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
[102.082358062481,∞)\left[102.082358062481, \infty\right)
Convexa en los intervalos
(−∞,−95.7974767616183]\left(-\infty, -95.7974767616183\right]
Asíntotas verticales
Hay:
x1=−1x_{1} = -1
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(cos⁡(x)x+1)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x + 1}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(cos⁡(x)x+1)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x + 1}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(x)/(x + 1), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡(x)x(x+1))=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{x \left(x + 1\right)}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(cos⁡(x)x(x+1))=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{x \left(x + 1\right)}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
cos⁡(x)x+1=cos⁡(x)1−x\frac{\cos{\left(x \right)}}{x + 1} = \frac{\cos{\left(x \right)}}{1 - x}
- No
cos⁡(x)x+1=−cos⁡(x)1−x\frac{\cos{\left(x \right)}}{x + 1} = - \frac{\cos{\left(x \right)}}{1 - x}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор