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Trazado el gráfico de la función/ 2*cos(3*x)-7*cos(2*x)*3*x-7*cos(2*x)-14*cos(x)

Gráfico de la función y = 2*cos(3*x)-7*cos(2*x)*3*x-7*cos(2*x)-14*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = 2*cos(3*x) - 7*cos(2*x)*3*x - 7*cos(2*x) - 14*cos(x)
f(x)=((−x3⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)f{\left(x \right)} = \left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} 
f = -x*3*(7*cos(2*x)) + 2*cos(3*x) - 7*cos(2*x) - 14*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-500500
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⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)=0\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−79.3286186868585x_{1} = -79.3286186868585
x2=0.96976315786421x_{2} = 0.96976315786421
x3=−33.7640958654435x_{3} = -33.7640958654435
x4=−13.330829611389x_{4} = -13.330829611389
x5=33.7800485957099x_{5} = 33.7800485957099
x6=54.1875203268219x_{6} = 54.1875203268219
x7=91.8886599233614x_{7} = 91.8886599233614
x8=19.6483440506237x_{8} = 19.6483440506237
x9=47.9036880055106x_{9} = 47.9036880055106
x10=−93.4652780164121x_{10} = -93.4652780164121
x11=−32.1928339429512x_{11} = -32.1928339429512
x12=96.6067567248107x_{12} = 96.6067567248107
x13=−82.4635219393152x_{13} = -82.4635219393152
x14=−90.3177997124238x_{14} = -90.3177997124238
x15=46.3442792234221x_{15} = 46.3442792234221
x16=−11.8047294380989x_{16} = -11.8047294380989
x17=68.3257245598241x_{17} = 68.3257245598241
x18=−76.1800639891199x_{18} = -76.1800639891199
x19=66.7548206083775x_{19} = 66.7548206083775
x20=5.45232194697703x_{20} = 5.45232194697703
x21=−47.9149332328647x_{21} = -47.9149332328647
x22=82.4700550384384x_{22} = 82.4700550384384
x23=−18.0794520134705x_{23} = -18.0794520134705
x24=13.3712307064103x_{24} = 13.3712307064103
x25=27.4986610579683x_{25} = 27.4986610579683
x26=−16.5098745115795x_{26} = -16.5098745115795
x27=24.3364836195886x_{27} = 24.3364836195886
x28=99.7428786869862x_{28} = 99.7428786869862
x29=−40.0485467217252x_{29} = -40.0485467217252
x30=30.6218642316085x_{30} = 30.6218642316085
x31=−10.237003770154x_{31} = -10.237003770154
x32=73.0383510985983x_{32} = 73.0383510985983
x33=25.9283439961946x_{33} = 25.9283439961946
x34=90.323764553498x_{34} = 90.323764553498
x35=77.7578736018635x_{35} = 77.7578736018635
x36=76.1871359366327x_{36} = 76.1871359366327
x37=−84.0343903781717x_{37} = -84.0343903781717
x38=−85.6115535855662x_{38} = -85.6115535855662
x39=−35.3505803351934x_{39} = -35.3505803351934
x40=60.4712186135938x_{40} = 60.4712186135938
x41=−5.55074154552555x_{41} = -5.55074154552555
x42=10.1842375562936x_{42} = 10.1842375562936
x43=−71.4674531971057x_{43} = -71.4674531971057
x44=−91.8945227984772x_{44} = -91.8945227984772
x45=−62.0508290562559x_{45} = -62.0508290562559
x46=−60.4801271546578x_{46} = -60.4801271546578
x47=41.6196612147716x_{47} = 41.6196612147716
x48=85.6052604062619x_{48} = 85.6052604062619
x49=11.7589450481684x_{49} = 11.7589450481684
x50=−27.4790617833793x_{50} = -27.4790617833793
x51=−77.7509447406708x_{51} = -77.7509447406708
x52=−41.6326038532267x_{52} = -41.6326038532267
x53=69.9042643658696x_{53} = 69.9042643658696
x54=16.4772092502488x_{54} = 16.4772092502488
x55=14.9403566810386x_{55} = 14.9403566810386
x56=63.6214543030474x_{56} = 63.6214543030474
x57=74.6092375807615x_{57} = 74.6092375807615
x58=38.4914241105263x_{58} = 38.4914241105263
x59=2.4573496807162x_{59} = 2.4573496807162
x60=−63.612985298967x_{60} = -63.612985298967
x61=49.4746906867931x_{61} = 49.4746906867931
x62=98.1720320747266x_{62} = 98.1720320747266
x63=−19.6208905627261x_{63} = -19.6208905627261
x64=−49.4855796988963x_{64} = -49.4855796988963
x65=62.042145652071x_{65} = 62.042145652071
x66=−55.7681406919688x_{66} = -55.7681406919688
x67=−24.3586179146243x_{67} = -24.3586179146243
x68=52.6267762292029x_{68} = 52.6267762292029
x69=−69.8965566871116x_{69} = -69.8965566871116
x70=−25.9075509819384x_{70} = -25.9075509819384
x71=84.0408011908752x_{71} = 84.0408011908752
x72=8.66974571901423x_{72} = 8.66974571901423
x73=40.0619969877346x_{73} = 40.0619969877346
x74=−2.22420547332476x_{74} = -2.22420547332476
x75=18.0496119247806x_{75} = 18.0496119247806
x76=−38.4774230870637x_{76} = -38.4774230870637
x77=32.209567896301x_{77} = 32.209567896301
x78=−57.3293285762611x_{78} = -57.3293285762611
x79=−3.99775823441916x_{79} = -3.99775823441916
x80=−46.332652760818x_{80} = -46.332652760818
x81=55.7584787653484x_{81} = 55.7584787653484
x82=−68.3336094231474x_{82} = -68.3336094231474
x83=−54.1974617496389x_{83} = -54.1974617496389
x84=−99.7482800134655x_{84} = -99.7482800134655
x85=3.86071461784559x_{85} = 3.86071461784559
x86=88.7530116308266x_{86} = 88.7530116308266
x87=−98.1775197248071x_{87} = -98.1775197248071
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*cos(3*x) - (7*cos(2*x))*3*x - 7*cos(2*x) - 14*cos(x).
−14cos⁡(0)+(−7cos⁡(0⋅2)+(−0⋅3⋅7cos⁡(0⋅2)+2cos⁡(0⋅3)))- 14 \cos{\left(0 \right)} + \left(- 7 \cos{\left(0 \cdot 2 \right)} + \left(- 0 \cdot 3 \cdot 7 \cos{\left(0 \cdot 2 \right)} + 2 \cos{\left(0 \cdot 3 \right)}\right)\right)
Resultado:
f(0)=−19f{\left(0 \right)} = -19
Punto:
(0, -19)
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
42xsin⁡(2x)+14sin⁡(x)+14sin⁡(2x)−6sin⁡(3x)−21cos⁡(2x)=042 x \sin{\left(2 x \right)} + 14 \sin{\left(x \right)} + 14 \sin{\left(2 x \right)} - 6 \sin{\left(3 x \right)} - 21 \cos{\left(2 x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−51.8365099303089x_{1} = -51.8365099303089
x2=−7.85556421545038x_{2} = -7.85556421545038
x3=95.8236518040196x_{3} = 95.8236518040196
x4=−86.399468922026x_{4} = -86.399468922026
x5=−94.2504401555016x_{5} = -94.2504401555016
x6=−42.4230955040777x_{6} = -42.4230955040777
x7=−83.2523488910586x_{7} = -83.2523488910586
x8=−89.5355240854703x_{8} = -89.5355240854703
x9=0.329878181493422x_{9} = 0.329878181493422
x10=−54.9868013201444x_{10} = -54.9868013201444
x11=−95.8187006107704x_{11} = -95.8187006107704
x12=72.2600725597578x_{12} = 72.2600725597578
x13=64.4101877947986x_{13} = 64.4101877947986
x14=−1.58033665004861x_{14} = -1.58033665004861
x15=22.0023157913067x_{15} = 22.0023157913067
x16=48.6949289448107x_{16} = 48.6949289448107
x17=50.2704272932174x_{17} = 50.2704272932174
x18=6.32095174977373x_{18} = 6.32095174977373
x19=−15.7242511883627x_{19} = -15.7242511883627
x20=−20.4209448887882x_{20} = -20.4209448887882
x21=−58.119670104785x_{21} = -58.119670104785
x22=100.533444581925x_{22} = 100.533444581925
x23=43.9879436077029x_{23} = 43.9879436077029
x24=−39.2702139148003x_{24} = -39.2702139148003
x25=−73.8340676969796x_{25} = -73.8340676969796
x26=−37.7057923529646x_{26} = -37.7057923529646
x27=−97.391949265849x_{27} = -97.391949265849
x28=86.3939352403536x_{28} = 86.3939352403536
x29=51.8456320657499x_{29} = 51.8456320657499
x30=87.9674270304944x_{30} = 87.9674270304944
x31=−67.5515029564298x_{31} = -67.5515029564298
x32=58.1278124542836x_{32} = 58.1278124542836
x33=1.78796740242292x_{33} = 1.78796740242292
x34=67.5444174374737x_{34} = 67.5444174374737
x35=−31.4239545634883x_{35} = -31.4239545634883
x36=−0.589149345698636x_{36} = -0.589149345698636
x37=56.5530660562027x_{37} = 56.5530660562027
x38=37.7056918967783x_{38} = 37.7056918967783
x39=−59.6944752084758x_{39} = -59.6944752084758
x40=−72.2601090360426x_{40} = -72.2601090360426
x41=−23.5829276401346x_{41} = -23.5829276401346
x42=26.7215715058841x_{42} = 26.7215715058841
x43=−22.0027089238939x_{43} = -22.0027089238939
x44=59.6944217613547x_{44} = 59.6944217613547
x45=28.2830547433159x_{45} = 28.2830547433159
x46=−12.5866832131152x_{46} = -12.5866832131152
x47=42.4117793291063x_{47} = 42.4117793291063
x48=7.91292734920106x_{48} = 7.91292734920106
x49=73.8275878854089x_{49} = 73.8275878854089
x50=45.5637266141872x_{50} = 45.5637266141872
x51=−80.1167301493193x_{51} = -80.1167301493193
x52=80.1107606545324x_{52} = 80.1107606545324
x53=−36.1419431785463x_{53} = -36.1419431785463
x54=−43.9880174241053x_{54} = -43.9880174241053
x55=−65.9772568416673x_{55} = -65.9772568416673
x56=−17.3074866297774x_{56} = -17.3074866297774
x57=−28.2832927385975x_{57} = -28.2832927385975
x58=20.4438287899401x_{58} = 20.4438287899401
x59=89.5408213115049x_{59} = 89.5408213115049
x60=−75.4015518300676x_{60} = -75.4015518300676
x61=−9.45230877575799x_{61} = -9.45230877575799
x62=−102.101878220453x_{62} = -102.101878220453
x63=70.6927063810377x_{63} = 70.6927063810377
x64=81.6844588452805x_{64} = 81.6844588452805
x65=−14.1380293069029x_{65} = -14.1380293069029
x66=−29.8616545835409x_{66} = -29.8616545835409
x67=23.5624430962496x_{67} = 23.5624430962496
x68=34.5646726754472x_{68} = 34.5646726754472
x69=29.8455246822244x_{69} = 29.8455246822244
x70=−50.2704838147943x_{70} = -50.2704838147943
x71=65.9772130881693x_{71} = 65.9772130881693
x72=92.6771112747014x_{72} = 92.6771112747014
x73=−81.6844802544329x_{73} = -81.6844802544329
x74=−87.9674454907549x_{74} = -87.9674454907549
x75=−45.5533567399819x_{75} = -45.5533567399819
x76=−53.4117892090852x_{76} = -53.4117892090852
x77=78.5429839043088x_{77} = 78.5429839043088
x78=−3.22844409727052x_{78} = -3.22844409727052
x79=94.2504240743329x_{79} = 94.2504240743329
x80=12.5857834640896x_{80} = 12.5857834640896
x81=−6.32449323163835x_{81} = -6.32449323163835
x82=14.1707740307198x_{82} = 14.1707740307198
x83=15.723482018271x_{83} = 15.723482018271
x84=−61.2690661353708x_{84} = -61.2690661353708
x85=36.128642014024x_{85} = 36.128642014024
x86=−64.4028352086649x_{86} = -64.4028352086649
Signos de extremos en los puntos:
(-51.836509930308914, -1081.56197004209)

(-7.8555642154503795, -157.934405664318)

(95.82365180401965, 2019.29415254338)

(-86.39946892202596, -1807.38601550549)

(-94.2504401555016, 1960.23130784285)

(-42.42309550407768, -883.87923915983)

(-83.25234889105865, -1741.29638350823)

(-89.53552408547027, -1873.24326990261)

(0.32987818149342163, -23.1518056066285)

(-54.986801320144444, -1147.71837690488)

(-95.81870061077038, -2005.19015696243)

(72.26007255975777, -1512.42538843195)

(64.41018779479862, 1359.61018298894)

(-1.5803366500486136, -25.9915061941676)

(22.002315791306742, -456.931400132763)

(48.69492894481069, 1029.58853015078)

(50.27042729321739, -1074.62705450104)

(6.320951749773726, -151.344392841563)

(-15.72425118836271, 335.038327796469)

(-20.420944888788178, -421.827693538391)

(-58.119670104785, -1213.50884892645)

(100.53344458192505, -2130.17629998341)

(43.98794360770294, -942.687531114567)

(-39.27021391480026, -817.668224440218)

(-73.83406769697959, -1543.51210727491)

(-37.70579235296464, 772.751499265023)

(-97.39194926584895, 2050.20387633462)

(86.39393524035363, 1821.26982608146)

(51.84563206574991, 1095.7536129686)

(87.96742703049442, -1866.28622437373)

(-67.5515029564298, -1411.57793922504)

(58.12781245428362, 1227.67989889822)

(1.7879674024229206, 44.6402996273095)

(67.54441743747374, 1425.42917078852)

(-31.423954563488316, 640.818760575166)

(-0.5891493456986355, -9.97573676148234)

(56.55306605620269, -1206.56820660964)

(37.705691896778276, -810.750444264482)

(-59.694475208475794, 1258.53972539218)

(-72.26010903604264, 1522.42577145744)

(-23.582927640134553, -488.231172284164)

(26.72157150588405, 568.144100965784)

(-22.002708923893866, 466.935530874201)

(59.69442176135469, -1248.53916414481)

(28.283054743315944, -588.852592144067)

(-12.58668321311524, 245.107210915045)

(42.41177932910629, 897.641656545856)

(7.912927349201056, 173.146061235533)

(73.82758788540889, 1557.37605480965)

(45.56372661418715, 963.832966172958)

(-80.11673014931932, -1675.4482789349)

(80.11076065453241, 1689.32293999138)

(-36.141943178546256, -751.974043111704)

(-43.98801742410533, 904.68830630049)

(-65.97725684166733, 1390.48237792393)

(-17.307486629777394, -356.443325827242)

(-28.283292738597506, 598.855092138194)

(20.443828789940113, 436.308922918765)

(89.54082131150487, 1887.35453537607)

(-75.40155183006765, 1564.39764356479)

(-9.45230877575799, 203.209779041118)

(-102.10187822045306, -2137.13704456445)

(70.69270638103765, 1491.54340459963)

(81.68445884528053, -1734.34161280238)

(-14.138029306902906, -289.880936956837)

(-29.861654583540886, -620.086573552288)

(23.562443096249623, 501.801092039431)

(34.564672675447234, -720.783020973452)

(29.845524682224376, 633.747931628655)

(-50.27048381479426, 1036.62764804426)

(65.9772130881693, -1380.48191847695)

(92.67711127470137, 1953.21671289581)

(-81.68448025443287, 1696.34183760805)

(-87.96744549075494, 1828.28641821358)

(-45.55335673998194, -949.615094649834)

(-53.411789209085235, 1126.59807719719)

(78.5429839043088, -1644.36940311819)

(-3.22844409727052, 71.8971567448386)

(94.25042407433291, -1998.23113898518)

(12.58578346408958, -283.097746629252)

(-6.324493231638353, 113.381841973545)

(14.170774030719816, 304.570203773481)

(15.723482018270955, -325.030240589651)

(-61.269066135370764, -1279.64639433796)

(36.12864201402404, 765.694789091334)

(-64.40283520866485, -1345.45573027554)


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=−51.8365099303089x_{1} = -51.8365099303089
x2=−7.85556421545038x_{2} = -7.85556421545038
x3=−86.399468922026x_{3} = -86.399468922026
x4=−42.4230955040777x_{4} = -42.4230955040777
x5=−83.2523488910586x_{5} = -83.2523488910586
x6=−89.5355240854703x_{6} = -89.5355240854703
x7=0.329878181493422x_{7} = 0.329878181493422
x8=−54.9868013201444x_{8} = -54.9868013201444
x9=−95.8187006107704x_{9} = -95.8187006107704
x10=72.2600725597578x_{10} = 72.2600725597578
x11=−1.58033665004861x_{11} = -1.58033665004861
x12=22.0023157913067x_{12} = 22.0023157913067
x13=50.2704272932174x_{13} = 50.2704272932174
x14=6.32095174977373x_{14} = 6.32095174977373
x15=−20.4209448887882x_{15} = -20.4209448887882
x16=−58.119670104785x_{16} = -58.119670104785
x17=100.533444581925x_{17} = 100.533444581925
x18=43.9879436077029x_{18} = 43.9879436077029
x19=−39.2702139148003x_{19} = -39.2702139148003
x20=−73.8340676969796x_{20} = -73.8340676969796
x21=87.9674270304944x_{21} = 87.9674270304944
x22=−67.5515029564298x_{22} = -67.5515029564298
x23=56.5530660562027x_{23} = 56.5530660562027
x24=37.7056918967783x_{24} = 37.7056918967783
x25=−23.5829276401346x_{25} = -23.5829276401346
x26=59.6944217613547x_{26} = 59.6944217613547
x27=28.2830547433159x_{27} = 28.2830547433159
x28=−80.1167301493193x_{28} = -80.1167301493193
x29=−36.1419431785463x_{29} = -36.1419431785463
x30=−17.3074866297774x_{30} = -17.3074866297774
x31=−102.101878220453x_{31} = -102.101878220453
x32=81.6844588452805x_{32} = 81.6844588452805
x33=−14.1380293069029x_{33} = -14.1380293069029
x34=−29.8616545835409x_{34} = -29.8616545835409
x35=34.5646726754472x_{35} = 34.5646726754472
x36=65.9772130881693x_{36} = 65.9772130881693
x37=−45.5533567399819x_{37} = -45.5533567399819
x38=78.5429839043088x_{38} = 78.5429839043088
x39=94.2504240743329x_{39} = 94.2504240743329
x40=12.5857834640896x_{40} = 12.5857834640896
x41=15.723482018271x_{41} = 15.723482018271
x42=−61.2690661353708x_{42} = -61.2690661353708
x43=−64.4028352086649x_{43} = -64.4028352086649
Puntos máximos de la función:
x43=95.8236518040196x_{43} = 95.8236518040196
x43=−94.2504401555016x_{43} = -94.2504401555016
x43=64.4101877947986x_{43} = 64.4101877947986
x43=48.6949289448107x_{43} = 48.6949289448107
x43=−15.7242511883627x_{43} = -15.7242511883627
x43=−37.7057923529646x_{43} = -37.7057923529646
x43=−97.391949265849x_{43} = -97.391949265849
x43=86.3939352403536x_{43} = 86.3939352403536
x43=51.8456320657499x_{43} = 51.8456320657499
x43=58.1278124542836x_{43} = 58.1278124542836
x43=1.78796740242292x_{43} = 1.78796740242292
x43=67.5444174374737x_{43} = 67.5444174374737
x43=−31.4239545634883x_{43} = -31.4239545634883
x43=−0.589149345698636x_{43} = -0.589149345698636
x43=−59.6944752084758x_{43} = -59.6944752084758
x43=−72.2601090360426x_{43} = -72.2601090360426
x43=26.7215715058841x_{43} = 26.7215715058841
x43=−22.0027089238939x_{43} = -22.0027089238939
x43=−12.5866832131152x_{43} = -12.5866832131152
x43=42.4117793291063x_{43} = 42.4117793291063
x43=7.91292734920106x_{43} = 7.91292734920106
x43=73.8275878854089x_{43} = 73.8275878854089
x43=45.5637266141872x_{43} = 45.5637266141872
x43=80.1107606545324x_{43} = 80.1107606545324
x43=−43.9880174241053x_{43} = -43.9880174241053
x43=−65.9772568416673x_{43} = -65.9772568416673
x43=−28.2832927385975x_{43} = -28.2832927385975
x43=20.4438287899401x_{43} = 20.4438287899401
x43=89.5408213115049x_{43} = 89.5408213115049
x43=−75.4015518300676x_{43} = -75.4015518300676
x43=−9.45230877575799x_{43} = -9.45230877575799
x43=70.6927063810377x_{43} = 70.6927063810377
x43=23.5624430962496x_{43} = 23.5624430962496
x43=29.8455246822244x_{43} = 29.8455246822244
x43=−50.2704838147943x_{43} = -50.2704838147943
x43=92.6771112747014x_{43} = 92.6771112747014
x43=−81.6844802544329x_{43} = -81.6844802544329
x43=−87.9674454907549x_{43} = -87.9674454907549
x43=−53.4117892090852x_{43} = -53.4117892090852
x43=−3.22844409727052x_{43} = -3.22844409727052
x43=−6.32449323163835x_{43} = -6.32449323163835
x43=14.1707740307198x_{43} = 14.1707740307198
x43=36.128642014024x_{43} = 36.128642014024
Decrece en los intervalos
[100.533444581925,∞)\left[100.533444581925, \infty\right)
Crece en los intervalos
(−∞,−102.101878220453]\left(-\infty, -102.101878220453\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(((−x3⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \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⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \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*cos(3*x) - (7*cos(2*x))*3*x - 7*cos(2*x) - 14*cos(x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(((−x3⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(((−x3⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)x)y = x \lim_{x \to \infty}\left(\frac{\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)}}{x}\right)
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⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)=21xcos⁡(2x)−14cos⁡(x)−7cos⁡(2x)+2cos⁡(3x)\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = 21 x \cos{\left(2 x \right)} - 14 \cos{\left(x \right)} - 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}
- No
((−x3⋅7cos⁡(2x)+2cos⁡(3x))−7cos⁡(2x))−14cos⁡(x)=−21xcos⁡(2x)+14cos⁡(x)+7cos⁡(2x)−2cos⁡(3x)\left(\left(- x 3 \cdot 7 \cos{\left(2 x \right)} + 2 \cos{\left(3 x \right)}\right) - 7 \cos{\left(2 x \right)}\right) - 14 \cos{\left(x \right)} = - 21 x \cos{\left(2 x \right)} + 14 \cos{\left(x \right)} + 7 \cos{\left(2 x \right)} - 2 \cos{\left(3 x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор