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Trazado el gráfico de la función/ 3*x*(sin(x)+cos(x))

Gráfico de la función y = 3*x*(sin(x)+cos(x))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = 3*x*(sin(x) + cos(x))
f(x)=3x(sin⁡(x)+cos⁡(x))f{\left(x \right)} = 3 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) 
f = (3*x)*(sin(x) + cos(x))
Gráfico de la función
02468-8-6-4-2-1010-100100
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:
3x(sin⁡(x)+cos⁡(x))=03 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=−π4x_{2} = - \frac{\pi}{4}
x3=3π4x_{3} = \frac{3 \pi}{4}
Solución numérica
x1=−38.484510006475x_{1} = -38.484510006475
x2=−51.0508806208341x_{2} = -51.0508806208341
x3=18.0641577581413x_{3} = 18.0641577581413
x4=−7.06858347057703x_{4} = -7.06858347057703
x5=−57.3340659280137x_{5} = -57.3340659280137
x6=30.6305283725005x_{6} = 30.6305283725005
x7=87.1791961371168x_{7} = 87.1791961371168
x8=−73.0420291959627x_{8} = -73.0420291959627
x9=−60.4756585816035x_{9} = -60.4756585816035
x10=−47.9092879672443x_{10} = -47.9092879672443
x11=96.6039740978861x_{11} = 96.6039740978861
x12=52.621676947629x_{12} = 52.621676947629
x13=68.329640215578x_{13} = 68.329640215578
x14=8.63937979737193x_{14} = 8.63937979737193
x15=55.7632696012188x_{15} = 55.7632696012188
x16=62.0464549083984x_{16} = 62.0464549083984
x17=43.1968989868597x_{17} = 43.1968989868597
x18=−91.8915851175014x_{18} = -91.8915851175014
x19=−98.174770424681x_{19} = -98.174770424681
x20=−44.7676953136546x_{20} = -44.7676953136546
x21=27.4889357189107x_{21} = 27.4889357189107
x22=71.4712328691678x_{22} = 71.4712328691678
x23=49.4800842940392x_{23} = 49.4800842940392
x24=99.7455667514759x_{24} = 99.7455667514759
x25=−3.92699081698724x_{25} = -3.92699081698724
x26=−126.449104306989x_{26} = -126.449104306989
x27=93.4623814442964x_{27} = 93.4623814442964
x28=−69.9004365423729x_{28} = -69.9004365423729
x29=−66.7588438887831x_{29} = -66.7588438887831
x30=36.9137136796801x_{30} = 36.9137136796801
x31=58.9048622548086x_{31} = 58.9048622548086
x32=−0.785398163397448x_{32} = -0.785398163397448
x33=−82.4668071567321x_{33} = -82.4668071567321
x34=−54.1924732744239x_{34} = -54.1924732744239
x35=84.037603483527x_{35} = 84.037603483527
x36=−19.6349540849362x_{36} = -19.6349540849362
x37=2.35619449019234x_{37} = 2.35619449019234
x38=80.8960108299372x_{38} = 80.8960108299372
x39=−63.6172512351933x_{39} = -63.6172512351933
x40=−22.776546738526x_{40} = -22.776546738526
x41=24.3473430653209x_{41} = 24.3473430653209
x42=−95.0331777710912x_{42} = -95.0331777710912
x43=−10.2101761241668x_{43} = -10.2101761241668
x44=−79.3252145031423x_{44} = -79.3252145031423
x45=−29.0597320457056x_{45} = -29.0597320457056
x46=−76.1836218495525x_{46} = -76.1836218495525
x47=−13.3517687777566x_{47} = -13.3517687777566
x48=−25.9181393921158x_{48} = -25.9181393921158
x49=65.1880475619882x_{49} = 65.1880475619882
x50=−16.4933614313464x_{50} = -16.4933614313464
x51=−35.3429173528852x_{51} = -35.3429173528852
x52=14.9225651045515x_{52} = 14.9225651045515
x53=33.7721210260903x_{53} = 33.7721210260903
x54=5.49778714378214x_{54} = 5.49778714378214
x55=46.3384916404494x_{55} = 46.3384916404494
x56=21.2057504117311x_{56} = 21.2057504117311
x57=−32.2013246992954x_{57} = -32.2013246992954
x58=11.7809724509617x_{58} = 11.7809724509617
x59=−85.6083998103219x_{59} = -85.6083998103219
x60=0x_{60} = 0
x61=90.3207887907066x_{61} = 90.3207887907066
x62=−41.6261026600648x_{62} = -41.6261026600648
x63=77.7544181763474x_{63} = 77.7544181763474
x64=−88.7499924639117x_{64} = -88.7499924639117
x65=74.6128255227576x_{65} = 74.6128255227576
x66=40.0553063332699x_{66} = 40.0553063332699
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 (3*x)*(sin(x) + cos(x)).
0⋅3(sin⁡(0)+cos⁡(0))0 \cdot 3 \left(\sin{\left(0 \right)} + \cos{\left(0 \right)}\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
3x(−sin⁡(x)+cos⁡(x))+3sin⁡(x)+3cos⁡(x)=03 x \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) + 3 \sin{\left(x \right)} + 3 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=16.5536975718234x_{1} = 16.5536975718234
x2=85.6200787826806x_{2} = 85.6200787826806
x3=−58.9218322634797x_{3} = -58.9218322634797
x4=1.40422360239197x_{4} = 1.40422360239197
x5=−30.6631292754598x_{5} = -30.6631292754598
x6=35.3711814271828x_{6} = 35.3711814271828
x7=−52.6406713811732x_{7} = -52.6406713811732
x8=47.9301486357051x_{8} = 47.9301486357051
x9=73.0557165239248x_{9} = 73.0557165239248
x10=76.1967450163399x_{10} = 76.1967450163399
x11=−74.6262248358581x_{11} = -74.6262248358581
x12=63.6329650666866x_{12} = 63.6329650666866
x13=−27.525250026105x_{13} = -27.525250026105
x14=88.7612581637789x_{14} = 88.7612581637789
x15=−96.6143241603692x_{15} = -96.6143241603692
x16=−71.485220862291x_{16} = -71.485220862291
x17=51.0704589102849x_{17} = 51.0704589102849
x18=−14.9891811736395x_{18} = -14.9891811736395
x19=98.1849549323352x_{19} = 98.1849549323352
x20=−5.67228968340682x_{20} = -5.67228968340682
x21=22.8203392800723x_{21} = 22.8203392800723
x22=4.1627493368126x_{22} = 4.1627493368126
x23=54.2109176513576x_{23} = 54.2109176513576
x24=32.2323394923898x_{24} = 32.2323394923898
x25=60.492188136142x_{25} = 60.492188136142
x26=−87.1906647520128x_{26} = -87.1906647520128
x27=−40.0802511015808x_{27} = -40.0802511015808
x28=−21.2527684271428x_{28} = -21.2527684271428
x29=41.6501075899818x_{29} = 41.6501075899818
x30=−8.75313144558265x_{30} = -8.75313144558265
x31=79.3378181652015x_{31} = 79.3378181652015
x32=−68.3442709758693x_{32} = -68.3442709758693
x33=−80.9083698613449x_{33} = -80.9083698613449
x34=−36.940777426275x_{34} = -36.940777426275
x35=13.4261132241755x_{35} = 13.4261132241755
x36=−43.2200322784808x_{36} = -43.2200322784808
x37=−24.3883233381018x_{37} = -24.3883233381018
x38=82.4789308711661x_{38} = 82.4789308711661
x39=25.9566461271548x_{39} = 25.9566461271548
x40=44.7900180082647x_{40} = 44.7900180082647
x41=19.6857087307627x_{41} = 19.6857087307627
x42=−11.8650548496173x_{42} = -11.8650548496173
x43=95.0436988589063x_{43} = 95.0436988589063
x44=7.20646720968486x_{44} = 7.20646720968486
x45=−65.2033829872561x_{45} = -65.2033829872561
x46=91.9024657889622x_{46} = 91.9024657889622
x47=−49.5002834509857x_{47} = -49.5002834509857
x48=−84.0495006728084x_{48} = -84.0495006728084
x49=−90.3318586299385x_{49} = -90.3318586299385
x50=57.3515004967328x_{50} = 57.3515004967328
x51=−99.7555909164973x_{51} = -99.7555909164973
x52=−62.0625662865258x_{52} = -62.0625662865258
x53=−33.8016967133026x_{53} = -33.8016967133026
x54=−18.119291621421x_{54} = -18.119291621421
x55=10.3068958192079x_{55} = 10.3068958192079
x56=66.7738186988218x_{56} = 66.7738186988218
x57=−55.781194869671x_{57} = -55.781194869671
x58=−77.7672763467182x_{58} = -77.7672763467182
x59=29.0940897621002x_{59} = 29.0940897621002
x60=101.326231870557x_{60} = 101.326231870557
x61=38.5104711360153x_{61} = 38.5104711360153
x62=−46.3600585879736x_{62} = -46.3600585879736
x63=69.9147387028857x_{63} = 69.9147387028857
x64=−0.402628174188112x_{64} = -0.402628174188112
x65=−93.4730793036062x_{65} = -93.4730793036062
x66=−2.70973013143952x_{66} = -2.70973013143952
Signos de extremos en los puntos:
(16.553697571823395, -70.1035926897306)

(85.6200787826806, -363.230456444119)

(-58.92183226347968, 249.948168415584)

(1.4042236023919696, 4.85283796609462)

(-30.66312927545978, -130.023513524698)

(35.371181427182776, -150.007276275512)

(-52.64067138117324, 223.295166977936)

(47.93014863570506, -203.306154604854)

(73.05571652392481, -309.920122410268)

(76.19674501633988, 323.247574189303)

(-74.62622483585812, -316.583835705634)

(63.63296506668664, 269.938475993109)

(-27.52525002610497, 116.702753732209)

(88.76125816377889, 376.558228431005)

(-96.61432416036915, 409.877907823205)

(-71.485220862291, 303.256435962818)

(51.070458910284906, 216.632081692015)

(-14.989181173639471, 63.4526571637)

(98.18495493233517, -416.541880989337)

(-5.672289683406819, -23.7000051457511)

(22.820339280072254, -96.7256761441122)

(4.162749336812597, -17.172499957657)

(54.21091765135759, -229.958324027762)

(32.23233949238981, 136.684469028892)

(60.492188136142026, -256.611558150825)

(-87.19066475201284, -369.894334541072)

(-40.08025110158081, 169.993201948217)

(-21.25276842714282, 90.0682116392527)

(41.650107589981786, -176.655531164169)

(-8.753131445582648, 36.8963885617201)

(79.33781816520154, -336.575120739862)

(-68.34427097586932, -289.929151012458)

(-80.90836986134488, -343.238926106065)

(-36.94077742627499, -156.669051967046)

(13.426113224175548, 56.8048290036502)

(-43.22003227848084, -183.318005263312)

(-24.388323338101774, -103.384021426717)

(82.47893087116606, 349.902751237113)

(25.956646127154848, 110.043088305049)

(44.790018008264745, 189.980609024213)

(19.685708730762727, 83.4118375112009)

(-11.865054849617264, -50.1613241073371)

(95.04369885890632, 403.213946264871)

(7.206467209684859, 30.2842715782654)

(-65.2033829872561, 276.601997437678)

(91.90246578896223, -389.886060351692)

(-49.50028345098569, -209.969074994893)

(-84.04950067280843, 356.566595025288)

(-90.33185862993847, 383.222137290318)

(57.35150049673278, 243.284829853574)

(-99.75559091649727, -423.205865215076)

(-62.06256628652584, -263.274995176569)

(-33.801696713302576, 143.345737128658)

(-18.11929162142097, -76.7568353925031)

(10.306895819207908, -43.5240816776818)

(66.77381869882177, -283.265556644862)

(-55.78119486967102, -236.621546784402)

(-77.76727634671825, 329.911336335666)

(29.094089762100186, -123.362921104039)

(101.32623187055665, 429.869859986209)

(38.51047113601533, 163.331035314911)

(-46.360058587973604, 196.643329284637)

(69.91473870288569, 296.592778171943)

(-0.4026281741881116, -0.638000560322241)

(-93.47307930360616, -396.549996899364)

(-2.7097301314395232, 10.7854097749431)


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=16.5536975718234x_{1} = 16.5536975718234
x2=85.6200787826806x_{2} = 85.6200787826806
x3=−30.6631292754598x_{3} = -30.6631292754598
x4=35.3711814271828x_{4} = 35.3711814271828
x5=47.9301486357051x_{5} = 47.9301486357051
x6=73.0557165239248x_{6} = 73.0557165239248
x7=−74.6262248358581x_{7} = -74.6262248358581
x8=98.1849549323352x_{8} = 98.1849549323352
x9=−5.67228968340682x_{9} = -5.67228968340682
x10=22.8203392800723x_{10} = 22.8203392800723
x11=4.1627493368126x_{11} = 4.1627493368126
x12=54.2109176513576x_{12} = 54.2109176513576
x13=60.492188136142x_{13} = 60.492188136142
x14=−87.1906647520128x_{14} = -87.1906647520128
x15=41.6501075899818x_{15} = 41.6501075899818
x16=79.3378181652015x_{16} = 79.3378181652015
x17=−68.3442709758693x_{17} = -68.3442709758693
x18=−80.9083698613449x_{18} = -80.9083698613449
x19=−36.940777426275x_{19} = -36.940777426275
x20=−43.2200322784808x_{20} = -43.2200322784808
x21=−24.3883233381018x_{21} = -24.3883233381018
x22=−11.8650548496173x_{22} = -11.8650548496173
x23=91.9024657889622x_{23} = 91.9024657889622
x24=−49.5002834509857x_{24} = -49.5002834509857
x25=−99.7555909164973x_{25} = -99.7555909164973
x26=−62.0625662865258x_{26} = -62.0625662865258
x27=−18.119291621421x_{27} = -18.119291621421
x28=10.3068958192079x_{28} = 10.3068958192079
x29=66.7738186988218x_{29} = 66.7738186988218
x30=−55.781194869671x_{30} = -55.781194869671
x31=29.0940897621002x_{31} = 29.0940897621002
x32=−0.402628174188112x_{32} = -0.402628174188112
x33=−93.4730793036062x_{33} = -93.4730793036062
Puntos máximos de la función:
x33=−58.9218322634797x_{33} = -58.9218322634797
x33=1.40422360239197x_{33} = 1.40422360239197
x33=−52.6406713811732x_{33} = -52.6406713811732
x33=76.1967450163399x_{33} = 76.1967450163399
x33=63.6329650666866x_{33} = 63.6329650666866
x33=−27.525250026105x_{33} = -27.525250026105
x33=88.7612581637789x_{33} = 88.7612581637789
x33=−96.6143241603692x_{33} = -96.6143241603692
x33=−71.485220862291x_{33} = -71.485220862291
x33=51.0704589102849x_{33} = 51.0704589102849
x33=−14.9891811736395x_{33} = -14.9891811736395
x33=32.2323394923898x_{33} = 32.2323394923898
x33=−40.0802511015808x_{33} = -40.0802511015808
x33=−21.2527684271428x_{33} = -21.2527684271428
x33=−8.75313144558265x_{33} = -8.75313144558265
x33=13.4261132241755x_{33} = 13.4261132241755
x33=82.4789308711661x_{33} = 82.4789308711661
x33=25.9566461271548x_{33} = 25.9566461271548
x33=44.7900180082647x_{33} = 44.7900180082647
x33=19.6857087307627x_{33} = 19.6857087307627
x33=95.0436988589063x_{33} = 95.0436988589063
x33=7.20646720968486x_{33} = 7.20646720968486
x33=−65.2033829872561x_{33} = -65.2033829872561
x33=−84.0495006728084x_{33} = -84.0495006728084
x33=−90.3318586299385x_{33} = -90.3318586299385
x33=57.3515004967328x_{33} = 57.3515004967328
x33=−33.8016967133026x_{33} = -33.8016967133026
x33=−77.7672763467182x_{33} = -77.7672763467182
x33=101.326231870557x_{33} = 101.326231870557
x33=38.5104711360153x_{33} = 38.5104711360153
x33=−46.3600585879736x_{33} = -46.3600585879736
x33=69.9147387028857x_{33} = 69.9147387028857
x33=−2.70973013143952x_{33} = -2.70973013143952
Decrece en los intervalos
[98.1849549323352,∞)\left[98.1849549323352, \infty\right)
Crece en los intervalos
(−∞,−99.7555909164973]\left(-\infty, -99.7555909164973\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
3(−x(sin⁡(x)+cos⁡(x))−2sin⁡(x)+2cos⁡(x))=03 \left(- x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−51.090007240869x_{1} = -51.090007240869
x2=68.3588892226045x_{2} = 68.3588892226045
x3=55.7990971376439x_{3} = 55.7990971376439
x4=−91.9133413109646x_{4} = -91.9133413109646
x5=40.1051339820311x_{5} = 40.1051339820311
x6=65.2187040039755x_{6} = 65.2187040039755
x7=−22.8637991711874x_{7} = -22.8637991711874
x8=−60.5086996509106x_{8} = -60.5086996509106
x9=−13.4988593824004x_{9} = -13.4988593824004
x10=46.3815855056281x_{10} = 46.3815855056281
x11=71.4991979186838x_{11} = 71.4991979186838
x12=93.483772268578x_{12} = 93.483772268578
x13=−47.9509730740431x_{13} = -47.9509730740431
x14=−113.900291105942x_{14} = -113.900291105942
x15=0.527514155354677x_{15} = 0.527514155354677
x16=62.0786609585108x_{16} = 62.0786609585108
x17=11.9468425812542x_{17} = 11.9468425812542
x18=96.6246697903533x_{18} = 96.6246697903533
x19=−57.3689139007406x_{19} = -57.3689139007406
x20=−63.6486633974297x_{20} = -63.6486633974297
x21=−29.1282862299341x_{21} = -29.1282862299341
x22=−101.336096820168x_{22} = -101.336096820168
x23=−32.2632355402841x_{23} = -32.2632355402841
x24=−16.6131712618349x_{24} = -16.6131712618349
x25=99.7656110545409x_{25} = 99.7656110545409
x26=−88.7725181482034x_{26} = -88.7725181482034
x27=−38.5363625190795x_{27} = -38.5363625190795
x28=−95.0542152909285x_{28} = -95.0542152909285
x29=−4.35730345610807x_{29} = -4.35730345610807
x30=77.7801260208492x_{30} = 77.7801260208492
x31=8.8613594616186x_{31} = 8.8613594616186
x32=−82.491047463018x_{32} = -82.491047463018
x33=52.659638453805x_{33} = 52.659638453805
x34=−76.209859151006x_{34} = -76.209859151006
x35=80.9207213475526x_{35} = 80.9207213475526
x36=2.95170991909117x_{36} = 2.95170991909117
x37=21.2993753559105x_{37} = 21.2993753559105
x38=87.2021273371782x_{38} = 87.2021273371782
x39=24.4290306880013x_{39} = 24.4290306880013
x40=36.9677621805666x_{40} = 36.9677621805666
x41=−79.3504138253443x_{41} = -79.3504138253443
x42=58.9387827530098x_{42} = 58.9387827530098
x43=18.1737654426084x_{43} = 18.1737654426084
x44=5.8283469489335x_{44} = 5.8283469489335
x45=−66.7887800922994x_{45} = -66.7887800922994
x46=84.0613911311506x_{46} = 84.0613911311506
x47=−44.8122963232296x_{47} = -44.8122963232296
x48=−25.9949262091953x_{48} = -25.9949262091953
x49=−85.6317513875535x_{49} = -85.6317513875535
x50=33.8311693836712x_{50} = 33.8311693836712
x51=15.0546411237447x_{51} = 15.0546411237447
x52=74.639614534939x_{52} = 74.639614534939
x53=−1.66264431270849x_{53} = -1.66264431270849
x54=−69.9290291736194x_{54} = -69.9290291736194
x55=−19.7359472423532x_{55} = -19.7359472423532
x56=−7.33478526965412x_{56} = -7.33478526965412
x57=−54.2293369735691x_{57} = -54.2293369735691
x58=49.5204497117403x_{58} = 49.5204497117403
x59=−73.0693936049058x_{59} = -73.0693936049058
x60=43.2431161875062x_{60} = 43.2431161875062
x61=27.5613740726847x_{61} = 27.5613740726847
x62=30.6955923389483x_{62} = 30.6955923389483
x63=−35.3993555564526x_{63} = -35.3993555564526
x64=−10.400161531748x_{64} = -10.400161531748
x65=90.3429230465513x_{65} = 90.3429230465513
x66=−41.6740573539444x_{66} = -41.6740573539444
x67=−98.1951352167328x_{67} = -98.1951352167328

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
[96.6246697903533,∞)\left[96.6246697903533, \infty\right)
Convexa en los intervalos
(−∞,−113.900291105942]\left(-\infty, -113.900291105942\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(3x(sin⁡(x)+cos⁡(x)))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(3 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\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→∞(3x(sin⁡(x)+cos⁡(x)))=⟨−∞,∞⟩\lim_{x \to \infty}\left(3 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\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 (3*x)*(sin(x) + cos(x)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(3sin⁡(x)+3cos⁡(x))=⟨−6,6⟩\lim_{x \to -\infty}\left(3 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) = \left\langle -6, 6\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−6,6⟩xy = \left\langle -6, 6\right\rangle x
lim⁡x→∞(3sin⁡(x)+3cos⁡(x))=⟨−6,6⟩\lim_{x \to \infty}\left(3 \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right) = \left\langle -6, 6\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−6,6⟩xy = \left\langle -6, 6\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:
3x(sin⁡(x)+cos⁡(x))=−3x(−sin⁡(x)+cos⁡(x))3 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = - 3 x \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)
- No
3x(sin⁡(x)+cos⁡(x))=3x(−sin⁡(x)+cos⁡(x))3 x \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 3 x \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор