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Trazado el gráfico de la función/ 4*sin(x)/125+22*cos(x)/125+3*x*sin(x)/25+4*x*cos(x)/25

Gráfico de la función y = 4*sin(x)/125+22*cos(x)/125+3*x*sin(x)/25+4*x*cos(x)/25

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       4*sin(x)   22*cos(x)   3*x*sin(x)   4*x*cos(x)
f(x) = -------- + --------- + ---------- + ----------
         125         125          25           25
f(x)=4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))f{\left(x \right)} = \frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right) 
f = ((4*x)*cos(x))/25 + ((3*x)*sin(x))/25 + (4*sin(x))/125 + (22*cos(x))/125
Gráfico de la función
02468-8-6-4-2-10105-5
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:
4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))=0\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right) = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=30.4758425915264x_{1} = 30.4758425915264
x2=−60.6108679881238x_{2} = -60.6108679881238
x3=−76.3202223591116x_{3} = -76.3202223591116
x4=−3.94227243940298x_{4} = -3.94227243940298
x5=−79.4620265558736x_{5} = -79.4620265558736
x6=58.7562489614793x_{6} = 58.7562489614793
x7=8.45428641607242x_{7} = 8.45428641607242
x8=−16.6099633809327x_{8} = -16.6099633809327
x9=68.1819446071759x_{9} = 68.1819446071759
x10=17.9008745905993x_{10} = 17.9008745905993
x11=55.6142822623642x_{11} = 55.6142822623642
x12=−88.8873486025157x_{12} = -88.8873486025157
x13=36.7611677314396x_{13} = 36.7611677314396
x14=−73.1783997961427x_{14} = -73.1783997961427
x15=87.0327450037952x_{15} = 87.0327450037952
x16=−35.4732786579961x_{16} = -35.4732786579961
x17=−29.1875393433459x_{17} = -29.1875393433459
x18=39.9035824501583x_{18} = 39.9035824501583
x19=33.6186028724351x_{19} = 33.6186028724351
x20=−19.7557524970779x_{20} = -19.7557524970779
x21=65.0400752549291x_{21} = 65.0400752549291
x22=83.8909834110804x_{22} = 83.8909834110804
x23=200.132643897524x_{23} = 200.132643897524
x24=52.4722714374577x_{24} = 52.4722714374577
x25=−63.7527944079589x_{25} = -63.7527944079589
x26=77.6074196079843x_{26} = 77.6074196079843
x27=−92.0290976341989x_{27} = -92.0290976341989
x28=93.3162343514881x_{28} = 93.3162343514881
x29=11.6068462959441x_{29} = 11.6068462959441
x30=96.4579642927467x_{30} = 96.4579642927467
x31=−41.7582339790618x_{31} = -41.7582339790618
x32=−7.14754727490131x_{32} = -7.14754727490131
x33=14.7549584431751x_{33} = 14.7549584431751
x34=−98.3125654668466x_{34} = -98.3125654668466
x35=−85.7455880030187x_{35} = -85.7455880030187
x36=−32.3305363197007x_{36} = -32.3305363197007
x37=74.4656140063042x_{37} = 74.4656140063042
x38=−13.4620859630903x_{38} = -13.4620859630903
x39=−44.9005224296412x_{39} = -44.9005224296412
x40=99.5996856417317x_{40} = 99.5996856417317
x41=−38.615829874639x_{41} = -38.615829874639
x42=71.3237898511611x_{42} = 71.3237898511611
x43=49.3302081879665x_{43} = 49.3302081879665
x44=43.0458793211947x_{44} = 43.0458793211947
x45=80.7492088008024x_{45} = 80.7492088008024
x46=−26.0441925440808x_{46} = -26.0441925440808
x47=−51.1848389461458x_{47} = -51.1848389461458
x48=−95.1708362534788x_{48} = -95.1708362534788
x49=−54.3268975896689x_{49} = -54.3268975896689
x50=−66.8946890938037x_{50} = -66.8946890938037
x51=5.29030613891898x_{51} = 5.29030613891898
x52=−57.4689045550682x_{52} = -57.4689045550682
x53=24.1894406167105x_{53} = 24.1894406167105
x54=−10.3100371317184x_{54} = -10.3100371317184
x55=21.0455450335874x_{55} = 21.0455450335874
x56=61.898178169648x_{56} = 61.898178169648
x57=2.07610697819715x_{57} = 2.07610697819715
x58=−48.0427183108668x_{58} = -48.0427183108668
x59=90.1744949277142x_{59} = 90.1744949277142
x60=27.3328213540808x_{60} = 27.3328213540808
x61=−70.0365563664099x_{61} = -70.0365563664099
x62=−82.6038145027753x_{62} = -82.6038145027753
x63=46.1880819945438x_{63} = 46.1880819945438
x64=−22.9003465053475x_{64} = -22.9003465053475
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 (4*sin(x))/125 + (22*cos(x))/125 + ((3*x)*sin(x))/25 + ((4*x)*cos(x))/25.
0⋅4cos⁡(0)25+(0⋅3sin⁡(0)25+(4sin⁡(0)125+22cos⁡(0)125))\frac{0 \cdot 4 \cos{\left(0 \right)}}{25} + \left(\frac{0 \cdot 3 \sin{\left(0 \right)}}{25} + \left(\frac{4 \sin{\left(0 \right)}}{125} + \frac{22 \cos{\left(0 \right)}}{125}\right)\right)
Resultado:
f(0)=22125f{\left(0 \right)} = \frac{22}{125}
Punto:
(0, 22/125)
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
−4xsin⁡(x)25+3xcos⁡(x)25−7sin⁡(x)125+24cos⁡(x)125=0- \frac{4 x \sin{\left(x \right)}}{25} + \frac{3 x \cos{\left(x \right)}}{25} - \frac{7 \sin{\left(x \right)}}{125} + \frac{24 \cos{\left(x \right)}}{125} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=60.3435741810726x_{1} = 60.3435741810726
x2=−55.916052346554x_{2} = -55.916052346554
x3=−71.6216017124802x_{3} = -71.6216017124802
x4=−77.9040967615667x_{4} = -77.9040967615667
x5=−43.3528952053232x_{5} = -43.3528952053232
x6=−68.4804022334892x_{6} = -68.4804022334892
x7=0.9702797191989x_{7} = 0.9702797191989
x8=7.00342474595104x_{8} = 7.00342474595104
x9=57.2025128838723x_{9} = 57.2025128838723
x10=−59.0570581265178x_{10} = -59.0570581265178
x11=−2.79081735122193x_{11} = -2.79081735122193
x12=−24.5145356614537x_{12} = -24.5145356614537
x13=−27.6531727847406x_{13} = -27.6531727847406
x14=41.4983895913798x_{14} = 41.4983895913798
x15=54.061512412669x_{15} = 54.061512412669
x16=−15.1063769354718x_{16} = -15.1063769354718
x17=44.6390020070488x_{17} = 44.6390020070488
x18=88.6148056066909x_{18} = 88.6148056066909
x19=−33.9321254135618x_{19} = -33.9321254135618
x20=94.8975503872968x_{20} = 94.8975503872968
x21=−52.7751174749286x_{21} = -52.7751174749286
x22=82.3321274030778x_{22} = 82.3321274030778
x23=−30.7924278084605x_{23} = -30.7924278084605
x24=38.3579343180476x_{24} = 38.3579343180476
x25=−37.072150842054x_{25} = -37.072150842054
x26=47.7797411121363x_{26} = 47.7797411121363
x27=−84.1866958063905x_{27} = -84.1866958063905
x28=19.5225722782886x_{28} = 19.5225722782886
x29=3.91175320615241x_{29} = 3.91175320615241
x30=79.1908181687649x_{30} = 79.1908181687649
x31=10.1231531192315x_{31} = 10.1231531192315
x32=−65.3392410183755x_{32} = -65.3392410183755
x33=66.6258452641675x_{33} = 66.6258452641675
x34=35.2176772443726x_{34} = 35.2176772443726
x35=−8.85562172330338x_{35} = -8.85562172330338
x36=76.0495321008973x_{36} = 76.0495321008973
x37=72.9082721605229x_{37} = 72.9082721605229
x38=−18.2404440436623x_{38} = -18.2404440436623
x39=−93.610743177676x_{39} = -93.610743177676
x40=−11.9765020817174x_{40} = -11.9765020817174
x41=25.7987959247262x_{41} = 25.7987959247262
x42=−87.3280272500001x_{42} = -87.3280272500001
x43=−81.0453848107283x_{43} = -81.0453848107283
x44=91.7561705220584x_{44} = 91.7561705220584
x45=−90.4693769930113x_{45} = -90.4693769930113
x46=−0.847798665221398x_{46} = -0.847798665221398
x47=−5.76006544608496x_{47} = -5.76006544608496
x48=50.9205838429843x_{48} = 50.9205838429843
x49=85.4734572738959x_{49} = 85.4734572738959
x50=98.0389437772169x_{50} = 98.0389437772169
x51=63.4846873920035x_{51} = 63.4846873920035
x52=69.7670418356969x_{52} = 69.7670418356969
x53=−62.1981239375045x_{53} = -62.1981239375045
x54=22.6602193184132x_{54} = 22.6602193184132
x55=101.180349442191x_{55} = 101.180349442191
x56=−49.6342671849204x_{56} = -49.6342671849204
x57=−21.3767982617586x_{57} = -21.3767982617586
x58=16.3863616069185x_{58} = 16.3863616069185
x59=−74.7628345817544x_{59} = -74.7628345817544
x60=−99.8935186185057x_{60} = -99.8935186185057
x61=−96.7521241894601x_{61} = -96.7521241894601
x62=−46.4935189054968x_{62} = -46.4935189054968
x63=28.9380084537933x_{63} = 28.9380084537933
x64=−40.2124258371891x_{64} = -40.2124258371891
x65=32.0776750847295x_{65} = 32.0776750847295
x66=13.2525427048988x_{66} = 13.2525427048988
Signos de extremos en los puntos:
(60.3435741810726, -12.2273411008631)

(-55.91605234655403, -11.0216865220558)

(-71.62160171248024, 14.1631343153847)

(-77.90409676156675, 15.4197299560894)

(-43.35289520532315, -8.50860526556136)

(-68.48040223348916, -13.5348393785407)

(0.9702797191989003, 0.309640261715011)

(7.00342474595104, 1.54995890251157)

(57.202512883872316, 11.5990544577366)

(-59.05705812651784, 11.6499698327822)

(-2.7908173512219285, 0.358140889352609)

(-24.51453566145369, -4.73936637691713)

(-27.65317278474062, 5.36750738276238)

(41.4983895913798, -8.45769226963505)

(54.06151241266902, -10.9707714656737)

(-15.106376935471832, 2.85541014104577)

(44.639002007048845, 9.08595196493008)

(88.61480560669094, 17.8820217052865)

(-33.932125413561785, 6.62389028369178)

(94.8975503872968, 19.1386323329934)

(-52.77511747492858, 10.393407467772)

(82.33212740307785, 16.6254150728938)

(-30.79242780846053, -5.99568553507477)

(38.357934318047576, 7.82944201021356)

(-37.07215084205401, -7.25211472677849)

(47.77974111213629, -9.71421926670766)

(-84.18669580639047, 16.6763318380014)

(19.522572278288568, 4.06038330655216)

(3.911753206152409, -0.924696172484364)

(79.19081816876492, -15.9971135490977)

(10.12315311923153, -2.17695459030595)

(-65.33924101837547, 12.9065467382233)

(66.62584526416754, -13.4839232996446)

(35.217677244372574, -7.201203653579)

(-8.855621723303384, 1.60073181180591)

(76.04953210089727, 15.3688134155889)

(72.9082721605229, -14.7405148500969)

(-18.2404440436623, -3.48327587534032)

(-93.61074317767604, -18.5612435908632)

(-11.976502081717385, -2.22779776890921)

(25.798795924726196, 5.31660212249623)

(-87.32802725000013, -17.3046346946212)

(-81.0453848107283, -16.0480302085025)

(91.75617052205843, -18.5103265705714)

(-90.46937699301132, 17.9329386494078)

(-0.8477986652213977, 0.0789881794087364)

(-5.760065446084964, -0.975226558431923)

(50.920583842984314, 10.3424927896896)

(85.47345727389586, -17.2537178351279)

(98.03894377721686, -19.7669389070187)

(63.48468739200345, 12.8556308599678)

(69.76704183569687, 14.1122180619904)

(-62.19812393750447, -12.2782567468409)

(22.66021931841318, -4.68846475568188)

(101.18034944219134, 20.3952462176515)

(-49.63426718492042, -9.76513349099207)

(-21.376798261758633, 4.11127949053971)

(16.38636160691848, -3.43238833820508)

(-74.76283458175439, -14.7914312561985)

(-99.89351861850574, -19.8178560584706)

(-96.75212418946008, 19.1895494220886)

(-46.49351890549679, 9.13686563841126)

(28.938008453793262, -5.94477772069325)

(-40.212425837189116, 7.88035415974942)

(32.07767508472954, 6.57298060824512)

(13.252542704898833, 2.80453758171173)


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=60.3435741810726x_{1} = 60.3435741810726
x2=−55.916052346554x_{2} = -55.916052346554
x3=−43.3528952053232x_{3} = -43.3528952053232
x4=−68.4804022334892x_{4} = -68.4804022334892
x5=−24.5145356614537x_{5} = -24.5145356614537
x6=41.4983895913798x_{6} = 41.4983895913798
x7=54.061512412669x_{7} = 54.061512412669
x8=−30.7924278084605x_{8} = -30.7924278084605
x9=−37.072150842054x_{9} = -37.072150842054
x10=47.7797411121363x_{10} = 47.7797411121363
x11=3.91175320615241x_{11} = 3.91175320615241
x12=79.1908181687649x_{12} = 79.1908181687649
x13=10.1231531192315x_{13} = 10.1231531192315
x14=66.6258452641675x_{14} = 66.6258452641675
x15=35.2176772443726x_{15} = 35.2176772443726
x16=72.9082721605229x_{16} = 72.9082721605229
x17=−18.2404440436623x_{17} = -18.2404440436623
x18=−93.610743177676x_{18} = -93.610743177676
x19=−11.9765020817174x_{19} = -11.9765020817174
x20=−87.3280272500001x_{20} = -87.3280272500001
x21=−81.0453848107283x_{21} = -81.0453848107283
x22=91.7561705220584x_{22} = 91.7561705220584
x23=−0.847798665221398x_{23} = -0.847798665221398
x24=−5.76006544608496x_{24} = -5.76006544608496
x25=85.4734572738959x_{25} = 85.4734572738959
x26=98.0389437772169x_{26} = 98.0389437772169
x27=−62.1981239375045x_{27} = -62.1981239375045
x28=22.6602193184132x_{28} = 22.6602193184132
x29=−49.6342671849204x_{29} = -49.6342671849204
x30=16.3863616069185x_{30} = 16.3863616069185
x31=−74.7628345817544x_{31} = -74.7628345817544
x32=−99.8935186185057x_{32} = -99.8935186185057
x33=28.9380084537933x_{33} = 28.9380084537933
Puntos máximos de la función:
x33=−71.6216017124802x_{33} = -71.6216017124802
x33=−77.9040967615667x_{33} = -77.9040967615667
x33=0.9702797191989x_{33} = 0.9702797191989
x33=7.00342474595104x_{33} = 7.00342474595104
x33=57.2025128838723x_{33} = 57.2025128838723
x33=−59.0570581265178x_{33} = -59.0570581265178
x33=−2.79081735122193x_{33} = -2.79081735122193
x33=−27.6531727847406x_{33} = -27.6531727847406
x33=−15.1063769354718x_{33} = -15.1063769354718
x33=44.6390020070488x_{33} = 44.6390020070488
x33=88.6148056066909x_{33} = 88.6148056066909
x33=−33.9321254135618x_{33} = -33.9321254135618
x33=94.8975503872968x_{33} = 94.8975503872968
x33=−52.7751174749286x_{33} = -52.7751174749286
x33=82.3321274030778x_{33} = 82.3321274030778
x33=38.3579343180476x_{33} = 38.3579343180476
x33=−84.1866958063905x_{33} = -84.1866958063905
x33=19.5225722782886x_{33} = 19.5225722782886
x33=−65.3392410183755x_{33} = -65.3392410183755
x33=−8.85562172330338x_{33} = -8.85562172330338
x33=76.0495321008973x_{33} = 76.0495321008973
x33=25.7987959247262x_{33} = 25.7987959247262
x33=−90.4693769930113x_{33} = -90.4693769930113
x33=50.9205838429843x_{33} = 50.9205838429843
x33=63.4846873920035x_{33} = 63.4846873920035
x33=69.7670418356969x_{33} = 69.7670418356969
x33=101.180349442191x_{33} = 101.180349442191
x33=−21.3767982617586x_{33} = -21.3767982617586
x33=−96.7521241894601x_{33} = -96.7521241894601
x33=−46.4935189054968x_{33} = -46.4935189054968
x33=−40.2124258371891x_{33} = -40.2124258371891
x33=32.0776750847295x_{33} = 32.0776750847295
x33=13.2525427048988x_{33} = 13.2525427048988
Decrece en los intervalos
[98.0389437772169,∞)\left[98.0389437772169, \infty\right)
Crece en los intervalos
(−∞,−99.8935186185057]\left(-\infty, -99.8935186185057\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
−15xsin⁡(x)−20xcos⁡(x)−44sin⁡(x)+8cos⁡(x)125=0\frac{- 15 x \sin{\left(x \right)} - 20 x \cos{\left(x \right)} - 44 \sin{\left(x \right)} + 8 \cos{\left(x \right)}}{125} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=105.90184893444x_{1} = 105.90184893444
x2=−38.6686332727791x_{2} = -38.6686332727791
x3=58.7898089792849x_{3} = 58.7898089792849
x4=−19.8605976077734x_{4} = -19.8605976077734
x5=−48.0850094788524x_{5} = -48.0850094788524
x6=−51.2244976413707x_{6} = -51.2244976413707
x7=−95.1920237873094x_{7} = -95.1920237873094
x8=−82.6282548682865x_{8} = -82.6282548682865
x9=−26.1231358967381x_{9} = -26.1231358967381
x10=65.0704358399357x_{10} = 65.0704358399357
x11=71.3515077394191x_{11} = 71.3515077394191
x12=55.6497087732532x_{12} = 55.6497087732532
x13=−10.5152967734811x_{13} = -10.5152967734811
x14=−7.44670685338892x_{14} = -7.44670685338892
x15=−44.9458200330202x_{15} = -44.9458200330202
x16=−76.3466946927892x_{16} = -76.3466946927892
x17=74.4921758182545x_{17} = 74.4921758182545
x18=0.121134236609965x_{18} = 0.121134236609965
x19=−98.3330707001031x_{19} = -98.3330707001031
x20=−29.2577935836348x_{20} = -29.2577935836348
x21=46.2306018724022x_{21} = 46.2306018724022
x22=−63.7845458844388x_{22} = -63.7845458844388
x23=24.2691829424395x_{23} = 24.2691829424395
x24=49.3700679595301x_{24} = 49.3700679595301
x25=33.6765989873912x_{25} = 33.6765989873912
x26=39.952650374408x_{26} = 39.952650374408
x27=21.1366616902466x_{27} = 21.1366616902466
x28=77.6329178907933x_{28} = 77.6329178907933
x29=18.0071304620294x_{29} = 18.0071304620294
x30=68.2109237434374x_{30} = 68.2109237434374
x31=−41.8069976636577x_{31} = -41.8069976636577
x32=−92.0510144271792x_{32} = -92.0510144271792
x33=52.5097841382339x_{33} = 52.5097841382339
x34=−13.6178494330745x_{34} = -13.6178494330745
x35=8.66494442086091x_{35} = 8.66494442086091
x36=83.9145911307246x_{36} = 83.9145911307246
x37=−1.89705509844521x_{37} = -1.89705509844521
x38=30.5396405836489x_{38} = 30.5396405836489
x39=−66.9249328447879x_{39} = -66.9249328447879
x40=−22.9904224088496x_{40} = -22.9904224088496
x41=2.64868705430995x_{41} = 2.64868705430995
x42=93.3374791719232x_{42} = 93.3374791719232
x43=−73.2060202648688x_{43} = -73.2060202648688
x44=43.0914393756427x_{44} = 43.0914393756427
x45=−32.3938213393924x_{45} = -32.3938213393924
x46=96.4785231784781x_{46} = 96.4785231784781
x47=14.8823418211057x_{47} = 14.8823418211057
x48=−60.6442853217463x_{48} = -60.6442853217463
x49=−16.7353289386048x_{49} = -16.7353289386048
x50=−70.0654290362533x_{50} = -70.0654290362533
x51=−79.4874423690774x_{51} = -79.4874423690774
x52=36.8143279797005x_{52} = 36.8143279797005
x53=5.60083794914673x_{53} = 5.60083794914673
x54=90.1964730234779x_{54} = 90.1964730234779
x55=87.0555087903417x_{55} = 87.0555087903417
x56=−85.7691250090222x_{56} = -85.7691250090222
x57=61.930058438504x_{57} = 61.930058438504
x58=80.7737254193725x_{58} = 80.7737254193725
x59=11.765724377565x_{59} = 11.765724377565
x60=−54.3642321289712x_{60} = -54.3642321289712
x61=−35.5308504106619x_{61} = -35.5308504106619
x62=−57.5041721163552x_{62} = -57.5041721163552
x63=27.4037080523579x_{63} = 27.4037080523579
x64=−4.47910423701347x_{64} = -4.47910423701347
x65=−88.910046632574x_{65} = -88.910046632574
x66=99.6196014930761x_{66} = 99.6196014930761

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
[96.4785231784781,∞)\left[96.4785231784781, \infty\right)
Convexa en los intervalos
(−∞,−95.1920237873094]\left(-\infty, -95.1920237873094\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125)))y = \lim_{x \to -\infty}\left(\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right)\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125)))y = \lim_{x \to \infty}\left(\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right)\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (4*sin(x))/125 + (22*cos(x))/125 + ((3*x)*sin(x))/25 + ((4*x)*cos(x))/25, 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→−∞(4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))x)y = x \lim_{x \to -\infty}\left(\frac{\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right)}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))x)y = x \lim_{x \to \infty}\left(\frac{\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\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:
4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))=3xsin⁡(x)25−4xcos⁡(x)25−4sin⁡(x)125+22cos⁡(x)125\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right) = \frac{3 x \sin{\left(x \right)}}{25} - \frac{4 x \cos{\left(x \right)}}{25} - \frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}
- No
4xcos⁡(x)25+(3xsin⁡(x)25+(4sin⁡(x)125+22cos⁡(x)125))=−3xsin⁡(x)25+4xcos⁡(x)25+4sin⁡(x)125−22cos⁡(x)125\frac{4 x \cos{\left(x \right)}}{25} + \left(\frac{3 x \sin{\left(x \right)}}{25} + \left(\frac{4 \sin{\left(x \right)}}{125} + \frac{22 \cos{\left(x \right)}}{125}\right)\right) = - \frac{3 x \sin{\left(x \right)}}{25} + \frac{4 x \cos{\left(x \right)}}{25} + \frac{4 \sin{\left(x \right)}}{125} - \frac{22 \cos{\left(x \right)}}{125}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор