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Trazado el gráfico de la función/ sin(x)+sin(10/3*x)+log(x)-(0,84*x+3)

Gráfico de la función y = sin(x)+sin(10/3*x)+log(x)-(0,84*x+3)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                   /10*x\              21*x    
f(x) = sin(x) + sin|----| + log(x) + - ---- - 3
                   \ 3  /               25
f(x)=(−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))f{\left(x \right)} = \left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right) 
f = -21*x/25 - 3 + sin(x) + sin(10*x/3) + log(x)
Gráfico de la función
7.53.03.54.04.55.05.56.06.57.00-10
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:
(−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))=0\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right) = 0
Resolvermos esta ecuación
Solución no hallada,
puede ser que el gráfico no cruce el eje X
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 sin(x) + sin(10*x/3) + log(x) - 21*x/25 - 3.
(log⁡(0)+(sin⁡(0)+sin⁡(0⋅103)))+(−3−0)\left(\log{\left(0 \right)} + \left(\sin{\left(0 \right)} + \sin{\left(\frac{0 \cdot 10}{3} \right)}\right)\right) + \left(-3 - 0\right)
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
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
cos⁡(x)+10cos⁡(10x3)3−2125+1x=0\cos{\left(x \right)} + \frac{10 \cos{\left(\frac{10 x}{3} \right)}}{3} - \frac{21}{25} + \frac{1}{x} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=20.3264748146376x_{1} = 20.3264748146376
x2=88.1071598626067x_{2} = 88.1071598626067
x3=52.4361080291788x_{3} = 52.4361080291788
x4=−92.7647687432498x_{4} = -92.7647687432498
x5=−29.7742294156023x_{5} = -29.7742294156023
x6=−41.8070217845034x_{6} = -41.8070217845034
x7=98.359379170854x_{7} = 98.359379170854
x8=38.1770248358623x_{8} = 38.1770248358623
x9=66.275733076055x_{9} = 66.275733076055
x10=25.9272097510098x_{10} = 25.9272097510098
x11=−77.6186305930536x_{11} = -77.6186305930536
x12=70.1835513162358x_{12} = 70.1835513162358
x13=61.7631772873456x_{13} = 61.7631772873456
x14=−43.8366138043001x_{14} = -43.8366138043001
x15=64.4777554082914x_{15} = 64.4777554082914
x16=50.4072732093096x_{16} = 50.4072732093096
x17=−39.918390002496x_{17} = -39.918390002496
x18=9.73660376229262x_{18} = 9.73660376229262
x19=6.15442632231374x_{19} = 6.15442632231374
x20=−7.91689597146521x_{20} = -7.91689597146521
x21=11.7763601051293x_{21} = 11.7763601051293
x22=−56.0745607596557x_{22} = -56.0745607596557
x23=90.136079953691x_{23} = 90.136079953691
x24=4.13613862668332x_{24} = 4.13613862668332
x25=−48.622668650569x_{25} = -48.622668650569
x26=−88.1092315832218x_{26} = -88.1092315832218
x27=27.9697803776456x_{27} = 27.9697803776456
x28=93.7712090449464x_{28} = 93.7712090449464
x29=58.0288294633648x_{29} = 58.0288294633648
x30=−27.9776669461112x_{30} = -27.9776669461112
x31=82.4784227417571x_{31} = 82.4784227417571
x32=2.2614896506161x_{32} = 2.2614896506161
x33=24.0619395875367x_{33} = 24.0619395875367
x34=−61.7658931604908x_{34} = -61.7658931604908
x35=18.3692013149437x_{35} = 18.3692013149437
x36=39.9230258540148x_{36} = 39.9230258540148
x37=−54.3287729735818x_{37} = -54.3287729735818
x38=−24.068910074225x_{38} = -24.068910074225
x39=−92.027185754873x_{39} = -92.027185754873
x40=9.11219368543285x_{40} = 9.11219368543285
x41=17.3734839772394x_{41} = 17.3734839772394
x42=−75.8727329848769x_{42} = -75.8727329848769
x43=−9.71390760670272x_{43} = -9.71390760670272
x44=−79.5073638088917x_{44} = -79.5073638088917
x45=−22.3226174929298x_{45} = -22.3226174929298
x46=71.9312325550698x_{46} = 71.9312325550698
x47=22.3133786277316x_{47} = 22.3133786277316
x48=68.3182665487933x_{48} = 68.3182665487933
x49=−33.5918373622021x_{49} = -33.5918373622021
x50=12.7027849488221x_{50} = 12.7027849488221
x51=−13.6275266737725x_{51} = -13.6275266737725
x52=7.9384956655144x_{52} = 7.9384956655144
x53=−11.7599928596994x_{53} = -11.7599928596994
x54=−53.0782995690826x_{54} = -53.0782995690826
x55=36.2200037715291x_{55} = 36.2200037715291
x56=−45.6249951099989x_{56} = -45.6249951099989
x57=−86.3210107602634x_{57} = -86.3210107602634
x58=100.388272620152x_{58} = 100.388272620152
x59=−71.9283661677536x_{59} = -71.9283661677536
x60=54.3253664735286x_{60} = 54.3253664735286
x61=56.0714773860368x_{61} = 56.0714773860368
x62=86.31902753419x_{62} = 86.31902753419
x63=−63.6315477237279x_{63} = -63.6315477237279
x64=−25.9346368631586x_{64} = -25.9346368631586
x65=60.0153752136686x_{65} = 60.0153752136686
x66=75.8750116841133x_{66} = 75.8750116841133
x67=−81.5366882177038x_{67} = -81.5366882177038
x68=76.878814699632x_{68} = 76.878814699632
x69=92.0251747595862x_{69} = 92.0251747595862
x70=−73.9149328337359x_{70} = -73.9149328337359
x71=41.8121934923855x_{71} = 41.8121934923855
x72=−65.6745022641783x_{72} = -65.6745022641783
x73=−6.1246828594817x_{73} = -6.1246828594817
x74=−58.0323358341671x_{74} = -58.0323358341671
x75=43.8407776298487x_{75} = 43.8407776298487
x76=29.7684791004839x_{76} = 29.7684791004839
x77=−38.1724957984287x_{77} = -38.1724957984287
x78=−31.5624194458159x_{78} = -31.5624194458159
x79=−93.7730528080635x_{79} = -93.7730528080635
x80=73.9176856251388x_{80} = 73.9176856251388
x81=−95.7307564609111x_{81} = -95.7307564609111
x82=−97.7172579586002x_{82} = -97.7172579586002
x83=−60.0188105569444x_{83} = -60.0188105569444
x84=84.521072452578x_{84} = 84.521072452578
x85=−47.4221840916411x_{85} = -47.4221840916411
x86=−90.1384787751391x_{86} = -90.1384787751391
x87=32.4858252883064x_{87} = 32.4858252883064
x88=−4.0833876927505x_{88} = -4.0833876927505
x89=34.2336921288663x_{89} = 34.2336921288663
x90=−70.1811611924326x_{90} = -70.1811611924326
Signos de extremos en los puntos:
(20.32647481463759, -17.0446080722536)

(88.10715986260668, -73.3882072766648)

(52.43610802917885, -43.1708374309715)

(-92.76476874324977, 79.4751796154569 + pi*I)

(-29.774229415602296, 27.3605065292784 + pi*I)

(-41.80702178450338, 35.7707777105377 + pi*I)

(98.35937917085398, -80.9499409822209)

(38.17702483586229, -29.9667874190284)

(66.275733076055, -53.9299305693658)

(25.927209751009848, -21.8096148571052)

(-77.61863059305364, 64.8558356762974 + pi*I)

(70.18355131623584, -55.8319330224968)

(61.763177287345584, -52.6290319957312)

(-43.83661380430008, 36.7491150091499 + pi*I)

(64.47775540829143, -51.0349132173157)

(50.4072732093096, -42.2793595709589)

(-39.91839000249605, 32.523632775985 + pi*I)

(9.736603762292622, -8.34754155306323)

(6.154426322313743, -5.4854026360725)

(-7.916895971465205, 3.77002883247696 + pi*I)

(11.77636010512928, -10.1365272015442)

(-56.07456075965573, 49.5858117164858 + pi*I)

(90.13607995369095, -74.296379261265)

(4.136138626683319, -4.95374583502061)

(-48.622668650569004, 43.6846103609719 + pi*I)

(-88.1092315832218, 76.3453383895366 + pi*I)

(27.96978037764564, -23.7131982437132)

(93.77120904494645, -78.6855343795832)

(58.02882946336478, -47.6629539746136)

(-27.97766694611117, 24.375728745064 + pi*I)

(82.47842274175714, -68.1533165605613)

(2.2614896506160975, -2.36223845461116)

(24.06193958753672, -21.9043926946554)

(-61.76589316049081, 54.875690660878 + pi*I)

(18.369201314943687, -16.9810857549881)

(39.92302585401478, -31.1498422743441)

(-54.32877297358182, 48.3264065890837 + pi*I)

(-24.068910074225002, 22.2659449020395 + pi*I)

(-92.02718575487302, 80.520700824583 + pi*I)

(9.112193685432853, -9.00049900430161)

(17.37348397723945, -14.7558217349856)

(-75.87273298487693, 63.6053104818516 + pi*I)

(-9.713907606702717, 6.89701379027883 + pi*I)

(-79.50736380889172, 68.0807945406636 + pi*I)

(-22.322617492929776, 20.0177822533006 + pi*I)

(71.93123255506983, -57.9801483296808)

(22.313378627731584, -19.8069965715063)

(68.31826654879333, -55.8789885760179)

(-33.591837362202064, 28.8110605395262 + pi*I)

(12.702784948822053, -11.990154871166)

(-13.627526673772486, 9.19447551278607 + pi*I)

(7.938495665514403, -5.62929365084291)

(-11.759992859699434, 9.06732647714134 + pi*I)

(-53.07829956908257, 44.3940084871237 + pi*I)

(36.220003771529065, -29.8546530150086)

(-45.62499510999886, 37.1880725303613 + pi*I)

(-86.32101076026342, 75.9258598585117 + pi*I)

(100.38827262015187, -81.8604619206263)

(-71.92836616775358, 60.5315296362215 + pi*I)

(54.32536647352862, -46.336361390362)

(56.0714773860368, -47.5325022097812)

(86.31902753419003, -73.0097367793979)

(-63.63154772372795, 54.8853308664576 + pi*I)

(-25.934636863158644, 22.3204872131055 + pi*I)

(60.01537521366864, -50.4849248115257)

(75.87501168411332, -60.9471657070446)

(-81.53668821770384, 69.0369357569637 + pi*I)

(76.87881469963196, -63.2152970397162)

(92.02517475958616, -77.4765546257793)

(-73.91493283373589, 63.4144039996088 + pi*I)

(41.81219349238551, -34.3045252112697)

(-65.67450226417832, 56.8963449026919 + pi*I)

(-6.1246828594816956, 3.11491142969842 + pi*I)

(-58.03233583416715, 49.7848942624748 + pi*I)

(43.84077762984872, -35.1880812285114)

(29.768479100483873, -26.5734133502736)

(-38.17249579842873, 31.2511365703267 + pi*I)

(-31.562419445815923, 27.8178073831611 + pi*I)

(-93.7730528080635, 81.7672697799159 + pi*I)

(73.91768562513876, -60.8085369909345)

(-95.73075646091108, 81.9526970379258 + pi*I)

(-97.71725795860019, 84.8288666017865 + pi*I)

(-60.01881055694437, 52.6741835546042 + pi*I)

(84.52107245257803, -70.10826534941)

(-47.42218409164112, 40.1492296240703 + pi*I)

(-90.13847877513908, 77.2990469130665 + pi*I)

(32.485825288306444, -24.9350203983231)

(-4.083387692750495, 1.7807028802751 + pi*I)

(34.23369212886632, -27.0554284999452)

(-70.18116119243255, 58.3341269159225 + pi*I)


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=20.3264748146376x_{1} = 20.3264748146376
x2=88.1071598626067x_{2} = 88.1071598626067
x3=52.4361080291788x_{3} = 52.4361080291788
x4=25.9272097510098x_{4} = 25.9272097510098
x5=61.7631772873456x_{5} = 61.7631772873456
x6=50.4072732093096x_{6} = 50.4072732093096
x7=90.136079953691x_{7} = 90.136079953691
x8=27.9697803776456x_{8} = 27.9697803776456
x9=93.7712090449464x_{9} = 93.7712090449464
x10=58.0288294633648x_{10} = 58.0288294633648
x11=82.4784227417571x_{11} = 82.4784227417571
x12=24.0619395875367x_{12} = 24.0619395875367
x13=18.3692013149437x_{13} = 18.3692013149437
x14=9.11219368543285x_{14} = 9.11219368543285
x15=22.3133786277316x_{15} = 22.3133786277316
x16=12.7027849488221x_{16} = 12.7027849488221
x17=54.3253664735286x_{17} = 54.3253664735286
x18=56.0714773860368x_{18} = 56.0714773860368
x19=86.31902753419x_{19} = 86.31902753419
x20=60.0153752136686x_{20} = 60.0153752136686
x21=76.878814699632x_{21} = 76.878814699632
x22=92.0251747595862x_{22} = 92.0251747595862
x23=29.7684791004839x_{23} = 29.7684791004839
x24=84.521072452578x_{24} = 84.521072452578
Puntos máximos de la función:
x24=98.359379170854x_{24} = 98.359379170854
x24=38.1770248358623x_{24} = 38.1770248358623
x24=66.275733076055x_{24} = 66.275733076055
x24=70.1835513162358x_{24} = 70.1835513162358
x24=64.4777554082914x_{24} = 64.4777554082914
x24=9.73660376229262x_{24} = 9.73660376229262
x24=6.15442632231374x_{24} = 6.15442632231374
x24=11.7763601051293x_{24} = 11.7763601051293
x24=4.13613862668332x_{24} = 4.13613862668332
x24=2.2614896506161x_{24} = 2.2614896506161
x24=39.9230258540148x_{24} = 39.9230258540148
x24=17.3734839772394x_{24} = 17.3734839772394
x24=71.9312325550698x_{24} = 71.9312325550698
x24=68.3182665487933x_{24} = 68.3182665487933
x24=7.9384956655144x_{24} = 7.9384956655144
x24=36.2200037715291x_{24} = 36.2200037715291
x24=100.388272620152x_{24} = 100.388272620152
x24=75.8750116841133x_{24} = 75.8750116841133
x24=41.8121934923855x_{24} = 41.8121934923855
x24=43.8407776298487x_{24} = 43.8407776298487
x24=73.9176856251388x_{24} = 73.9176856251388
x24=32.4858252883064x_{24} = 32.4858252883064
x24=34.2336921288663x_{24} = 34.2336921288663
Decrece en los intervalos
[93.7712090449464,∞)\left[93.7712090449464, \infty\right)
Crece en los intervalos
(−∞,9.11219368543285]\left(-\infty, 9.11219368543285\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
−(sin⁡(x)+100sin⁡(10x3)9+1x2)=0- (\sin{\left(x \right)} + \frac{100 \sin{\left(\frac{10 x}{3} \right)}}{9} + \frac{1}{x^{2}}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=10.3459891535317x_{1} = 10.3459891535317
x2=46.202939898987x_{2} = 46.202939898987
x3=69.7278155833422x_{3} = 69.7278155833422
x4=26.3638514509402x_{4} = 26.3638514509402
x5=48.0448637230843x_{5} = 48.0448637230843
x6=33.9129460846312x_{6} = 33.9129460846312
x7=−39.5581665318107x_{7} = -39.5581665318107
x8=−78.2337880522672x_{8} = -78.2337880522672
x9=44.3050347680876x_{9} = 44.3050347680876
x10=−46.202914946311x_{10} = -46.202914946311
x11=76.3629170154809x_{11} = 76.3629170154809
x12=28.2742991713x_{12} = 28.2742991713
x13=−71.6120873471365x_{13} = -71.6120873471365
x14=65.9734393499088x_{14} = 65.9734393499088
x15=41.4852375128148x_{15} = 41.4852375128148
x16=−69.7278264642108x_{16} = -69.7278264642108
x17=−12.2434621894089x_{17} = -12.2434621894089
x18=99.9181796206136x_{18} = 99.9181796206136
x19=74.4335400357424x_{19} = 74.4335400357424
x20=−30.1848071507631x_{20} = -30.1848071507631
x21=−57.5133480651066x_{21} = -57.5133480651066
x22=−19.8141744945723x_{22} = -19.8141744945723
x23=17.8849532736588x_{23} = 17.8849532736588
x24=−62.2190772597939x_{24} = -62.2190772597939
x25=52.7625161090086x_{25} = 52.7625161090086
x26=−65.97345210086x_{26} = -65.97345210086
x27=62.2190635941936x_{27} = 62.2190635941936
x28=73.5391814003115x_{28} = 73.5391814003115
x29=−35.8400958696204x_{29} = -35.8400958696204
x30=−33.9129941451064x_{30} = -33.9129941451064
x31=−73.53919150069x_{31} = -73.53919150069
x32=−16.0138845726635x_{32} = -16.0138845726635
x33=60.3348019007869x_{33} = 60.3348019007869
x34=12.2438320340066x_{34} = 12.2438320340066
x35=14.1643286529706x_{35} = 14.1643286529706
x36=−40.5346644853485x_{36} = -40.5346644853485
x37=−83.902035482328x_{37} = -83.902035482328
x38=−55.5839702505857x_{38} = -55.5839702505857
x39=16.0140899303021x_{39} = 16.0140899303021
x40=90.4616345023349x_{40} = 90.4616345023349
x41=−23.5348693098294x_{41} = -23.5348693098294
x42=−32.0287349655944x_{42} = -32.0287349655944
x43=−29.1952650169188x_{43} = -29.1952650169188
x44=49.9427700757633x_{44} = 49.9427700757633
x45=−99.9181849195256x_{45} = -99.9181849195256
x46=85.743967650719x_{46} = 85.743967650719
x47=35.8400533452899x_{47} = 35.8400533452899
x48=−1.86686645640636x_{48} = -1.86686645640636
x49=−7.51480968625305x_{49} = -7.51480968625305
x50=30.1847482007348x_{50} = 30.1847482007348
x51=−21.6850685938247x_{51} = -21.6850685938247
x52=19.8143145760038x_{52} = 19.8143145760038
x53=78.2337966566762x_{53} = 78.2337966566762
x54=82.0041366111785x_{54} = 82.0041366111785
x55=98.0339184601643x_{55} = 98.0339184601643
x56=−3.78806804379283x_{56} = -3.78806804379283
x57=−17.8847813387092x_{57} = -17.8847813387092
x58=−96.1068198002513x_{58} = -96.1068198002513
x59=96.1068138864476x_{59} = 96.1068138864476
x60=−5.67122513222173x_{60} = -5.67122513222173
x61=8.50418385952301x_{61} = 8.50418385952301
x62=67.8838836910847x_{62} = 67.8838836910847
x63=−87.641867195962x_{63} = -87.641867195962
x64=−53.7130899694754x_{64} = -53.7130899694754
x65=3.78421210948768x_{65} = 3.78421210948768
x66=−98.0339242114768x_{66} = -98.0339242114768
x67=94.2477766479706x_{67} = 94.2477766479706
x68=31.0932317137121x_{68} = 31.0932317137121
x69=83.9020430491075x_{69} = 83.9020430491075
x70=−89.5624139330734x_{70} = -89.5624139330734
x71=21.6851805855588x_{71} = 21.6851805855588
x72=51.8633155386264x_{72} = 51.8633155386264
x73=80.0835902075532x_{73} = 80.0835902075532
x74=−37.6991303413281x_{74} = -37.6991303413281
x75=−94.2477825674166x_{75} = -94.2477825674166
x76=−80.0835817595622x_{76} = -80.0835817595622
x77=58.4076969944574x_{77} = 58.4076969944574
x78=24.5199145886044x_{78} = 24.5199145886044
x79=−67.8838953464676x_{79} = -67.8838953464676
x80=−82.0041283665825x_{80} = -82.0041283665825
x81=64.0629953884117x_{81} = 64.0629953884117
x82=32.0286833956245x_{82} = 32.0286833956245
x83=−85.7439604055421x_{83} = -85.7439604055421
x84=−48.0448406469855x_{84} = -48.0448406469855
x85=−14.1640585951392x_{85} = -14.1640585951392
x86=−75.3982283107216x_{86} = -75.3982283107216
x87=−64.0630084755717x_{87} = -64.0630084755717
x88=−51.863295395815x_{88} = -51.863295395815
x89=92.3887391723532x_{89} = 92.3887391723532
x90=42.3844892202862x_{90} = 42.3844892202862
x91=1.85105698812704x_{91} = 1.85105698812704
x92=−49.9427478479982x_{92} = -49.9427478479982

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
[85.743967650719,∞)\left[85.743967650719, \infty\right)
Convexa en los intervalos
(−∞,−89.5624139330734]\left(-\infty, -89.5624139330734\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x)))=∞\lim_{x \to -\infty}\left(\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right)\right) = \infty
Tomamos como el límite
es decir,
no hay asíntota horizontal a la izquierda
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞((−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x)))y = \lim_{x \to \infty}\left(\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right)\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sin(x) + sin(10*x/3) + log(x) - 21*x/25 - 3, dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))x)=−2125\lim_{x \to -\infty}\left(\frac{\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right)}{x}\right) = - \frac{21}{25}
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=−21x25y = - \frac{21 x}{25}
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞((−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))x)y = x \lim_{x \to \infty}\left(\frac{\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \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:
(−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))=21x25+log⁡(−x)−sin⁡(x)−sin⁡(10x3)−3\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right) = \frac{21 x}{25} + \log{\left(- x \right)} - \sin{\left(x \right)} - \sin{\left(\frac{10 x}{3} \right)} - 3
- No
(−21x25−3)+((sin⁡(x)+sin⁡(10x3))+log⁡(x))=−21x25−log⁡(−x)+sin⁡(x)+sin⁡(10x3)+3\left(- \frac{21 x}{25} - 3\right) + \left(\left(\sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)}\right) + \log{\left(x \right)}\right) = - \frac{21 x}{25} - \log{\left(- x \right)} + \sin{\left(x \right)} + \sin{\left(\frac{10 x}{3} \right)} + 3
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор