Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ 3*sin(x)-5*x*cos(x)

Gráfico de la función y = 3*sin(x)-5*x*cos(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = 3*sin(x) - 5*x*cos(x)
f(x)=−5xcos⁡(x)+3sin⁡(x)f{\left(x \right)} = - 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)} 
f = -5*x*cos(x) + 3*sin(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:
−5xcos⁡(x)+3sin⁡(x)=0- 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=67.5353580507902x_{1} = 67.5353580507902
x2=1.05279429376987x_{2} = 1.05279429376987
x3=45.5399189853199x_{3} = 45.5399189853199
x4=73.8192995825974x_{4} = 73.8192995825974
x5=−42.3973499401921x_{5} = -42.3973499401921
x6=−83.2449978046495x_{6} = -83.2449978046495
x7=−76.9612240370931x_{7} = -76.9612240370931
x8=−98.9541052454241x_{8} = -98.9541052454241
x9=70.6773456265368x_{9} = 70.6773456265368
x10=20.3909358974269x_{10} = 20.3909358974269
x11=−32.9685256955917x_{11} = -32.9685256955917
x12=−92.6705088196718x_{12} = -92.6705088196718
x13=−64.3933319332748x_{13} = -64.3933319332748
x14=−23.5364580560657x_{14} = -23.5364580560657
x15=−45.5399189853199x_{15} = -45.5399189853199
x16=−7.77698342612727x_{16} = -7.77698342612727
x17=10.9407885120283x_{17} = 10.9407885120283
x18=−80.1031224619024x_{18} = -80.1031224619024
x19=−17.2439788724295x_{19} = -17.2439788724295
x20=−73.8192995825974x_{20} = -73.8192995825974
x21=−4.58218792604656x_{21} = -4.58218792604656
x22=4.58218792604656x_{22} = 4.58218792604656
x23=−1.05279429376987x_{23} = -1.05279429376987
x24=98.9541052454241x_{24} = 98.9541052454241
x25=−14.0946232027546x_{25} = -14.0946232027546
x26=29.8250155816177x_{26} = 29.8250155816177
x27=−51.8247018108283x_{27} = -51.8247018108283
x28=39.2546245367091x_{28} = 39.2546245367091
x29=7.77698342612727x_{29} = 7.77698342612727
x30=95.8123137732547x_{30} = 95.8123137732547
x31=−29.8250155816177x_{31} = -29.8250155816177
x32=61.2512613416615x_{32} = 61.2512613416615
x33=48.6823619623294x_{33} = 48.6823619623294
x34=−54.9669562223418x_{34} = -54.9669562223418
x35=−61.2512613416615x_{35} = -61.2512613416615
x36=−26.6810534774259x_{36} = -26.6810534774259
x37=23.5364580560657x_{37} = 23.5364580560657
x38=86.3868525840641x_{38} = 86.3868525840641
x39=−58.1091390601287x_{39} = -58.1091390601287
x40=−70.6773456265368x_{40} = -70.6773456265368
x41=−124.088074579195x_{41} = -124.088074579195
x42=26.6810534774259x_{42} = 26.6810534774259
x43=−95.8123137732547x_{43} = -95.8123137732547
x44=−36.1117019321908x_{44} = -36.1117019321908
x45=76.9612240370931x_{45} = 76.9612240370931
x46=80.1031224619024x_{46} = 80.1031224619024
x47=−86.3868525840641x_{47} = -86.3868525840641
x48=42.3973499401921x_{48} = 42.3973499401921
x49=89.5286889652558x_{49} = 89.5286889652558
x50=−67.5353580507902x_{50} = -67.5353580507902
x51=−39.2546245367091x_{51} = -39.2546245367091
x52=83.2449978046495x_{52} = 83.2449978046495
x53=51.8247018108283x_{53} = 51.8247018108283
x54=0x_{54} = 0
x55=14.0946232027546x_{55} = 14.0946232027546
x56=17.2439788724295x_{56} = 17.2439788724295
x57=92.6705088196718x_{57} = 92.6705088196718
x58=−48.6823619623294x_{58} = -48.6823619623294
x59=64.3933319332748x_{59} = 64.3933319332748
x60=−10.9407885120283x_{60} = -10.9407885120283
x61=36.1117019321908x_{61} = 36.1117019321908
x62=−20.3909358974269x_{62} = -20.3909358974269
x63=−89.5286889652558x_{63} = -89.5286889652558
x64=54.9669562223418x_{64} = 54.9669562223418
x65=32.9685256955917x_{65} = 32.9685256955917
x66=58.1091390601287x_{66} = 58.1091390601287
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*sin(x) - 5*x*cos(x).
3sin⁡(0)−0⋅5cos⁡(0)3 \sin{\left(0 \right)} - 0 \cdot 5 \cos{\left(0 \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
5xsin⁡(x)−2cos⁡(x)=05 x \sin{\left(x \right)} - 2 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−43.991389588134x_{1} = -43.991389588134
x2=−59.6969608265415x_{2} = -59.6969608265415
x3=−69.1208252823183x_{3} = -69.1208252823183
x4=−91.1105771955273x_{4} = -91.1105771955273
x5=−100.534943609991x_{5} = -100.534943609991
x6=−50.2734387773004x_{6} = -50.2734387773004
x7=−22.0093206929551x_{7} = -22.0093206929551
x8=18.8707495740317x_{8} = 18.8707495740317
x9=0.59324192798782x_{9} = 0.59324192798782
x10=−81.6863057358096x_{10} = -81.6863057358096
x11=−34.56908970387x_{11} = -34.56908970387
x12=53.4145635654169x_{12} = 53.4145635654169
x13=6.3461325499601x_{13} = 6.3461325499601
x14=91.1105771955273x_{14} = 91.1105771955273
x15=−25.1486453169527x_{15} = -25.1486453169527
x16=59.6969608265415x_{16} = 59.6969608265415
x17=15.7333814435165x_{17} = 15.7333814435165
x18=78.5449089236889x_{18} = 78.5449089236889
x19=−97.3934792893299x_{19} = -97.3934792893299
x20=−75.4035284279396x_{20} = -75.4035284279396
x21=−6.3461325499601x_{21} = -6.3461325499601
x22=−62.8382185386524x_{22} = -62.8382185386524
x23=62.8382185386524x_{23} = 62.8382185386524
x24=47.1323763353614x_{24} = 47.1323763353614
x25=9.46700485615128x_{25} = 9.46700485615128
x26=−94.2520235229288x_{26} = -94.2520235229288
x27=31.428653088426x_{27} = 31.428653088426
x28=3.26355028875359x_{28} = 3.26355028875359
x29=65.9795081394728x_{29} = 65.9795081394728
x30=25.1486453169527x_{30} = 25.1486453169527
x31=72.2621663760889x_{31} = 72.2621663760889
x32=87.9691413182216x_{32} = 87.9691413182216
x33=−0.59324192798782x_{33} = -0.59324192798782
x34=22.0093206929551x_{34} = 22.0093206929551
x35=28.2884729751041x_{35} = 28.2884729751041
x36=−15.7333814435165x_{36} = -15.7333814435165
x37=−18.8707495740317x_{37} = -18.8707495740317
x38=40.8504959865172x_{38} = 40.8504959865172
x39=100.534943609991x_{39} = 100.534943609991
x40=97.3934792893299x_{40} = 97.3934792893299
x41=−40.8504959865172x_{41} = -40.8504959865172
x42=−65.9795081394728x_{42} = -65.9795081394728
x43=−78.5449089236889x_{43} = -78.5449089236889
x44=37.7097187903511x_{44} = 37.7097187903511
x45=−84.827717051856x_{45} = -84.827717051856
x46=−37.7097187903511x_{46} = -37.7097187903511
x47=−31.428653088426x_{47} = -31.428653088426
x48=−47.1323763353614x_{48} = -47.1323763353614
x49=43.991389588134x_{49} = 43.991389588134
x50=81.6863057358096x_{50} = 81.6863057358096
x51=−28.2884729751041x_{51} = -28.2884729751041
x52=50.2734387773004x_{52} = 50.2734387773004
x53=−56.5557403151352x_{53} = -56.5557403151352
x54=69.1208252823183x_{54} = 69.1208252823183
x55=−12.5981107438383x_{55} = -12.5981107438383
x56=−3.26355028875359x_{56} = -3.26355028875359
x57=34.56908970387x_{57} = 34.56908970387
x58=−87.9691413182216x_{58} = -87.9691413182216
x59=−72.2621663760889x_{59} = -72.2621663760889
x60=75.4035284279396x_{60} = 75.4035284279396
x61=84.827717051856x_{61} = 84.827717051856
x62=94.2520235229288x_{62} = 94.2520235229288
x63=−53.4145635654169x_{63} = -53.4145635654169
x64=12.5981107438383x_{64} = 12.5981107438383
x65=−9.46700485615128x_{65} = -9.46700485615128
x66=56.5557403151352x_{66} = 56.5557403151352
Signos de extremos en los puntos:
(-43.99138958813401, 219.920578878213)

(-59.696960826541456, -298.458002775115)

(-69.12082528231835, 345.580978975864)

(-91.11057719552726, -455.53532508951)

(-100.53494360999137, 502.658803327219)

(-50.273438777300406, 251.335369068734)

(-22.00932069295512, -109.973920494231)

(18.870749574031652, -94.2689819863186)

(0.5932419279878203, -0.782225376550445)

(-81.68630573580955, 408.411941816778)

(-34.569089703869984, -172.799167881752)

(53.414563565416934, 267.042864394458)

(6.346132549960095, -31.4791023801429)

(91.11057719552726, 455.53532508951)

(-25.148645316952685, 125.679613919341)

(59.696960826541456, 298.458002775115)

(15.733381443516532, 78.5652495687041)

(78.5449089236889, 392.704174403735)

(-97.39347928932995, -486.950968397967)

(-75.40352842793959, 376.996423309397)

(-6.346132549960095, 31.4791023801429)

(-62.83821853865237, 314.165631062265)

(62.83821853865237, -314.165631062265)

(47.132376335361435, 235.627936111024)

(9.46700485615128, 47.1661857153802)

(-94.25202352292875, 471.243142023771)

(31.428653088425957, -157.092361121493)

(3.2635502887535903, 15.8315827984104)

(65.97950813947278, 329.873291245259)

(25.148645316952685, -125.679613919341)

(72.26216637608889, 361.288690661819)

(87.96914131822163, -439.827518606455)

(-0.5932419279878203, 0.782225376550445)

(22.00932069295512, 109.973920494231)

(28.28847297510414, 141.38581109537)

(-15.733381443516532, -78.5652495687041)

(-18.870749574031652, 94.2689819863186)

(40.85049598651721, 204.213314833697)

(100.53494360999137, -502.658803327219)

(97.39347928932995, 486.950968397967)

(-40.85049598651721, -204.213314833697)

(-65.97950813947278, -329.873291245259)

(-78.5449089236889, -392.704174403735)

(37.70971879035108, -188.506167256569)

(-84.82771705185603, -424.119723735664)

(-37.70971879035108, 188.506167256569)

(-31.428653088425957, 157.092361121493)

(-47.132376335361435, -235.627936111024)

(43.99138958813401, -219.920578878213)

(81.68630573580955, -408.411941816778)

(-28.28847297510414, -141.38581109537)

(50.273438777300406, -251.335369068734)

(-56.55574031513522, 282.750411697894)

(69.12082528231835, -345.580978975864)

(-12.598110743838287, 62.863622511666)

(-3.2635502887535903, -15.8315827984104)

(34.569089703869984, 172.799167881752)

(-87.96914131822163, 439.827518606455)

(-72.26216637608889, -361.288690661819)

(75.40352842793959, -376.996423309397)

(84.82771705185603, 424.119723735664)

(94.25202352292875, -471.243142023771)

(-53.414563565416934, -267.042864394458)

(12.598110743838287, -62.863622511666)

(-9.46700485615128, -47.1661857153802)

(56.55574031513522, -282.750411697894)


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=−59.6969608265415x_{1} = -59.6969608265415
x2=−91.1105771955273x_{2} = -91.1105771955273
x3=−22.0093206929551x_{3} = -22.0093206929551
x4=18.8707495740317x_{4} = 18.8707495740317
x5=0.59324192798782x_{5} = 0.59324192798782
x6=−34.56908970387x_{6} = -34.56908970387
x7=6.3461325499601x_{7} = 6.3461325499601
x8=−97.3934792893299x_{8} = -97.3934792893299
x9=62.8382185386524x_{9} = 62.8382185386524
x10=31.428653088426x_{10} = 31.428653088426
x11=25.1486453169527x_{11} = 25.1486453169527
x12=87.9691413182216x_{12} = 87.9691413182216
x13=−15.7333814435165x_{13} = -15.7333814435165
x14=100.534943609991x_{14} = 100.534943609991
x15=−40.8504959865172x_{15} = -40.8504959865172
x16=−65.9795081394728x_{16} = -65.9795081394728
x17=−78.5449089236889x_{17} = -78.5449089236889
x18=37.7097187903511x_{18} = 37.7097187903511
x19=−84.827717051856x_{19} = -84.827717051856
x20=−47.1323763353614x_{20} = -47.1323763353614
x21=43.991389588134x_{21} = 43.991389588134
x22=81.6863057358096x_{22} = 81.6863057358096
x23=−28.2884729751041x_{23} = -28.2884729751041
x24=50.2734387773004x_{24} = 50.2734387773004
x25=69.1208252823183x_{25} = 69.1208252823183
x26=−3.26355028875359x_{26} = -3.26355028875359
x27=−72.2621663760889x_{27} = -72.2621663760889
x28=75.4035284279396x_{28} = 75.4035284279396
x29=94.2520235229288x_{29} = 94.2520235229288
x30=−53.4145635654169x_{30} = -53.4145635654169
x31=12.5981107438383x_{31} = 12.5981107438383
x32=−9.46700485615128x_{32} = -9.46700485615128
x33=56.5557403151352x_{33} = 56.5557403151352
Puntos máximos de la función:
x33=−43.991389588134x_{33} = -43.991389588134
x33=−69.1208252823183x_{33} = -69.1208252823183
x33=−100.534943609991x_{33} = -100.534943609991
x33=−50.2734387773004x_{33} = -50.2734387773004
x33=−81.6863057358096x_{33} = -81.6863057358096
x33=53.4145635654169x_{33} = 53.4145635654169
x33=91.1105771955273x_{33} = 91.1105771955273
x33=−25.1486453169527x_{33} = -25.1486453169527
x33=59.6969608265415x_{33} = 59.6969608265415
x33=15.7333814435165x_{33} = 15.7333814435165
x33=78.5449089236889x_{33} = 78.5449089236889
x33=−75.4035284279396x_{33} = -75.4035284279396
x33=−6.3461325499601x_{33} = -6.3461325499601
x33=−62.8382185386524x_{33} = -62.8382185386524
x33=47.1323763353614x_{33} = 47.1323763353614
x33=9.46700485615128x_{33} = 9.46700485615128
x33=−94.2520235229288x_{33} = -94.2520235229288
x33=3.26355028875359x_{33} = 3.26355028875359
x33=65.9795081394728x_{33} = 65.9795081394728
x33=72.2621663760889x_{33} = 72.2621663760889
x33=−0.59324192798782x_{33} = -0.59324192798782
x33=22.0093206929551x_{33} = 22.0093206929551
x33=28.2884729751041x_{33} = 28.2884729751041
x33=−18.8707495740317x_{33} = -18.8707495740317
x33=40.8504959865172x_{33} = 40.8504959865172
x33=97.3934792893299x_{33} = 97.3934792893299
x33=−37.7097187903511x_{33} = -37.7097187903511
x33=−31.428653088426x_{33} = -31.428653088426
x33=−56.5557403151352x_{33} = -56.5557403151352
x33=−12.5981107438383x_{33} = -12.5981107438383
x33=34.56908970387x_{33} = 34.56908970387
x33=−87.9691413182216x_{33} = -87.9691413182216
x33=84.827717051856x_{33} = 84.827717051856
Decrece en los intervalos
[100.534943609991,∞)\left[100.534943609991, \infty\right)
Crece en los intervalos
(−∞,−97.3934792893299]\left(-\infty, -97.3934792893299\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
5xcos⁡(x)+7sin⁡(x)=05 x \cos{\left(x \right)} + 7 \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−64.4243768836685x_{1} = -64.4243768836685
x2=−80.1280829156087x_{2} = -80.1280829156087
x3=89.5510228994423x_{3} = 89.5510228994423
x4=−76.9872028492856x_{4} = -76.9872028492856
x5=−39.3055115330905x_{5} = -39.3055115330905
x6=45.5837964935821x_{6} = 45.5837964935821
x7=17.3592341409419x_{7} = 17.3592341409419
x8=95.8331836138588x_{8} = 95.8331836138588
x9=2.14834147539713x_{9} = 2.14834147539713
x10=−2.14834147539713x_{10} = -2.14834147539713
x11=61.2838972724256x_{11} = 61.2838972724256
x12=23.6211445792393x_{12} = 23.6211445792393
x13=58.1435377819664x_{13} = 58.1435377819664
x14=14.2351994477349x_{14} = 14.2351994477349
x15=42.4444731402791x_{15} = 42.4444731402791
x16=36.1670055142409x_{16} = 36.1670055142409
x17=80.1280829156087x_{17} = 80.1280829156087
x18=8.02666319872566x_{18} = 8.02666319872566
x19=−111.539090196748x_{19} = -111.539090196748
x20=−51.8632662880759x_{20} = -51.8632662880759
x21=4.98612029941719x_{21} = 4.98612029941719
x22=76.9872028492856x_{22} = 76.9872028492856
x23=−89.5510228994423x_{23} = -89.5510228994423
x24=−26.7558149540646x_{24} = -26.7558149540646
x25=−83.2690167124347x_{25} = -83.2690167124347
x26=−86.4099983850814x_{26} = -86.4099983850814
x27=33.0290843901998x_{27} = 33.0290843901998
x28=−29.8919313899594x_{28} = -29.8919313899594
x29=−55.0033189528342x_{29} = -55.0033189528342
x30=−58.1435377819664x_{30} = -58.1435377819664
x31=73.8463833629566x_{31} = 73.8463833629566
x32=−11.1208056508636x_{32} = -11.1208056508636
x33=64.4243768836685x_{33} = 64.4243768836685
x34=−95.8331836138588x_{34} = -95.8331836138588
x35=−17.3592341409419x_{35} = -17.3592341409419
x36=−45.5837964935821x_{36} = -45.5837964935821
x37=48.7234118468414x_{37} = 48.7234118468414
x38=−98.9743127291222x_{38} = -98.9743127291222
x39=102.115470352432x_{39} = 102.115470352432
x40=29.8919313899594x_{40} = 29.8919313899594
x41=−8.02666319872566x_{41} = -8.02666319872566
x42=26.7558149540646x_{42} = 26.7558149540646
x43=98.9743127291222x_{43} = 98.9743127291222
x44=−42.4444731402791x_{44} = -42.4444731402791
x45=0x_{45} = 0
x46=−4.98612029941719x_{46} = -4.98612029941719
x47=70.7056325214982x_{47} = 70.7056325214982
x48=11.1208056508636x_{48} = 11.1208056508636
x49=39.3055115330905x_{49} = 39.3055115330905
x50=−23.6211445792393x_{50} = -23.6211445792393
x51=67.5649598871336x_{51} = 67.5649598871336
x52=−92.6920859031251x_{52} = -92.6920859031251
x53=20.4885769560323x_{53} = 20.4885769560323
x54=−70.7056325214982x_{54} = -70.7056325214982
x55=−48.7234118468414x_{55} = -48.7234118468414
x56=92.6920859031251x_{56} = 92.6920859031251
x57=55.0033189528342x_{57} = 55.0033189528342
x58=−73.8463833629566x_{58} = -73.8463833629566
x59=−14.2351994477349x_{59} = -14.2351994477349
x60=−36.1670055142409x_{60} = -36.1670055142409
x61=−61.2838972724256x_{61} = -61.2838972724256
x62=83.2690167124347x_{62} = 83.2690167124347
x63=−67.5649598871336x_{63} = -67.5649598871336
x64=51.8632662880759x_{64} = 51.8632662880759
x65=86.4099983850814x_{65} = 86.4099983850814
x66=−20.4885769560323x_{66} = -20.4885769560323
x67=−33.0290843901998x_{67} = -33.0290843901998

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
[98.9743127291222,∞)\left[98.9743127291222, \infty\right)
Convexa en los intervalos
(−∞,−111.539090196748]\left(-\infty, -111.539090196748\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(−5xcos⁡(x)+3sin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(- 5 x \cos{\left(x \right)} + 3 \sin{\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→∞(−5xcos⁡(x)+3sin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(- 5 x \cos{\left(x \right)} + 3 \sin{\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 3*sin(x) - 5*x*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→−∞(−5xcos⁡(x)+3sin⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{- 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(−5xcos⁡(x)+3sin⁡(x)x)y = x \lim_{x \to \infty}\left(\frac{- 5 x \cos{\left(x \right)} + 3 \sin{\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:
−5xcos⁡(x)+3sin⁡(x)=5xcos⁡(x)−3sin⁡(x)- 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)} = 5 x \cos{\left(x \right)} - 3 \sin{\left(x \right)}
- No
−5xcos⁡(x)+3sin⁡(x)=−5xcos⁡(x)+3sin⁡(x)- 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)} = - 5 x \cos{\left(x \right)} + 3 \sin{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор