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Trazado el gráfico de la función/ sinx+x*cosx

Gráfico de la función y = sinx+x*cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = sin(x) + x*cos(x)
f(x)=xcos⁡(x)+sin⁡(x)f{\left(x \right)} = x \cos{\left(x \right)} + \sin{\left(x \right)} 
f = x*cos(x) + sin(x)
Gráfico de la función
02468-8-6-4-2-1010-2020
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:
xcos⁡(x)+sin⁡(x)=0x \cos{\left(x \right)} + \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=61.2773745335697x_{1} = 61.2773745335697
x2=−36.1559664195367x_{2} = -36.1559664195367
x3=80.1230928148503x_{3} = 80.1230928148503
x4=33.0170010333572x_{4} = 33.0170010333572
x5=−42.4350618814099x_{5} = -42.4350618814099
x6=−17.3363779239834x_{6} = -17.3363779239834
x7=23.6042847729804x_{7} = 23.6042847729804
x8=67.5590428388084x_{8} = 67.5590428388084
x9=−83.2642147040886x_{9} = -83.2642147040886
x10=42.4350618814099x_{10} = 42.4350618814099
x11=−95.8290108090195x_{11} = -95.8290108090195
x12=20.469167402741x_{12} = 20.469167402741
x13=−11.085538406497x_{13} = -11.085538406497
x14=64.4181717218392x_{14} = 64.4181717218392
x15=−51.855560729152x_{15} = -51.855560729152
x16=−7.97866571241324x_{16} = -7.97866571241324
x17=−20.469167402741x_{17} = -20.469167402741
x18=−86.4053708116885x_{18} = -86.4053708116885
x19=−39.295350981473x_{19} = -39.295350981473
x20=−48.7152107175577x_{20} = -48.7152107175577
x21=54.9960525574964x_{21} = 54.9960525574964
x22=−23.6042847729804x_{22} = -23.6042847729804
x23=86.4053708116885x_{23} = 86.4053708116885
x24=−4.91318043943488x_{24} = -4.91318043943488
x25=29.8785865061074x_{25} = 29.8785865061074
x26=76.9820093304187x_{26} = 76.9820093304187
x27=2.02875783811043x_{27} = 2.02875783811043
x28=−58.1366632448992x_{28} = -58.1366632448992
x29=11.085538406497x_{29} = 11.085538406497
x30=14.2074367251912x_{30} = 14.2074367251912
x31=7.97866571241324x_{31} = 7.97866571241324
x32=−80.1230928148503x_{32} = -80.1230928148503
x33=−73.8409691490209x_{33} = -73.8409691490209
x34=−54.9960525574964x_{34} = -54.9960525574964
x35=83.2642147040886x_{35} = 83.2642147040886
x36=58.1366632448992x_{36} = 58.1366632448992
x37=−64.4181717218392x_{37} = -64.4181717218392
x38=−45.57503179559x_{38} = -45.57503179559
x39=26.7409160147873x_{39} = 26.7409160147873
x40=−26.7409160147873x_{40} = -26.7409160147873
x41=17.3363779239834x_{41} = 17.3363779239834
x42=−98.9702722883957x_{42} = -98.9702722883957
x43=89.5465575382492x_{43} = 89.5465575382492
x44=70.69997803861x_{44} = 70.69997803861
x45=39.295350981473x_{45} = 39.295350981473
x46=−29.8785865061074x_{46} = -29.8785865061074
x47=45.57503179559x_{47} = 45.57503179559
x48=−67.5590428388084x_{48} = -67.5590428388084
x49=102.111554139654x_{49} = 102.111554139654
x50=51.855560729152x_{50} = 51.855560729152
x51=98.9702722883957x_{51} = 98.9702722883957
x52=−89.5465575382492x_{52} = -89.5465575382492
x53=0x_{53} = 0
x54=−70.69997803861x_{54} = -70.69997803861
x55=−76.9820093304187x_{55} = -76.9820093304187
x56=−33.0170010333572x_{56} = -33.0170010333572
x57=73.8409691490209x_{57} = 73.8409691490209
x58=36.1559664195367x_{58} = 36.1559664195367
x59=48.7152107175577x_{59} = 48.7152107175577
x60=−61.2773745335697x_{60} = -61.2773745335697
x61=95.8290108090195x_{61} = 95.8290108090195
x62=−2.02875783811043x_{62} = -2.02875783811043
x63=4.91318043943488x_{63} = 4.91318043943488
x64=−92.687771772017x_{64} = -92.687771772017
x65=−14.2074367251912x_{65} = -14.2074367251912
x66=92.687771772017x_{66} = 92.687771772017
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) + x*cos(x).
sin⁡(0)+0cos⁡(0)\sin{\left(0 \right)} + 0 \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
−xsin⁡(x)+2cos⁡(x)=0- x \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=69.1439554764926x_{1} = 69.1439554764926
x2=−1.0768739863118x_{2} = -1.0768739863118
x3=−47.1662676027767x_{3} = -47.1662676027767
x4=15.8336114149477x_{4} = 15.8336114149477
x5=25.2119030642106x_{5} = 25.2119030642106
x6=18.954681766529x_{6} = 18.954681766529
x7=1.0768739863118x_{7} = 1.0768739863118
x8=−18.954681766529x_{8} = -18.954681766529
x9=−84.8465692433091x_{9} = -84.8465692433091
x10=−25.2119030642106x_{10} = -25.2119030642106
x11=34.6152330552306x_{11} = 34.6152330552306
x12=−40.8895777660408x_{12} = -40.8895777660408
x13=62.863657228703x_{13} = 62.863657228703
x14=−81.7058821480364x_{14} = -81.7058821480364
x15=44.0276918992479x_{15} = 44.0276918992479
x16=−66.0037377708277x_{16} = -66.0037377708277
x17=100.550852725424x_{17} = 100.550852725424
x18=31.479374920314x_{18} = 31.479374920314
x19=−91.1281305511393x_{19} = -91.1281305511393
x20=−100.550852725424x_{20} = -100.550852725424
x21=40.8895777660408x_{21} = 40.8895777660408
x22=91.1281305511393x_{22} = 91.1281305511393
x23=−59.7237354324305x_{23} = -59.7237354324305
x24=−97.4099011706723x_{24} = -97.4099011706723
x25=66.0037377708277x_{25} = 66.0037377708277
x26=−34.6152330552306x_{26} = -34.6152330552306
x27=12.7222987717666x_{27} = 12.7222987717666
x28=81.7058821480364x_{28} = 81.7058821480364
x29=−53.4444796697636x_{29} = -53.4444796697636
x30=50.3052188363296x_{30} = 50.3052188363296
x31=−62.863657228703x_{31} = -62.863657228703
x32=−31.479374920314x_{32} = -31.479374920314
x33=−9.62956034329743x_{33} = -9.62956034329743
x34=−78.5652673845995x_{34} = -78.5652673845995
x35=−50.3052188363296x_{35} = -50.3052188363296
x36=−94.2689923093066x_{36} = -94.2689923093066
x37=−28.3447768697864x_{37} = -28.3447768697864
x38=28.3447768697864x_{38} = 28.3447768697864
x39=84.8465692433091x_{39} = 84.8465692433091
x40=47.1662676027767x_{40} = 47.1662676027767
x41=−69.1439554764926x_{41} = -69.1439554764926
x42=78.5652673845995x_{42} = 78.5652673845995
x43=−6.57833373272234x_{43} = -6.57833373272234
x44=−44.0276918992479x_{44} = -44.0276918992479
x45=9.62956034329743x_{45} = 9.62956034329743
x46=75.4247339745236x_{46} = 75.4247339745236
x47=−75.4247339745236x_{47} = -75.4247339745236
x48=6.57833373272234x_{48} = 6.57833373272234
x49=−128.820822990274x_{49} = -128.820822990274
x50=−72.2842925036825x_{50} = -72.2842925036825
x51=−37.7520396346102x_{51} = -37.7520396346102
x52=87.9873209346887x_{52} = 87.9873209346887
x53=72.2842925036825x_{53} = 72.2842925036825
x54=97.4099011706723x_{54} = 97.4099011706723
x55=3.6435971674254x_{55} = 3.6435971674254
x56=59.7237354324305x_{56} = 59.7237354324305
x57=53.4444796697636x_{57} = 53.4444796697636
x58=−3.6435971674254x_{58} = -3.6435971674254
x59=−22.0814757672807x_{59} = -22.0814757672807
x60=94.2689923093066x_{60} = 94.2689923093066
x61=−56.5839987378634x_{61} = -56.5839987378634
x62=−12.7222987717666x_{62} = -12.7222987717666
x63=−87.9873209346887x_{63} = -87.9873209346887
x64=56.5839987378634x_{64} = 56.5839987378634
x65=−15.8336114149477x_{65} = -15.8336114149477
x66=37.7520396346102x_{66} = 37.7520396346102
x67=22.0814757672807x_{67} = 22.0814757672807
Signos de extremos en los puntos:
(69.1439554764926, 69.1439615216012)

(-1.0768739863118038, -1.39100784545588)

(-47.1662676027767, 47.1662866291145)

(15.833611414947718, -15.834107331638)

(25.21190306421058, 25.2120270830452)

(18.954681766529042, 18.9549722147554)

(1.0768739863118038, 1.39100784545588)

(-18.954681766529042, -18.9549722147554)

(-84.84656924330915, 84.8465725158561)

(-25.21190306421058, -25.2120270830452)

(34.61523305523058, -34.6152811148717)

(-40.889577766040844, 40.8896069506711)

(62.863657228703005, 62.8636652712142)

(-81.70588214803641, -81.7058858124955)

(44.02769189924788, 44.0277152852979)

(-66.00373777082767, 66.0037447198836)

(100.55085272542402, 100.550854691956)

(31.479374920314047, 31.4794387763188)

(-91.1281305511393, 91.1281331927175)

(-100.55085272542402, -100.550854691956)

(40.889577766040844, -40.8896069506711)

(91.1281305511393, -91.1281331927175)

(-59.72373543243046, 59.7237448102597)

(-97.40990117067226, 97.4099033335782)

(66.00373777082767, -66.0037447198836)

(-34.61523305523058, 34.6152811148717)

(12.722298771766635, 12.7232465674385)

(81.70588214803641, 81.7058858124955)

(-53.44447966976355, 53.4444927529527)

(50.30521883632959, 50.3052345220647)

(-62.863657228703005, -62.8636652712142)

(-31.479374920314047, -31.4794387763188)

(-9.62956034329743, 9.63170728857969)

(-78.56526738459954, 78.5652715061143)

(-50.30521883632959, -50.3052345220647)

(-94.26899230930657, -94.2689946956226)

(-28.344776869786372, 28.3448642580985)

(28.344776869786372, -28.3448642580985)

(84.84656924330915, -84.8465725158561)

(47.1662676027767, -47.1662866291145)

(-69.1439554764926, -69.1439615216012)

(78.56526738459954, -78.5652715061143)

(-6.578333732722339, -6.58476172355643)

(-44.02769189924788, -44.0277152852979)

(9.62956034329743, -9.63170728857969)

(75.4247339745236, 75.4247386323507)

(-75.4247339745236, -75.4247386323507)

(6.578333732722339, 6.58476172355643)

(-128.8208229902735, 128.820823925608)

(-72.2842925036825, 72.2842977950245)

(-37.75203963461023, -37.7520767019434)

(87.9873209346887, 87.9873238692648)

(72.2842925036825, -72.2842977950245)

(97.40990117067226, -97.4099033335782)

(3.643597167425401, -3.67523306366032)

(59.72373543243046, -59.7237448102597)

(53.44447966976355, -53.4444927529527)

(-3.643597167425401, 3.67523306366032)

(-22.081475767280747, 22.0816600122592)

(94.26899230930657, 94.2689946956226)

(-56.58399873786344, -56.5840097635798)

(-12.722298771766635, -12.7232465674385)

(-87.9873209346887, -87.9873238692648)

(56.58399873786344, 56.5840097635798)

(-15.833611414947718, 15.834107331638)

(37.75203963461023, 37.7520767019434)

(22.081475767280747, -22.0816600122592)


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=−1.0768739863118x_{1} = -1.0768739863118
x2=15.8336114149477x_{2} = 15.8336114149477
x3=−18.954681766529x_{3} = -18.954681766529
x4=−25.2119030642106x_{4} = -25.2119030642106
x5=34.6152330552306x_{5} = 34.6152330552306
x6=−81.7058821480364x_{6} = -81.7058821480364
x7=−100.550852725424x_{7} = -100.550852725424
x8=40.8895777660408x_{8} = 40.8895777660408
x9=91.1281305511393x_{9} = 91.1281305511393
x10=66.0037377708277x_{10} = 66.0037377708277
x11=−62.863657228703x_{11} = -62.863657228703
x12=−31.479374920314x_{12} = -31.479374920314
x13=−50.3052188363296x_{13} = -50.3052188363296
x14=−94.2689923093066x_{14} = -94.2689923093066
x15=28.3447768697864x_{15} = 28.3447768697864
x16=84.8465692433091x_{16} = 84.8465692433091
x17=47.1662676027767x_{17} = 47.1662676027767
x18=−69.1439554764926x_{18} = -69.1439554764926
x19=78.5652673845995x_{19} = 78.5652673845995
x20=−6.57833373272234x_{20} = -6.57833373272234
x21=−44.0276918992479x_{21} = -44.0276918992479
x22=9.62956034329743x_{22} = 9.62956034329743
x23=−75.4247339745236x_{23} = -75.4247339745236
x24=−37.7520396346102x_{24} = -37.7520396346102
x25=72.2842925036825x_{25} = 72.2842925036825
x26=97.4099011706723x_{26} = 97.4099011706723
x27=3.6435971674254x_{27} = 3.6435971674254
x28=59.7237354324305x_{28} = 59.7237354324305
x29=53.4444796697636x_{29} = 53.4444796697636
x30=−56.5839987378634x_{30} = -56.5839987378634
x31=−12.7222987717666x_{31} = -12.7222987717666
x32=−87.9873209346887x_{32} = -87.9873209346887
x33=22.0814757672807x_{33} = 22.0814757672807
Puntos máximos de la función:
x33=69.1439554764926x_{33} = 69.1439554764926
x33=−47.1662676027767x_{33} = -47.1662676027767
x33=25.2119030642106x_{33} = 25.2119030642106
x33=18.954681766529x_{33} = 18.954681766529
x33=1.0768739863118x_{33} = 1.0768739863118
x33=−84.8465692433091x_{33} = -84.8465692433091
x33=−40.8895777660408x_{33} = -40.8895777660408
x33=62.863657228703x_{33} = 62.863657228703
x33=44.0276918992479x_{33} = 44.0276918992479
x33=−66.0037377708277x_{33} = -66.0037377708277
x33=100.550852725424x_{33} = 100.550852725424
x33=31.479374920314x_{33} = 31.479374920314
x33=−91.1281305511393x_{33} = -91.1281305511393
x33=−59.7237354324305x_{33} = -59.7237354324305
x33=−97.4099011706723x_{33} = -97.4099011706723
x33=−34.6152330552306x_{33} = -34.6152330552306
x33=12.7222987717666x_{33} = 12.7222987717666
x33=81.7058821480364x_{33} = 81.7058821480364
x33=−53.4444796697636x_{33} = -53.4444796697636
x33=50.3052188363296x_{33} = 50.3052188363296
x33=−9.62956034329743x_{33} = -9.62956034329743
x33=−78.5652673845995x_{33} = -78.5652673845995
x33=−28.3447768697864x_{33} = -28.3447768697864
x33=75.4247339745236x_{33} = 75.4247339745236
x33=6.57833373272234x_{33} = 6.57833373272234
x33=−128.820822990274x_{33} = -128.820822990274
x33=−72.2842925036825x_{33} = -72.2842925036825
x33=87.9873209346887x_{33} = 87.9873209346887
x33=−3.6435971674254x_{33} = -3.6435971674254
x33=−22.0814757672807x_{33} = -22.0814757672807
x33=94.2689923093066x_{33} = 94.2689923093066
x33=56.5839987378634x_{33} = 56.5839987378634
x33=−15.8336114149477x_{33} = -15.8336114149477
x33=37.7520396346102x_{33} = 37.7520396346102
Decrece en los intervalos
[97.4099011706723,∞)\left[97.4099011706723, \infty\right)
Crece en los intervalos
(−∞,−100.550852725424]\left(-\infty, -100.550852725424\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
−(xcos⁡(x)+3sin⁡(x))=0- (x \cos{\left(x \right)} + 3 \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=51.894024636399x_{1} = 51.894024636399
x2=95.8498646688189x_{2} = 95.8498646688189
x3=89.5688718899173x_{3} = 89.5688718899173
x4=−73.8680180276454x_{4} = -73.8680180276454
x5=61.3099494475655x_{5} = 61.3099494475655
x6=−70.7282251775385x_{6} = -70.7282251775385
x7=48.75613936684x_{7} = 48.75613936684
x8=−45.6187613383417x_{8} = -45.6187613383417
x9=−48.75613936684x_{9} = -48.75613936684
x10=45.6187613383417x_{10} = 45.6187613383417
x11=17.4490243427188x_{11} = 17.4490243427188
x12=92.7093311956205x_{12} = 92.7093311956205
x13=−39.3460075465194x_{13} = -39.3460075465194
x14=67.5885991217338x_{14} = 67.5885991217338
x15=−61.3099494475655x_{15} = -61.3099494475655
x16=29.9449807735163x_{16} = 29.9449807735163
x17=−86.4284948180722x_{17} = -86.4284948180722
x18=−33.0771723843072x_{18} = -33.0771723843072
x19=58.170990540028x_{19} = 58.170990540028
x20=−98.9904652640992x_{20} = -98.9904652640992
x21=−5.23293845351241x_{21} = -5.23293845351241
x22=−51.894024636399x_{22} = -51.894024636399
x23=70.7282251775385x_{23} = 70.7282251775385
x24=−64.4491641378738x_{24} = -64.4491641378738
x25=−8.20453136258127x_{25} = -8.20453136258127
x26=98.9904652640992x_{26} = 98.9904652640992
x27=5.23293845351241x_{27} = 5.23293845351241
x28=−67.5885991217338x_{28} = -67.5885991217338
x29=33.0771723843072x_{29} = 33.0771723843072
x30=−29.9449807735163x_{30} = -29.9449807735163
x31=−36.2109745555852x_{31} = -36.2109745555852
x32=−14.3433507883915x_{32} = -14.3433507883915
x33=36.2109745555852x_{33} = 36.2109745555852
x34=−77.0079573362515x_{34} = -77.0079573362515
x35=0x_{35} = 0
x36=−83.2882092591146x_{36} = -83.2882092591146
x37=2.45564386287944x_{37} = 2.45564386287944
x38=−20.5652079398333x_{38} = -20.5652079398333
x39=−26.814952130975x_{39} = -26.814952130975
x40=14.3433507883915x_{40} = 14.3433507883915
x41=42.4820019253669x_{41} = 42.4820019253669
x42=83.2882092591146x_{42} = 83.2882092591146
x43=−17.4490243427188x_{43} = -17.4490243427188
x44=8.20453136258127x_{44} = 8.20453136258127
x45=77.0079573362515x_{45} = 77.0079573362515
x46=55.0323309441547x_{46} = 55.0323309441547
x47=−42.4820019253669x_{47} = -42.4820019253669
x48=23.6879210560017x_{48} = 23.6879210560017
x49=73.8680180276454x_{49} = 73.8680180276454
x50=−80.1480259413025x_{50} = -80.1480259413025
x51=−89.5688718899173x_{51} = -89.5688718899173
x52=−92.7093311956205x_{52} = -92.7093311956205
x53=−2.45564386287944x_{53} = -2.45564386287944
x54=−55.0323309441547x_{54} = -55.0323309441547
x55=26.814952130975x_{55} = 26.814952130975
x56=−95.8498646688189x_{56} = -95.8498646688189
x57=−23.6879210560017x_{57} = -23.6879210560017
x58=80.1480259413025x_{58} = 80.1480259413025
x59=86.4284948180722x_{59} = 86.4284948180722
x60=11.2560430143535x_{60} = 11.2560430143535
x61=20.5652079398333x_{61} = 20.5652079398333
x62=−11.2560430143535x_{62} = -11.2560430143535
x63=−58.170990540028x_{63} = -58.170990540028
x64=64.4491641378738x_{64} = 64.4491641378738
x65=39.3460075465194x_{65} = 39.3460075465194

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
[95.8498646688189,∞)\left[95.8498646688189, \infty\right)
Convexa en los intervalos
(−∞,−95.8498646688189]\left(-\infty, -95.8498646688189\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xcos⁡(x)+sin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \cos{\left(x \right)} + \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→∞(xcos⁡(x)+sin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \cos{\left(x \right)} + \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 sin(x) + 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→−∞(xcos⁡(x)+sin⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right)
True

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