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Trazado el gráfico de la función/ cos(x)/(2*sqrt(x))-sin(x)*sqrt(x)

Gráfico de la función y = cos(x)/(2*sqrt(x))-sin(x)*sqrt(x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
        cos(x)            ___
f(x) = ------- - sin(x)*\/ x 
           ___               
       2*\/ x
f(x)=−xsin⁡(x)+cos⁡(x)2xf{\left(x \right)} = - \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}} 
f = -sqrt(x)*sin(x) + cos(x)/((2*sqrt(x)))
Gráfico de la función
02468-8-6-4-2-10105-5
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
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:
−xsin⁡(x)+cos⁡(x)2x=0- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=43.9936619344429x_{1} = 43.9936619344429
x2=84.8288957966139x_{2} = 84.8288957966139
x3=0.653271187094403x_{3} = 0.653271187094403
x4=91.1116746699497x_{4} = 91.1116746699497
x5=40.8529429059734x_{5} = 40.8529429059734
x6=−34.5719807601687x_{6} = -34.5719807601687
x7=34.5719807601687x_{7} = 34.5719807601687
x8=−62.8398096434599x_{8} = -62.8398096434599
x9=94.253084424113x_{9} = 94.253084424113
x10=62.8398096434599x_{10} = 62.8398096434599
x11=78.5461819355535x_{11} = 78.5461819355535
x12=−94.253084424113x_{12} = -94.253084424113
x13=−31.43183263459x_{13} = -31.43183263459
x14=−56.5575080935408x_{14} = -56.5575080935408
x15=−28.2920048800691x_{15} = -28.2920048800691
x16=−40.8529429059734x_{16} = -40.8529429059734
x17=−84.8288957966139x_{17} = -84.8288957966139
x18=37.7123693157661x_{18} = 37.7123693157661
x19=15.7397193560049x_{19} = 15.7397193560049
x20=−65.9810235167388x_{20} = -65.9810235167388
x21=−12.6060134442754x_{21} = -12.6060134442754
x22=81.6875298021918x_{22} = 81.6875298021918
x23=−78.5461819355535x_{23} = -78.5461819355535
x24=97.3945059759883x_{24} = 97.3945059759883
x25=−22.013857636623x_{25} = -22.013857636623
x26=18.8760383379859x_{26} = 18.8760383379859
x27=47.1344973476771x_{27} = 47.1344973476771
x28=−47.1344973476771x_{28} = -47.1344973476771
x29=69.1222718113619x_{29} = 69.1222718113619
x30=−15.7397193560049x_{30} = -15.7397193560049
x31=−75.4048544617952x_{31} = -75.4048544617952
x32=−59.6986356231676x_{32} = -59.6986356231676
x33=−91.1116746699497x_{33} = -91.1116746699497
x34=−9.4774857054208x_{34} = -9.4774857054208
x35=3.29231002128209x_{35} = 3.29231002128209
x36=25.1526172579356x_{36} = 25.1526172579356
x37=−100.535938219808x_{37} = -100.535938219808
x38=28.2920048800691x_{38} = 28.2920048800691
x39=−43.9936619344429x_{39} = -43.9936619344429
x40=50.2754273458806x_{40} = 50.2754273458806
x41=72.26355003974x_{41} = 72.26355003974
x42=56.5575080935408x_{42} = 56.5575080935408
x43=−97.3945059759883x_{43} = -97.3945059759883
x44=12.6060134442754x_{44} = 12.6060134442754
x45=−53.4164352526291x_{45} = -53.4164352526291
x46=75.4048544617952x_{46} = 75.4048544617952
x47=−18.8760383379859x_{47} = -18.8760383379859
x48=87.970277977177x_{48} = 87.970277977177
x49=−72.26355003974x_{49} = -72.26355003974
x50=−3.29231002128209x_{50} = -3.29231002128209
x51=53.4164352526291x_{51} = 53.4164352526291
x52=−37.7123693157661x_{52} = -37.7123693157661
x53=−69.1222718113619x_{53} = -69.1222718113619
x54=−6.36162039206566x_{54} = -6.36162039206566
x55=−25.1526172579356x_{55} = -25.1526172579356
x56=9.4774857054208x_{56} = 9.4774857054208
x57=65.9810235167388x_{57} = 65.9810235167388
x58=−81.6875298021918x_{58} = -81.6875298021918
x59=100.535938219808x_{59} = 100.535938219808
x60=22.013857636623x_{60} = 22.013857636623
x61=−87.970277977177x_{61} = -87.970277977177
x62=59.6986356231676x_{62} = 59.6986356231676
x63=31.43183263459x_{63} = 31.43183263459
x64=−50.2754273458806x_{64} = -50.2754273458806
x65=6.36162039206566x_{65} = 6.36162039206566
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 cos(x)/((2*sqrt(x))) - sin(x)*sqrt(x).
cos⁡(0)20−0sin⁡(0)\frac{\cos{\left(0 \right)}}{2 \sqrt{0}} - \sqrt{0} \sin{\left(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
−12xsin⁡(x)−xcos⁡(x)−sin⁡(x)2x−cos⁡(x)4x32=0- \frac{1}{2 \sqrt{x}} \sin{\left(x \right)} - \sqrt{x} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{2 \sqrt{x}} - \frac{\cos{\left(x \right)}}{4 x^{\frac{3}{2}}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−36.1559611393004x_{1} = -36.1559611393004
x2=−48.7152085571549x_{2} = -48.7152085571549
x3=70.6999773315004x_{3} = 70.6999773315004
x4=−39.2953468672842x_{4} = -39.2953468672842
x5=23.6042658400483x_{5} = 23.6042658400483
x6=−124.100967466518x_{6} = -124.100967466518
x7=14.2073505099925x_{7} = 14.2073505099925
x8=2.0090972384408x_{8} = 2.0090972384408
x9=−80.1230923289863x_{9} = -80.1230923289863
x10=83.2642142711524x_{10} = 83.2642142711524
x11=20.4691384083001x_{11} = 20.4691384083001
x12=−83.2642142711524x_{12} = -83.2642142711524
x13=−64.4181707871237x_{13} = -64.4181707871237
x14=−92.6877714581404x_{14} = -92.6877714581404
x15=−58.136661973445x_{15} = -58.136661973445
x16=−23.6042658400483x_{16} = -23.6042658400483
x17=−17.3363302997334x_{17} = -17.3363302997334
x18=7.97819025123437x_{18} = 7.97819025123437
x19=80.1230923289863x_{19} = 80.1230923289863
x20=26.7409029817025x_{20} = 26.7409029817025
x21=−14.2073505099925x_{21} = -14.2073505099925
x22=42.4350586138523x_{22} = 42.4350586138523
x23=−7.97819025123437x_{23} = -7.97819025123437
x24=17.3363302997334x_{24} = 17.3363302997334
x25=−86.4053704242642x_{25} = -86.4053704242642
x26=−42.4350586138523x_{26} = -42.4350586138523
x27=−76.9820087826371x_{27} = -76.9820087826371
x28=4.91125081295869x_{28} = 4.91125081295869
x29=48.7152085571549x_{29} = 48.7152085571549
x30=76.9820087826371x_{30} = 76.9820087826371
x31=61.2773734476957x_{31} = 61.2773734476957
x32=58.136661973445x_{32} = 58.136661973445
x33=54.9960510556604x_{33} = 54.9960510556604
x34=89.5465571901753x_{34} = 89.5465571901753
x35=−11.0853581860961x_{35} = -11.0853581860961
x36=39.2953468672842x_{36} = 39.2953468672842
x37=−29.8785771570692x_{37} = -29.8785771570692
x38=−2.0090972384408x_{38} = -2.0090972384408
x39=92.6877714581404x_{39} = 92.6877714581404
x40=−51.8555589377593x_{40} = -51.8555589377593
x41=−70.6999773315004x_{41} = -70.6999773315004
x42=−67.559042028453x_{42} = -67.559042028453
x43=51.8555589377593x_{43} = 51.8555589377593
x44=−45.5750291575042x_{44} = -45.5750291575042
x45=67.559042028453x_{45} = 67.559042028453
x46=36.1559611393004x_{46} = 36.1559611393004
x47=−4.91125081295869x_{47} = -4.91125081295869
x48=95.8290105250036x_{48} = 95.8290105250036
x49=−20.4691384083001x_{49} = -20.4691384083001
x50=−95.8290105250036x_{50} = -95.8290105250036
x51=73.8409685283396x_{51} = 73.8409685283396
x52=−33.0169941017832x_{52} = -33.0169941017832
x53=−26.7409029817025x_{53} = -26.7409029817025
x54=45.5750291575042x_{54} = 45.5750291575042
x55=33.0169941017832x_{55} = 33.0169941017832
x56=29.8785771570692x_{56} = 29.8785771570692
x57=11.0853581860961x_{57} = 11.0853581860961
x58=−98.9702720305701x_{58} = -98.9702720305701
x59=−73.8409685283396x_{59} = -73.8409685283396
x60=98.9702720305701x_{60} = 98.9702720305701
x61=−133.525176756856x_{61} = -133.525176756856
x62=−89.5465571901753x_{62} = -89.5465571901753
x63=86.4053704242642x_{63} = 86.4053704242642
x64=−61.2773734476957x_{64} = -61.2773734476957
x65=64.4181707871237x_{65} = 64.4181707871237
x66=−54.9960510556604x_{66} = -54.9960510556604
Signos de extremos en los puntos:
(-36.15596113930037, -6.012983594342*I)

(-48.715208557154924, -6.97962841986057*I)

(70.6999773315004, -8.40832793996118)

(-39.29534686728419, 6.26860072900286*I)

(23.604265840048264, 4.85842605755917)

(-124.10096746651843, -11.140061387986*I)

(14.20735050999248, -3.76928687912344)

(2.009097238440804, -1.43315125662761)

(-80.12309232898626, -8.95115038980062*I)

(83.26421427115243, -9.12492274691236)

(20.469138408300097, -4.52428961282046)

(-83.26421427115243, 9.12492274691236*I)

(-64.4181707871237, 8.0260932374906*I)

(-92.68777145814039, -9.62744888773492*I)

(-58.13666197344501, 7.62474029176846*I)

(-23.604265840048264, -4.85842605755917*I)

(-17.33633029973344, -4.16370337379293*I)

(7.978190251234368, -2.82473930857575)

(80.12309232898626, 8.95115038980062)

(26.74090298170248, -5.17116322263798)

(-14.20735050999248, 3.76928687912344*I)

(42.43505861385231, 6.51422022591249)

(-7.978190251234368, 2.82473930857575*I)

(17.33633029973344, 4.16370337379293)

(-86.40537042426418, -9.29544895092167*I)

(-42.43505861385231, -6.51422022591249*I)

(-76.98200878263714, 8.77393924519306*I)

(4.911250812958692, 2.21703046556035)

(48.715208557154924, 6.97962841986057)

(76.98200878263714, -8.77393924519306)

(61.277373447695695, 7.82798669006771)

(58.13666197344501, -7.62474029176846)

(54.99605105566035, 7.41593244710852)

(89.54655719017528, -9.46290430504231)

(-11.08535818609612, -3.32952260910702*I)

(39.29534686728419, -6.26860072900286)

(-29.87857715706918, -5.46613170997848*I)

(-2.009097238440804, 1.43315125662761*I)

(92.68777145814039, 9.62744888773492)

(-51.85555893775929, 7.20108064956528*I)

(-70.6999773315004, 8.40832793996118*I)

(-67.55904202845302, -8.21943085921586*I)

(51.85555893775929, -7.20108064956528)

(-45.57502915750418, 6.75092841286144*I)

(67.55904202845302, 8.21943085921586)

(36.15596113930037, 6.012983594342)

(-4.911250812958692, -2.21703046556035*I)

(95.82901052500361, -9.78922934112189)

(-20.469138408300097, 4.52428961282046*I)

(-95.82901052500361, 9.78922934112189*I)

(73.84096852833959, 8.59307685115599)

(-33.01699410178322, 5.74604281000918*I)

(-26.74090298170248, 5.17116322263798*I)

(45.57502915750418, -6.75092841286144)

(33.01699410178322, -5.74604281000918)

(29.87857715706918, 5.46613170997848)

(11.08535818609612, 3.32952260910702)

(-98.97027203057014, -9.94838039814827*I)

(-73.84096852833959, -8.59307685115599*I)

(98.97027203057014, 9.94838039814827)

(-133.5251767568555, 11.5553094708393*I)

(-89.54655719017528, 9.46290430504231*I)

(86.40537042426418, 9.29544895092167)

(-61.277373447695695, -7.82798669006771*I)

(64.4181707871237, -8.0260932374906)

(-54.99605105566035, -7.41593244710852*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=70.6999773315004x_{1} = 70.6999773315004
x2=14.2073505099925x_{2} = 14.2073505099925
x3=2.0090972384408x_{3} = 2.0090972384408
x4=83.2642142711524x_{4} = 83.2642142711524
x5=20.4691384083001x_{5} = 20.4691384083001
x6=7.97819025123437x_{6} = 7.97819025123437
x7=26.7409029817025x_{7} = 26.7409029817025
x8=76.9820087826371x_{8} = 76.9820087826371
x9=58.136661973445x_{9} = 58.136661973445
x10=89.5465571901753x_{10} = 89.5465571901753
x11=39.2953468672842x_{11} = 39.2953468672842
x12=51.8555589377593x_{12} = 51.8555589377593
x13=95.8290105250036x_{13} = 95.8290105250036
x14=45.5750291575042x_{14} = 45.5750291575042
x15=33.0169941017832x_{15} = 33.0169941017832
x16=64.4181707871237x_{16} = 64.4181707871237
Puntos máximos de la función:
x16=23.6042658400483x_{16} = 23.6042658400483
x16=80.1230923289863x_{16} = 80.1230923289863
x16=42.4350586138523x_{16} = 42.4350586138523
x16=17.3363302997334x_{16} = 17.3363302997334
x16=4.91125081295869x_{16} = 4.91125081295869
x16=48.7152085571549x_{16} = 48.7152085571549
x16=61.2773734476957x_{16} = 61.2773734476957
x16=54.9960510556604x_{16} = 54.9960510556604
x16=92.6877714581404x_{16} = 92.6877714581404
x16=67.559042028453x_{16} = 67.559042028453
x16=36.1559611393004x_{16} = 36.1559611393004
x16=73.8409685283396x_{16} = 73.8409685283396
x16=29.8785771570692x_{16} = 29.8785771570692
x16=11.0853581860961x_{16} = 11.0853581860961
x16=98.9702720305701x_{16} = 98.9702720305701
x16=86.4053704242642x_{16} = 86.4053704242642
Decrece en los intervalos
[95.8290105250036,∞)\left[95.8290105250036, \infty\right)
Crece en los intervalos
(−∞,2.0090972384408]\left(-\infty, 2.0090972384408\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
xsin⁡(x)−3cos⁡(x)2x+3sin⁡(x)4x32+3cos⁡(x)8x52=0\sqrt{x} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{2 \sqrt{x}} + \frac{3 \sin{\left(x \right)}}{4 x^{\frac{3}{2}}} + \frac{3 \cos{\left(x \right)}}{8 x^{\frac{5}{2}}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−18.9284172407774x_{1} = -18.9284172407774
x2=−44.0163446553649x_{2} = -44.0163446553649
x3=62.8557066890505x_{3} = 62.8557066890505
x4=−9.57846466792013x_{4} = -9.57846466792013
x5=−97.4047690781613x_{5} = -97.4047690781613
x6=18.9284172407774x_{6} = 18.9284172407774
x7=75.4181066923052x_{7} = 75.4181066923052
x8=−56.5751666784434x_{8} = -56.5751666784434
x9=−37.7388099640801x_{9} = -37.7388099640801
x10=59.7153672610065x_{10} = 59.7153672610065
x11=15.8022274019163x_{11} = 15.8022274019163
x12=44.0163446553649x_{12} = 44.0163446553649
x13=−59.7153672610065x_{13} = -59.7153672610065
x14=6.50473400583617x_{14} = 6.50473400583617
x15=−12.6833672169842x_{15} = -12.6833672169842
x16=−25.1921200618651x_{16} = -25.1921200618651
x17=47.1556743292414x_{17} = 47.1556743292414
x18=−22.0589049145233x_{18} = -22.0589049145233
x19=40.8773612463173x_{19} = 40.8773612463173
x20=34.6008075318479x_{20} = 34.6008075318479
x21=−47.1556743292414x_{21} = -47.1556743292414
x22=−69.1367265780171x_{22} = -69.1367265780171
x23=56.5751666784434x_{23} = 56.5751666784434
x24=100.5458808954x_{24} = 100.5458808954
x25=37.7388099640801x_{25} = 37.7388099640801
x26=−53.4351293408419x_{26} = -53.4351293408419
x27=25.1921200618651x_{27} = 25.1921200618651
x28=−94.2636892826412x_{28} = -94.2636892826412
x29=91.1226448164971x_{29} = 91.1226448164971
x30=−87.9816394589817x_{30} = -87.9816394589817
x31=−31.4635167177703x_{31} = -31.4635167177703
x32=78.5589048799689x_{32} = 78.5589048799689
x33=−50.2952857125789x_{33} = -50.2952857125789
x34=−6.50473400583617x_{34} = -6.50473400583617
x35=−15.8022274019163x_{35} = -15.8022274019163
x36=65.9961651913669x_{36} = 65.9961651913669
x37=22.0589049145233x_{37} = 22.0589049145233
x38=28.3271714203016x_{38} = 28.3271714203016
x39=12.6833672169842x_{39} = 12.6833672169842
x40=−78.5589048799689x_{40} = -78.5589048799689
x41=−40.8773612463173x_{41} = -40.8773612463173
x42=94.2636892826412x_{42} = 94.2636892826412
x43=53.4351293408419x_{43} = 53.4351293408419
x44=69.1367265780171x_{44} = 69.1367265780171
x45=3.51691468883013x_{45} = 3.51691468883013
x46=72.2773774650779x_{46} = 72.2773774650779
x47=−28.3271714203016x_{47} = -28.3271714203016
x48=−75.4181066923052x_{48} = -75.4181066923052
x49=−84.8406775480584x_{49} = -84.8406775480584
x50=−65.9961651913669x_{50} = -65.9961651913669
x51=50.2952857125789x_{51} = 50.2952857125789
x52=−72.2773774650779x_{52} = -72.2773774650779
x53=−62.8557066890505x_{53} = -62.8557066890505
x54=−100.5458808954x_{54} = -100.5458808954
x55=87.9816394589817x_{55} = 87.9816394589817
x56=97.4047690781613x_{56} = 97.4047690781613
x57=−34.6008075318479x_{57} = -34.6008075318479
x58=84.8406775480584x_{58} = 84.8406775480584
x59=81.699764087558x_{59} = 81.699764087558
x60=9.57846466792013x_{60} = 9.57846466792013
x61=−91.1226448164971x_{61} = -91.1226448164971
x62=31.4635167177703x_{62} = 31.4635167177703
x63=−81.699764087558x_{63} = -81.699764087558
x64=−3.51691468883013x_{64} = -3.51691468883013
Además hay que calcular los límites de y'' para los argumentos tendientes a los puntos de indeterminación de la función:
Puntos donde hay indeterminación:
x1=0x_{1} = 0

lim⁡x→0−(xsin⁡(x)−3cos⁡(x)2x+3sin⁡(x)4x32+3cos⁡(x)8x52)=−∞i\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{2 \sqrt{x}} + \frac{3 \sin{\left(x \right)}}{4 x^{\frac{3}{2}}} + \frac{3 \cos{\left(x \right)}}{8 x^{\frac{5}{2}}}\right) = - \infty i
lim⁡x→0+(xsin⁡(x)−3cos⁡(x)2x+3sin⁡(x)4x32+3cos⁡(x)8x52)=∞\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{2 \sqrt{x}} + \frac{3 \sin{\left(x \right)}}{4 x^{\frac{3}{2}}} + \frac{3 \cos{\left(x \right)}}{8 x^{\frac{5}{2}}}\right) = \infty
- los límites no son iguales, signo
x1=0x_{1} = 0
- es el punto de flexión

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
[100.5458808954,∞)\left[100.5458808954, \infty\right)
Convexa en los intervalos
(−∞,6.50473400583617]\left(-\infty, 6.50473400583617\right]
Asíntotas verticales
Hay:
x1=0x_{1} = 0
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→−∞(−xsin⁡(x)+cos⁡(x)2x)y = \lim_{x \to -\infty}\left(- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(−xsin⁡(x)+cos⁡(x)2x)y = \lim_{x \to \infty}\left(- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(x)/((2*sqrt(x))) - sin(x)*sqrt(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→−∞(−xsin⁡(x)+cos⁡(x)2xx)y = x \lim_{x \to -\infty}\left(\frac{- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(−xsin⁡(x)+cos⁡(x)2xx)y = x \lim_{x \to \infty}\left(\frac{- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}}}{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:
−xsin⁡(x)+cos⁡(x)2x=−xsin⁡(x)+cos⁡(x)2−x- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}} = \sqrt{- x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{- x}}
- No
−xsin⁡(x)+cos⁡(x)2x=−−xsin⁡(x)−cos⁡(x)2−x- \sqrt{x} \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2 \sqrt{x}} = - \sqrt{- x} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2 \sqrt{- x}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор