Sr Examen

Otras calculadoras

Trazado el gráfico de la función/ xsinx+(+e^x-e^x)/(e^-x+e^x)

Gráfico de la función y = xsinx+(+e^x-e^x)/(e^-x+e^x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                   x    x 
                  E  - E  
f(x) = x*sin(x) + --------
                   -x    x
                  E   + E
f(x)=xsin⁡(x)+−ex+exex+e−xf{\left(x \right)} = x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}} 
f = x*sin(x) + (-E^x + E^x)/(E^x + E^(-x))
Gráfico de la función
02468-8-6-4-2-1010-1010
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)+−ex+exex+e−x=0x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=40.8407044966673x_{1} = 40.8407044966673
x2=0x_{2} = 0
x3=−18.8495559215388x_{3} = -18.8495559215388
x4=−56.5486677646163x_{4} = -56.5486677646163
x5=97.3893722612836x_{5} = 97.3893722612836
x6=34.5575191894877x_{6} = 34.5575191894877
x7=53.4070751110265x_{7} = 53.4070751110265
x8=47.1238898038469x_{8} = 47.1238898038469
x9=−97.3893722612836x_{9} = -97.3893722612836
x10=62.8318530717959x_{10} = 62.8318530717959
x11=87.9645943005142x_{11} = 87.9645943005142
x12=43.9822971502571x_{12} = 43.9822971502571
x13=37.6991118430775x_{13} = 37.6991118430775
x14=−21.9911485751286x_{14} = -21.9911485751286
x15=3.14159265358979x_{15} = 3.14159265358979
x16=69.1150383789755x_{16} = 69.1150383789755
x17=65.9734457253857x_{17} = 65.9734457253857
x18=−50.2654824574367x_{18} = -50.2654824574367
x19=−94.2477796076938x_{19} = -94.2477796076938
x20=−75.398223686155x_{20} = -75.398223686155
x21=−53.4070751110265x_{21} = -53.4070751110265
x22=12.5663706143592x_{22} = 12.5663706143592
x23=−9.42477796076938x_{23} = -9.42477796076938
x24=−34.5575191894877x_{24} = -34.5575191894877
x25=21.9911485751286x_{25} = 21.9911485751286
x26=−47.1238898038469x_{26} = -47.1238898038469
x27=−43.9822971502571x_{27} = -43.9822971502571
x28=28.2743338823081x_{28} = 28.2743338823081
x29=−31.4159265358979x_{29} = -31.4159265358979
x30=−3.14159265358979x_{30} = -3.14159265358979
x31=−6.28318530717959x_{31} = -6.28318530717959
x32=−25.1327412287183x_{32} = -25.1327412287183
x33=−62.8318530717959x_{33} = -62.8318530717959
x34=31.4159265358979x_{34} = 31.4159265358979
x35=−65.9734457253857x_{35} = -65.9734457253857
x36=72.2566310325652x_{36} = 72.2566310325652
x37=−59.6902604182061x_{37} = -59.6902604182061
x38=94.2477796076938x_{38} = 94.2477796076938
x39=81.6814089933346x_{39} = 81.6814089933346
x40=−91.106186954104x_{40} = -91.106186954104
x41=−100.530964914873x_{41} = -100.530964914873
x42=59.6902604182061x_{42} = 59.6902604182061
x43=−40.8407044966673x_{43} = -40.8407044966673
x44=91.106186954104x_{44} = 91.106186954104
x45=78.5398163397448x_{45} = 78.5398163397448
x46=−12.5663706143592x_{46} = -12.5663706143592
x47=56.5486677646163x_{47} = 56.5486677646163
x48=697.433569096934x_{48} = 697.433569096934
x49=84.8230016469244x_{49} = 84.8230016469244
x50=100.530964914873x_{50} = 100.530964914873
x51=−69.1150383789755x_{51} = -69.1150383789755
x52=9.42477796076938x_{52} = 9.42477796076938
x53=−84.8230016469244x_{53} = -84.8230016469244
x54=−78.5398163397448x_{54} = -78.5398163397448
x55=−87.9645943005142x_{55} = -87.9645943005142
x56=−81.6814089933346x_{56} = -81.6814089933346
x57=15.707963267949x_{57} = 15.707963267949
x58=−28.2743338823081x_{58} = -28.2743338823081
x59=−15.707963267949x_{59} = -15.707963267949
x60=−37.6991118430775x_{60} = -37.6991118430775
x61=18.8495559215388x_{61} = 18.8495559215388
x62=25.1327412287183x_{62} = 25.1327412287183
x63=50.2654824574367x_{63} = 50.2654824574367
x64=−72.2566310325652x_{64} = -72.2566310325652
x65=75.398223686155x_{65} = 75.398223686155
x66=6.28318530717959x_{66} = 6.28318530717959
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 x*sin(x) + (E^x - E^x)/(E^(-x) + E^x).
0sin⁡(0)+−e0+e0e−0+e00 \sin{\left(0 \right)} + \frac{- e^{0} + e^{0}}{e^{- 0} + e^{0}}
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
xcos⁡(x)+(−ex+ex)(−ex+e−x)(ex+e−x)2+sin⁡(x)+ex−exex+e−x=0x \cos{\left(x \right)} + \frac{\left(- e^{x} + e^{x}\right) \left(- e^{x} + e^{- x}\right)}{\left(e^{x} + e^{- x}\right)^{2}} + \sin{\left(x \right)} + \frac{e^{x} - e^{x}}{e^{x} + e^{- x}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−67.5590428388084x_{1} = -67.5590428388084
x2=−92.687771772017x_{2} = -92.687771772017
x3=2.02875783811043x_{3} = 2.02875783811043
x4=20.469167402741x_{4} = 20.469167402741
x5=0x_{5} = 0
x6=−83.2642147040886x_{6} = -83.2642147040886
x7=58.1366632448992x_{7} = 58.1366632448992
x8=−54.9960525574964x_{8} = -54.9960525574964
x9=39.295350981473x_{9} = 39.295350981473
x10=80.1230928148503x_{10} = 80.1230928148503
x11=92.687771772017x_{11} = 92.687771772017
x12=−4.91318043943488x_{12} = -4.91318043943488
x13=61.2773745335697x_{13} = 61.2773745335697
x14=−95.8290108090195x_{14} = -95.8290108090195
x15=73.8409691490209x_{15} = 73.8409691490209
x16=−20.469167402741x_{16} = -20.469167402741
x17=26.7409160147873x_{17} = 26.7409160147873
x18=−36.1559664195367x_{18} = -36.1559664195367
x19=42.4350618814099x_{19} = 42.4350618814099
x20=−11.085538406497x_{20} = -11.085538406497
x21=70.69997803861x_{21} = 70.69997803861
x22=−45.57503179559x_{22} = -45.57503179559
x23=89.5465575382492x_{23} = 89.5465575382492
x24=54.9960525574964x_{24} = 54.9960525574964
x25=48.7152107175577x_{25} = 48.7152107175577
x26=−73.8409691490209x_{26} = -73.8409691490209
x27=98.9702722883957x_{27} = 98.9702722883957
x28=−86.4053708116885x_{28} = -86.4053708116885
x29=−23.6042847729804x_{29} = -23.6042847729804
x30=−51.855560729152x_{30} = -51.855560729152
x31=−17.3363779239834x_{31} = -17.3363779239834
x32=11.085538406497x_{32} = 11.085538406497
x33=−7.97866571241324x_{33} = -7.97866571241324
x34=−33.0170010333572x_{34} = -33.0170010333572
x35=−14.2074367251912x_{35} = -14.2074367251912
x36=4.91318043943488x_{36} = 4.91318043943488
x37=−29.8785865061074x_{37} = -29.8785865061074
x38=45.57503179559x_{38} = 45.57503179559
x39=86.4053708116885x_{39} = 86.4053708116885
x40=64.4181717218392x_{40} = 64.4181717218392
x41=−58.1366632448992x_{41} = -58.1366632448992
x42=−89.5465575382492x_{42} = -89.5465575382492
x43=17.3363779239834x_{43} = 17.3363779239834
x44=−61.2773745335697x_{44} = -61.2773745335697
x45=33.0170010333572x_{45} = 33.0170010333572
x46=−39.295350981473x_{46} = -39.295350981473
x47=−48.7152107175577x_{47} = -48.7152107175577
x48=51.855560729152x_{48} = 51.855560729152
x49=−70.69997803861x_{49} = -70.69997803861
x50=67.5590428388084x_{50} = 67.5590428388084
x51=83.2642147040886x_{51} = 83.2642147040886
x52=95.8290108090195x_{52} = 95.8290108090195
x53=102.111554139654x_{53} = 102.111554139654
x54=14.2074367251912x_{54} = 14.2074367251912
x55=−64.4181717218392x_{55} = -64.4181717218392
x56=−98.9702722883957x_{56} = -98.9702722883957
x57=−42.4350618814099x_{57} = -42.4350618814099
x58=−76.9820093304187x_{58} = -76.9820093304187
x59=76.9820093304187x_{59} = 76.9820093304187
x60=−2.02875783811043x_{60} = -2.02875783811043
x61=7.97866571241324x_{61} = 7.97866571241324
x62=36.1559664195367x_{62} = 36.1559664195367
x63=23.6042847729804x_{63} = 23.6042847729804
x64=−80.1230928148503x_{64} = -80.1230928148503
x65=29.8785865061074x_{65} = 29.8785865061074
x66=−26.7409160147873x_{66} = -26.7409160147873
Signos de extremos en los puntos:
(-67.5590428388084, -67.5516431209725)

(-92.687771772017, -92.6823777880592)

(2.028757838110434, 1.81970574115965)

(20.46916740274095, 20.4447840582523)

(0, 0)

(-83.26421470408864, 83.2582103729533)

(58.13666324489916, 58.1280647280857)

(-54.99605255749639, -54.9869632496976)

(39.295350981472986, 39.2826330068918)

(80.12309281485025, -80.1168531456592)

(92.687771772017, -92.6823777880592)

(-4.913180439434884, -4.81446988971227)

(61.277374533569656, -61.2692165444766)

(-95.82901080901948, 95.8237936084657)

(73.8409691490209, -73.8341987715416)

(-20.46916740274095, 20.4447840582523)

(26.74091601478731, 26.7222376646974)

(-36.15596641953672, -36.1421453722421)

(42.43506188140989, -42.4232840772591)

(-11.085538406497022, -11.04070801593)

(70.69997803861, 70.6929069615931)

(-45.57503179559002, 45.5640648360268)

(89.54655753824919, 89.5409743728852)

(54.99605255749639, -54.9869632496976)

(48.715210717557724, -48.7049502253679)

(-73.8409691490209, -73.8341987715416)

(98.9702722883957, -98.9652206531187)

(-86.40537081168854, -86.3995847156108)

(-23.604284772980407, -23.5831306496334)

(-51.85556072915197, 51.8459212502015)

(-17.33637792398336, -17.3076086078585)

(11.085538406497022, -11.04070801593)

(-7.978665712413241, 7.91672737158778)

(-33.017001033357246, 33.0018677308454)

(-14.207436725191188, 14.1723741137743)

(4.913180439434884, -4.81446988971227)

(-29.878586506107393, -29.8618661591868)

(45.57503179559002, 45.5640648360268)

(86.40537081168854, -86.3995847156108)

(64.41817172183916, 64.4104113393753)

(-58.13666324489916, 58.1280647280857)

(-89.54655753824919, 89.5409743728852)

(17.33637792398336, -17.3076086078585)

(-61.277374533569656, -61.2692165444766)

(33.017001033357246, 33.0018677308454)

(-39.295350981472986, 39.2826330068918)

(-48.715210717557724, -48.7049502253679)

(51.85556072915197, 51.8459212502015)

(-70.69997803861, 70.6929069615931)

(67.5590428388084, -67.5516431209725)

(83.26421470408864, 83.2582103729533)

(95.82901080901948, 95.8237936084657)

(102.11155413965392, 102.106657886316)

(14.207436725191188, 14.1723741137743)

(-64.41817172183916, 64.4104113393753)

(-98.9702722883957, -98.9652206531187)

(-42.43506188140989, -42.4232840772591)

(-76.98200933041872, 76.9755151282637)

(76.98200933041872, 76.9755151282637)

(-2.028757838110434, 1.81970574115965)

(7.978665712413241, 7.91672737158778)

(36.15596641953672, -36.1421453722421)

(23.604284772980407, -23.5831306496334)

(-80.12309281485025, -80.1168531456592)

(29.878586506107393, -29.8618661591868)

(-26.74091601478731, 26.7222376646974)


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

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
[97.4099011706723,∞)\left[97.4099011706723, \infty\right)
Convexa en los intervalos
(−∞,−100.550852725424]\left(-\infty, -100.550852725424\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(xsin⁡(x)+−ex+exex+e−x)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}}\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→∞(xsin⁡(x)+−ex+exex+e−x)=⟨−∞,∞⟩\lim_{x \to \infty}\left(x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}}\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 x*sin(x) + (E^x - E^x)/(E^(-x) + E^x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(xsin⁡(x)+−ex+exex+e−xx)=⟨−1,1⟩\lim_{x \to -\infty}\left(\frac{x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞(xsin⁡(x)+−ex+exex+e−xx)=⟨−1,1⟩\lim_{x \to \infty}\left(\frac{x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
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)+−ex+exex+e−x=xsin⁡(x)x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}} = x \sin{\left(x \right)}
- No
xsin⁡(x)+−ex+exex+e−x=−xsin⁡(x)x \sin{\left(x \right)} + \frac{- e^{x} + e^{x}}{e^{x} + e^{- x}} = - x \sin{\left(x \right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор