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Trazado el gráfico de la función/ sqrt(x^4+1)sinx

Gráfico de la función y = sqrt(x^4+1)sinx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
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         /  4            
f(x) = \/  x  + 1 *sin(x)
f(x)=x4+1sin⁡(x)f{\left(x \right)} = \sqrt{x^{4} + 1} \sin{\left(x \right)} 
f = sqrt(x^4 + 1)*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:
x4+1sin⁡(x)=0\sqrt{x^{4} + 1} \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
x2=πx_{2} = \pi
Solución numérica
x1=62.8318530717959x_{1} = 62.8318530717959
x2=−50.2654824574367x_{2} = -50.2654824574367
x3=47.1238898038469x_{3} = 47.1238898038469
x4=84.8230016469244x_{4} = 84.8230016469244
x5=−53.4070751110265x_{5} = -53.4070751110265
x6=91.106186954104x_{6} = 91.106186954104
x7=−84.8230016469244x_{7} = -84.8230016469244
x8=25.1327412287183x_{8} = 25.1327412287183
x9=−3.14159265358979x_{9} = -3.14159265358979
x10=−6.28318530717959x_{10} = -6.28318530717959
x11=−40.8407044966673x_{11} = -40.8407044966673
x12=−18.8495559215388x_{12} = -18.8495559215388
x13=78.5398163397448x_{13} = 78.5398163397448
x14=−75.398223686155x_{14} = -75.398223686155
x15=−9.42477796076938x_{15} = -9.42477796076938
x16=72.2566310325652x_{16} = 72.2566310325652
x17=−43.9822971502571x_{17} = -43.9822971502571
x18=31.4159265358979x_{18} = 31.4159265358979
x19=9.42477796076938x_{19} = 9.42477796076938
x20=40.8407044966673x_{20} = 40.8407044966673
x21=−69.1150383789755x_{21} = -69.1150383789755
x22=12.5663706143592x_{22} = 12.5663706143592
x23=87.9645943005142x_{23} = 87.9645943005142
x24=59.6902604182061x_{24} = 59.6902604182061
x25=−37.6991118430775x_{25} = -37.6991118430775
x26=−100.530964914873x_{26} = -100.530964914873
x27=−91.106186954104x_{27} = -91.106186954104
x28=97.3893722612836x_{28} = 97.3893722612836
x29=0x_{29} = 0
x30=−12.5663706143592x_{30} = -12.5663706143592
x31=−78.5398163397448x_{31} = -78.5398163397448
x32=18.8495559215388x_{32} = 18.8495559215388
x33=34.5575191894877x_{33} = 34.5575191894877
x34=−94.2477796076938x_{34} = -94.2477796076938
x35=43.9822971502571x_{35} = 43.9822971502571
x36=−31.4159265358979x_{36} = -31.4159265358979
x37=−81.6814089933346x_{37} = -81.6814089933346
x38=−65.9734457253857x_{38} = -65.9734457253857
x39=75.398223686155x_{39} = 75.398223686155
x40=56.5486677646163x_{40} = 56.5486677646163
x41=3.14159265358979x_{41} = 3.14159265358979
x42=15.707963267949x_{42} = 15.707963267949
x43=−106.814150222053x_{43} = -106.814150222053
x44=−56.5486677646163x_{44} = -56.5486677646163
x45=−21.9911485751286x_{45} = -21.9911485751286
x46=50.2654824574367x_{46} = 50.2654824574367
x47=−15.707963267949x_{47} = -15.707963267949
x48=28.2743338823081x_{48} = 28.2743338823081
x49=94.2477796076938x_{49} = 94.2477796076938
x50=−59.6902604182061x_{50} = -59.6902604182061
x51=−62.8318530717959x_{51} = -62.8318530717959
x52=69.1150383789755x_{52} = 69.1150383789755
x53=−34.5575191894877x_{53} = -34.5575191894877
x54=−97.3893722612836x_{54} = -97.3893722612836
x55=21.9911485751286x_{55} = 21.9911485751286
x56=65.9734457253857x_{56} = 65.9734457253857
x57=37.6991118430775x_{57} = 37.6991118430775
x58=−87.9645943005142x_{58} = -87.9645943005142
x59=−72.2566310325652x_{59} = -72.2566310325652
x60=−25.1327412287183x_{60} = -25.1327412287183
x61=−28.2743338823081x_{61} = -28.2743338823081
x62=81.6814089933346x_{62} = 81.6814089933346
x63=6.28318530717959x_{63} = 6.28318530717959
x64=100.530964914873x_{64} = 100.530964914873
x65=53.4070751110265x_{65} = 53.4070751110265
x66=−47.1238898038469x_{66} = -47.1238898038469
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 sqrt(x^4 + 1)*sin(x).
04+1sin⁡(0)\sqrt{0^{4} + 1} \sin{\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
2x3sin⁡(x)x4+1+x4+1cos⁡(x)=0\frac{2 x^{3} \sin{\left(x \right)}}{\sqrt{x^{4} + 1}} + \sqrt{x^{4} + 1} \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−58.1538420756433x_{1} = -58.1538420756433
x2=55.0142096748772x_{2} = 55.0142096748772
x3=−48.7357007876494x_{3} = -48.7357007876494
x4=26.7780869315087x_{4} = 26.7780869315087
x5=8.09611093920912x_{5} = 8.09611093920912
x6=86.416937453702x_{6} = 86.416937453702
x7=80.1355651934698x_{7} = 80.1355651934698
x8=2.27401098372717x_{8} = 2.27401098372717
x9=−33.0471686442417x_{9} = -33.0471686442417
x10=17.3932427326438x_{10} = 17.3932427326438
x11=−36.1835330586538x_{11} = -36.1835330586538
x12=76.9949898884292x_{12} = 76.9949898884292
x13=−14.2763496424155x_{13} = -14.2763496424155
x14=23.6463235519488x_{14} = 23.6463235519488
x15=61.2936749639348x_{15} = 61.2936749639348
x16=−51.8748140481145x_{16} = -51.8748140481145
x17=29.9118937865844x_{17} = 29.9118937865844
x18=−95.8394411409859x_{18} = -95.8394411409859
x19=83.2762171644786x_{19} = 83.2762171644786
x20=−83.2762171644786x_{20} = -83.2762171644786
x21=−2.27401098372717x_{21} = -2.27401098372717
x22=−23.6463235519488x_{22} = -23.6463235519488
x23=48.7357007876494x_{23} = 48.7357007876494
x24=−70.7141100654188x_{24} = -70.7141100654188
x25=−67.5738306694413x_{25} = -67.5738306694413
x26=−26.7780869315087x_{26} = -26.7780869315087
x27=−80.1355651934698x_{27} = -80.1355651934698
x28=11.1726949079708x_{28} = 11.1726949079708
x29=67.5738306694413x_{29} = 67.5738306694413
x30=−17.3932427326438x_{30} = -17.3932427326438
x31=−11.1726949079708x_{31} = -11.1726949079708
x32=5.08650888897104x_{32} = 5.08650888897104
x33=45.5969279739554x_{33} = 45.5969279739554
x34=−92.6985552431049x_{34} = -92.6985552431049
x35=−64.4336791019334x_{35} = -64.4336791019334
x36=64.4336791019334x_{36} = 64.4336791019334
x37=20.5175223676203x_{37} = 20.5175223676203
x38=−73.8545010139956x_{38} = -73.8545010139956
x39=−61.2936749639348x_{39} = -61.2936749639348
x40=−8.09611093920912x_{40} = -8.09611093920912
x41=70.7141100654188x_{41} = 70.7141100654188
x42=−98.9803718649419x_{42} = -98.9803718649419
x43=−55.0142096748772x_{43} = -55.0142096748772
x44=33.0471686442417x_{44} = 33.0471686442417
x45=14.2763496424155x_{45} = 14.2763496424155
x46=−20.5175223676203x_{46} = -20.5175223676203
x47=39.3207281110568x_{47} = 39.3207281110568
x48=73.8545010139956x_{48} = 73.8545010139956
x49=95.8394411409859x_{49} = 95.8394411409859
x50=36.1835330586538x_{50} = 36.1835330586538
x51=89.5577188823775x_{51} = 89.5577188823775
x52=58.1538420756433x_{52} = 58.1538420756433
x53=98.9803718649419x_{53} = 98.9803718649419
x54=−29.9118937865844x_{54} = -29.9118937865844
x55=92.6985552431049x_{55} = 92.6985552431049
x56=−39.3207281110568x_{56} = -39.3207281110568
x57=−86.416937453702x_{57} = -86.416937453702
x58=42.4585707572526x_{58} = 42.4585707572526
x59=−120.967848975616x_{59} = -120.967848975616
x60=−45.5969279739554x_{60} = -45.5969279739554
x61=−76.9949898884292x_{61} = -76.9949898884292
x62=−42.4585707572526x_{62} = -42.4585707572526
x63=−5.08650888897104x_{63} = -5.08650888897104
x64=−89.5577188823775x_{64} = -89.5577188823775
x65=51.8748140481145x_{65} = 51.8748140481145
Signos de extremos en los puntos:
(-58.15384207564329, -3379.87126868766)

(55.01420967487721, -3024.5654119477)

(-48.73570078764938, 2373.17126490142)

(26.77808693150872, 715.074971498585)

(8.09611093920912, 63.6423870222484)

(86.41693745370205, -7465.88794896579)

(80.13556519346982, -6419.70982065644)

(2.274010983727173, 4.017441396991)

(-33.04716864424169, -1090.12129293741)

(17.393242732643767, -300.546194590824)

(-36.18353305865376, 1307.25301939262)

(76.99498988842922, 5926.2295638848)

(-14.276349642415454, -201.845647358065)

(23.646323551948804, -557.160188243519)

(61.29367496393478, -3754.9163195241)

(-51.87481404811451, -2688.9987456436)

(29.911893786584415, -892.728633563238)

(-95.83944114098585, -9183.19918567532)

(83.27621716447861, 6932.92928215645)

(-83.27621716447861, -6932.92928215645)

(-2.274010983727173, -4.017441396991)

(-23.646323551948804, 557.160188243519)

(48.73570078764938, -2373.17126490142)

(-70.71411006541877, -4998.4866615385)

(-67.57383066944135, 4564.2240140236)

(-26.77808693150872, -715.074971498585)

(-80.13556519346982, 6419.70982065644)

(11.172694907970815, -122.880116253604)

(67.57383066944135, -4564.2240140236)

(-17.393242732643767, 300.546194590824)

(-11.172694907970815, 122.880116253604)

(5.086508888971037, -24.1009388795436)

(45.59692797395535, 2077.08296311772)

(-92.69855524310493, 8591.02290035653)

(-64.43367910193336, -4149.70056724943)

(64.43367910193336, 4149.70056724943)

(20.51752236762027, 418.984069404483)

(-73.85450101399563, 5452.48851113455)

(-61.29367496393478, 3754.9163195241)

(-8.09611093920912, -63.6423870222484)

(70.71411006541877, 4998.4866615385)

(-98.98037186494189, 9795.11467780581)

(-55.01420967487721, 3024.5654119477)

(33.04716864424169, 1090.12129293741)

(14.276349642415454, 201.845647358065)

(-20.51752236762027, -418.984069404483)

(39.32072811105681, 1544.12385615838)

(73.85450101399563, -5452.48851113455)

(95.83944114098585, 9183.19918567532)

(36.18353305865376, -1307.25301939262)

(89.55771888237753, 8018.58582156549)

(58.15384207564329, 3379.87126868766)

(98.98037186494189, -9795.11467780581)

(-29.911893786584415, 892.728633563238)

(92.69855524310493, -8591.02290035653)

(-39.32072811105681, -1544.12385615838)

(-86.41693745370205, 7465.88794896579)

(42.45857075725264, -1800.73383116802)

(-120.9678489756161, -14631.2209299029)

(-45.59692797395535, -2077.08296311772)

(-76.99498988842922, -5926.2295638848)

(-42.45857075725264, 1800.73383116802)

(-5.086508888971037, 24.1009388795436)

(-89.55771888237753, -8018.58582156549)

(51.87481404811451, 2688.9987456436)


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=−58.1538420756433x_{1} = -58.1538420756433
x2=55.0142096748772x_{2} = 55.0142096748772
x3=86.416937453702x_{3} = 86.416937453702
x4=80.1355651934698x_{4} = 80.1355651934698
x5=−33.0471686442417x_{5} = -33.0471686442417
x6=17.3932427326438x_{6} = 17.3932427326438
x7=−14.2763496424155x_{7} = -14.2763496424155
x8=23.6463235519488x_{8} = 23.6463235519488
x9=61.2936749639348x_{9} = 61.2936749639348
x10=−51.8748140481145x_{10} = -51.8748140481145
x11=29.9118937865844x_{11} = 29.9118937865844
x12=−95.8394411409859x_{12} = -95.8394411409859
x13=−83.2762171644786x_{13} = -83.2762171644786
x14=−2.27401098372717x_{14} = -2.27401098372717
x15=48.7357007876494x_{15} = 48.7357007876494
x16=−70.7141100654188x_{16} = -70.7141100654188
x17=−26.7780869315087x_{17} = -26.7780869315087
x18=11.1726949079708x_{18} = 11.1726949079708
x19=67.5738306694413x_{19} = 67.5738306694413
x20=5.08650888897104x_{20} = 5.08650888897104
x21=−64.4336791019334x_{21} = -64.4336791019334
x22=−8.09611093920912x_{22} = -8.09611093920912
x23=−20.5175223676203x_{23} = -20.5175223676203
x24=73.8545010139956x_{24} = 73.8545010139956
x25=36.1835330586538x_{25} = 36.1835330586538
x26=98.9803718649419x_{26} = 98.9803718649419
x27=92.6985552431049x_{27} = 92.6985552431049
x28=−39.3207281110568x_{28} = -39.3207281110568
x29=42.4585707572526x_{29} = 42.4585707572526
x30=−120.967848975616x_{30} = -120.967848975616
x31=−45.5969279739554x_{31} = -45.5969279739554
x32=−76.9949898884292x_{32} = -76.9949898884292
x33=−89.5577188823775x_{33} = -89.5577188823775
Puntos máximos de la función:
x33=−48.7357007876494x_{33} = -48.7357007876494
x33=26.7780869315087x_{33} = 26.7780869315087
x33=8.09611093920912x_{33} = 8.09611093920912
x33=2.27401098372717x_{33} = 2.27401098372717
x33=−36.1835330586538x_{33} = -36.1835330586538
x33=76.9949898884292x_{33} = 76.9949898884292
x33=83.2762171644786x_{33} = 83.2762171644786
x33=−23.6463235519488x_{33} = -23.6463235519488
x33=−67.5738306694413x_{33} = -67.5738306694413
x33=−80.1355651934698x_{33} = -80.1355651934698
x33=−17.3932427326438x_{33} = -17.3932427326438
x33=−11.1726949079708x_{33} = -11.1726949079708
x33=45.5969279739554x_{33} = 45.5969279739554
x33=−92.6985552431049x_{33} = -92.6985552431049
x33=64.4336791019334x_{33} = 64.4336791019334
x33=20.5175223676203x_{33} = 20.5175223676203
x33=−73.8545010139956x_{33} = -73.8545010139956
x33=−61.2936749639348x_{33} = -61.2936749639348
x33=70.7141100654188x_{33} = 70.7141100654188
x33=−98.9803718649419x_{33} = -98.9803718649419
x33=−55.0142096748772x_{33} = -55.0142096748772
x33=33.0471686442417x_{33} = 33.0471686442417
x33=14.2763496424155x_{33} = 14.2763496424155
x33=39.3207281110568x_{33} = 39.3207281110568
x33=95.8394411409859x_{33} = 95.8394411409859
x33=89.5577188823775x_{33} = 89.5577188823775
x33=58.1538420756433x_{33} = 58.1538420756433
x33=−29.9118937865844x_{33} = -29.9118937865844
x33=−86.416937453702x_{33} = -86.416937453702
x33=−42.4585707572526x_{33} = -42.4585707572526
x33=−5.08650888897104x_{33} = -5.08650888897104
x33=51.8748140481145x_{33} = 51.8748140481145
Decrece en los intervalos
[98.9803718649419,∞)\left[98.9803718649419, \infty\right)
Crece en los intervalos
(−∞,−120.967848975616]\left(-\infty, -120.967848975616\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
4x3cos⁡(x)x4+1−2x2(2x4x4+1−3)sin⁡(x)x4+1−x4+1sin⁡(x)=0\frac{4 x^{3} \cos{\left(x \right)}}{\sqrt{x^{4} + 1}} - \frac{2 x^{2} \left(\frac{2 x^{4}}{x^{4} + 1} - 3\right) \sin{\left(x \right)}}{\sqrt{x^{4} + 1}} - \sqrt{x^{4} + 1} \sin{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−53.4817799789455x_{1} = -53.4817799789455
x2=28.41453048646x_{2} = 28.41453048646
x3=−50.3448302918139x_{3} = -50.3448302918139
x4=53.4817799789455x_{4} = 53.4817799789455
x5=75.45120707484x_{5} = 75.45120707484
x6=−6.83196356018755x_{6} = -6.83196356018755
x7=37.8046732358694x_{7} = 37.8046732358694
x8=−81.7303260370767x_{8} = -81.7303260370767
x9=0x_{9} = 0
x10=−31.5423182463494x_{10} = -31.5423182463494
x11=−47.2084939664123x_{11} = -47.2084939664123
x12=97.4304127975961x_{12} = 97.4304127975961
x13=−69.1728243282305x_{13} = -69.1728243282305
x14=−94.2901859448715x_{14} = -94.2901859448715
x15=91.1500530445447x_{15} = 91.1500530445447
x16=66.0339743689613x_{16} = 66.0339743689613
x17=−66.0339743689613x_{17} = -66.0339743689613
x18=3.99300538818266x_{18} = 3.99300538818266
x19=−40.93821913714x_{19} = -40.93821913714
x20=−25.2900901212458x_{20} = -25.2900901212458
x21=19.057554646609x_{21} = 19.057554646609
x22=25.2900901212458x_{22} = 25.2900901212458
x23=50.3448302918139x_{23} = 50.3448302918139
x24=84.8701107007429x_{24} = 84.8701107007429
x25=−44.0729006524718x_{25} = -44.0729006524718
x26=9.81896741633234x_{26} = 9.81896741633234
x27=69.1728243282305x_{27} = 69.1728243282305
x28=−75.45120707484x_{28} = -75.45120707484
x29=−78.5906855181598x_{29} = -78.5906855181598
x30=62.8953972306274x_{30} = 62.8953972306274
x31=6.83196356018755x_{31} = 6.83196356018755
x32=78.5906855181598x_{32} = 78.5906855181598
x33=12.8711305060002x_{33} = 12.8711305060002
x34=100.570724821458x_{34} = 100.570724821458
x35=−72.311911736267x_{35} = -72.311911736267
x36=−62.8953972306274x_{36} = -62.8953972306274
x37=22.1703623904462x_{37} = 22.1703623904462
x38=−34.6725660577115x_{38} = -34.6725660577115
x39=34.6725660577115x_{39} = 34.6725660577115
x40=47.2084939664123x_{40} = 47.2084939664123
x41=−91.1500530445447x_{41} = -91.1500530445447
x42=−9.81896741633234x_{42} = -9.81896741633234
x43=−37.8046732358694x_{43} = -37.8046732358694
x44=−56.6192418182967x_{44} = -56.6192418182967
x45=−100.570724821458x_{45} = -100.570724821458
x46=−84.8701107007429x_{46} = -84.8701107007429
x47=−1.54003325855922x_{47} = -1.54003325855922
x48=−88.0100241268019x_{48} = -88.0100241268019
x49=94.2901859448715x_{49} = 94.2901859448715
x50=−59.7571356630462x_{50} = -59.7571356630462
x51=1.54003325855922x_{51} = 1.54003325855922
x52=59.7571356630462x_{52} = 59.7571356630462
x53=−97.4304127975961x_{53} = -97.4304127975961
x54=72.311911736267x_{54} = 72.311911736267
x55=40.93821913714x_{55} = 40.93821913714
x56=−19.057554646609x_{56} = -19.057554646609
x57=81.7303260370767x_{57} = 81.7303260370767
x58=15.9554618481138x_{58} = 15.9554618481138
x59=−3.99300538818266x_{59} = -3.99300538818266
x60=56.6192418182967x_{60} = 56.6192418182967
x61=44.0729006524718x_{61} = 44.0729006524718
x62=−15.9554618481138x_{62} = -15.9554618481138
x63=31.5423182463494x_{63} = 31.5423182463494
x64=−28.41453048646x_{64} = -28.41453048646
x65=−12.8711305060002x_{65} = -12.8711305060002
x66=−22.1703623904462x_{66} = -22.1703623904462
x67=88.0100241268019x_{67} = 88.0100241268019

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
[97.4304127975961,∞)\left[97.4304127975961, \infty\right)
Convexa en los intervalos
(−∞,−97.4304127975961]\left(-\infty, -97.4304127975961\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x4+1sin⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\sqrt{x^{4} + 1} \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→∞(x4+1sin⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\sqrt{x^{4} + 1} \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 sqrt(x^4 + 1)*sin(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(x4+1sin⁡(x)x)=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\frac{\sqrt{x^{4} + 1} \sin{\left(x \right)}}{x}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\right\rangle x
lim⁡x→∞(x4+1sin⁡(x)x)=⟨−∞,∞⟩\lim_{x \to \infty}\left(\frac{\sqrt{x^{4} + 1} \sin{\left(x \right)}}{x}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−∞,∞⟩xy = \left\langle -\infty, \infty\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:
x4+1sin⁡(x)=−x4+1sin⁡(x)\sqrt{x^{4} + 1} \sin{\left(x \right)} = - \sqrt{x^{4} + 1} \sin{\left(x \right)}
- No
x4+1sin⁡(x)=x4+1sin⁡(x)\sqrt{x^{4} + 1} \sin{\left(x \right)} = \sqrt{x^{4} + 1} \sin{\left(x \right)}
- Sí
es decir, función
es
impar
    © Sr Examen – Калькулятор