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absolute(10-x^(2-(x/8)))*sin(7*x)
Trazado el gráfico de la función/ absolute(10-x^(2-(x/8)))*sin(7*x)

Gráfico de la función y = absolute(10-x^(2-(x/8)))*sin(7*x)

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       |          x|         
       |      2 - -|         
       |          8|         
f(x) = |10 - x     |*sin(7*x)
f(x)=sin⁡(7x)∣10−x−x8+2∣f{\left(x \right)} = \sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| 
f = sin(7*x)*Abs(10 - x^(-x/8 + 2))
Gráfico de la función
02468-8-6-4-2-1010-25002500
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:
sin⁡(7x)∣10−x−x8+2∣=0\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución numérica
x1=−4.03919055461545x_{1} = -4.03919055461545
x2=−26.030339129744x_{2} = -26.030339129744
x3=60.1390593687189x_{3} = 60.1390593687189
x4=83.4766047953859x_{4} = 83.4766047953859
x5=87.9645943005142x_{5} = 87.9645943005142
x6=−19.7471538225644x_{6} = -19.7471538225644
x7=−37.6991118430775x_{7} = -37.6991118430775
x8=74.0518268346165x_{8} = 74.0518268346165
x9=8.0783811092309x_{9} = 8.0783811092309
x10=−41.738302397693x_{10} = -41.738302397693
x11=−21.9911485751286x_{11} = -21.9911485751286
x12=64.1782499233343x_{12} = 64.1782499233343
x13=−15.707963267949x_{13} = -15.707963267949
x14=−9.87357691128221x_{14} = -9.87357691128221
x15=72.2566310325652x_{15} = 72.2566310325652
x16=38.1479107935903x_{16} = 38.1479107935903
x17=17.9519580205131x_{17} = 17.9519580205131
x18=20.1959527730772x_{18} = 20.1959527730772
x19=−1.79519580205131x_{19} = -1.79519580205131
x20=100.082165964361x_{20} = 100.082165964361
x21=16.1567622184618x_{21} = 16.1567622184618
x22=63.2806520223087x_{22} = 63.2806520223087
x23=12.1175716638463x_{23} = 12.1175716638463
x24=−31.8647254864108x_{24} = -31.8647254864108
x25=30.0695296843594x_{25} = 30.0695296843594
x26=26.030339129744x_{26} = 26.030339129744
x27=61.0366572697446x_{27} = 61.0366572697446
x28=−5.83438635666676x_{28} = -5.83438635666676
x29=6.28318530717959x_{29} = 6.28318530717959
x30=−23.7863443771799x_{30} = -23.7863443771799
x31=92.0037848551297x_{31} = 92.0037848551297
x32=54.3046730120521x_{32} = 54.3046730120521
x33=46.2262919028212x_{33} = 46.2262919028212
x34=65.9734457253857x_{34} = 65.9734457253857
x35=0x_{35} = 0
x36=−17.9519580205131x_{36} = -17.9519580205131
x37=96.0429754097451x_{37} = 96.0429754097451
x38=82.1302079438475x_{38} = 82.1302079438475
x39=39.9431065956417x_{39} = 39.9431065956417
x40=48.0214877048726x_{40} = 48.0214877048726
x41=70.0126362800011x_{41} = 70.0126362800011
x42=86.1693984984629x_{42} = 86.1693984984629
x43=−43.9822971502571x_{43} = -43.9822971502571
x44=34.1087202389749x_{44} = 34.1087202389749
x45=−45.7774929523084x_{45} = -45.7774929523084
x46=52.060678259488x_{46} = 52.060678259488
x47=43.9822971502571x_{47} = 43.9822971502571
x48=90.2085890530783x_{48} = 90.2085890530783
x49=−39.9431065956417x_{49} = -39.9431065956417
x50=−13.9127674658977x_{50} = -13.9127674658977
x51=68.2174404779498x_{51} = 68.2174404779498
x52=4.03919055461545x_{52} = 4.03919055461545
x53=76.2958215871807x_{53} = 76.2958215871807
x54=24.2351433276927x_{54} = 24.2351433276927
x55=56.0998688141035x_{55} = 56.0998688141035
x56=−8.0783811092309x_{56} = -8.0783811092309
x57=−35.9039160410262x_{57} = -35.9039160410262
x58=−10.7711748123079x_{58} = -10.7711748123079
x59=32.3135244369236x_{59} = 32.3135244369236
x60=28.2743338823081x_{60} = 28.2743338823081
x61=2.24399475256414x_{61} = 2.24399475256414
x62=61.9342551707702x_{62} = 61.9342551707702
x63=10.7711748123079x_{63} = 10.7711748123079
x64=21.9911485751286x_{64} = 21.9911485751286
x65=78.091017389232x_{65} = 78.091017389232
x66=−27.8255349317953x_{66} = -27.8255349317953
x67=98.2869701623092x_{67} = 98.2869701623092
x68=50.2654824574367x_{68} = 50.2654824574367
x69=13.015169564872x_{69} = 13.015169564872
x70=94.2477796076938x_{70} = 94.2477796076938
x71=42.1871013482058x_{71} = 42.1871013482058
x72=−24.2351433276927x_{72} = -24.2351433276927
x73=−30.5183286348723x_{73} = -30.5183286348723
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 Abs(10 - x^(2 - x/8))*sin(7*x).
sin⁡(0⋅7)∣10−0−08+2∣\sin{\left(0 \cdot 7 \right)} \left|{10 - 0^{- \frac{0}{8} + 2}}\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
7cos⁡(7x)∣10−x−x8+2∣+(−x2(−x2((−log⁡(xsign⁡(x))8−18)im⁡(x−x8)−re⁡(x−x8)arg⁡(x)8)−2xim⁡(x−x8))im⁡(x−x8)+(−x2((−log⁡(xsign⁡(x))8−18)re⁡(x−x8)+im⁡(x−x8)arg⁡(x)8)−2xre⁡(x−x8))(−x2re⁡(x−x8)+10))sin⁡(7x)sign⁡(10−x2−x8)10−x2−x8=07 \cos{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| + \frac{\left(- x^{2} \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} - \frac{\operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + \frac{\operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(- x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + 10\right)\right) \sin{\left(7 x \right)} \operatorname{sign}{\left(10 - x^{2 - \frac{x}{8}} \right)}}{10 - x^{2 - \frac{x}{8}}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=4.24636798025675x_{1} = 4.24636798025675
x2=19.9717417744427x_{2} = 19.9717417744427
x3=6142.48683619382x_{3} = 6142.48683619382
x4=−4.72759136513997x_{4} = -4.72759136513997
x5=30.2939313939915x_{5} = 30.2939313939915
x6=96.2673748850015x_{6} = 96.2673748850015
x7=22.2156262736786x_{7} = 22.2156262736786
x8=−28.0624142679307x_{8} = -28.0624142679307
x9=15.9331666622884x_{9} = 15.9331666622884
x10=26.2547527780997x_{10} = 26.2547527780997
x11=−11.9054253078556x_{11} = -11.9054253078556
x12=48.2458871803189x_{12} = 48.2458871803189
x13=−21.779003635354x_{13} = -21.779003635354
x14=−17.7397179845236x_{14} = -17.7397179845236
x15=32.5379246730646x_{15} = 32.5379246730646
x16=62.1586546460267x_{16} = 62.1586546460267
x17=−43.7709846921923x_{17} = -43.7709846921923
x18=85.9449990232065x_{18} = 85.9449990232065
x19=92.2281843303861x_{19} = 92.2281843303861
x20=56.7730672398741x_{20} = 56.7730672398741
x21=−25.8183339647636x_{21} = -25.8183339647636
x22=80.1106126665397x_{22} = 80.1106126665397
x23=89.9841895778219x_{23} = 89.9841895778219
x24=−7.86668762434289x_{24} = -7.86668762434289
x25=52.2850777347635x_{25} = 52.2850777347635
x26=70.2370357552575x_{26} = 70.2370357552575
x27=66.1978452006421x_{27} = 66.1978452006421
x28=84.1498032211552x_{28} = 84.1498032211552
x29=−30.7553135565143x_{29} = -30.7553135565143
x30=44.2066966272963x_{30} = 44.2066966272963
x31=72.0322315573088x_{31} = 72.0322315573088
x32=−39.7316432015658x_{32} = -39.7316432015658
x33=98.0625706870528x_{33} = 98.0625706870528
x34=−13.7005464888531x_{34} = -13.7005464888531
x35=74.276226309873x_{35} = 74.276226309873
x36=76.0714221119243x_{36} = 76.0714221119243
x37=67.9930410026934x_{37} = 67.9930410026934
x38=−41.9757224936161x_{38} = -41.9757224936161
x39=40.1675060865455x_{39} = 40.1675060865455
x40=10.5514238710837x_{40} = 10.5514238710837
x41=−19.9837572345766x_{41} = -19.9837572345766
x42=−29.8576802662963x_{42} = -29.8576802662963
x43=−15.9445102597766x_{43} = -15.9445102597766
x44=18.1767240959622x_{44} = 18.1767240959622
x45=32.089125907985x_{45} = 32.089125907985
x46=50.0410829822491x_{46} = 50.0410829822491
x47=46.001892428229x_{47} = 46.001892428229
x48=14.1386265914265x_{48} = 14.1386265914265
x49=−33.8970303519454x_{49} = -33.8970303519454
x50=10.1033656763697x_{50} = 10.1033656763697
x51=88.1889937757706x_{51} = 88.1889937757706
x52=54.0802735368025x_{52} = 54.0802735368025
x53=78.3154168644884x_{53} = 78.3154168644884
x54=−24.0230729340526x_{54} = -24.0230729340526
x55=2.01140565955222x_{55} = 2.01140565955222
x56=36.1283156435024x_{56} = 36.1283156435024
x57=−3.83237040119932x_{57} = -3.83237040119932
x58=24.0107811622753x_{58} = 24.0107811622753
x59=100.306565439617x_{59} = 100.306565439617
x60=28.0499407408494x_{60} = 28.0499407408494
x61=58.1194640914118x_{61} = 58.1194640914118
x62=8.31268468377379x_{62} = 8.31268468377379
x63=−2.01999283384361x_{63} = -2.01999283384361
x64=41.9627018789613x_{64} = 41.9627018789613
x65=37.4747124316737x_{65} = 37.4747124316737
x66=94.0233801324374x_{66} = 94.0233801324374
x67=−35.6922966757149x_{67} = -35.6922966757149
x68=6.06512520307101x_{68} = 6.06512520307101
x69=−37.9363786258816x_{69} = -37.9363786258816
x70=63.953850448078x_{70} = 63.953850448078
Signos de extremos en los puntos:
(4.246367980256752, -1.61892436595126)

(19.971741774442737, 9.77384729042186)

(6142.486836193815, 10)

(-4.72759136513997, -59.2296504606914)

(30.293931393991457, -9.99774471851857)

(96.26737488500152, 10)

(22.215626273678552, -9.91010896389814)

(-28.06241426793075, -94259761.7099744)

(15.933166662288436, -8.97646064510337)

(26.254752778099718, 9.9848365474899)

(-11.905425307855554, -5634.03633751414)

(48.24588718031892, -9.99999983616143)

(-21.779003635354034, -2075483.7659437)

(-17.73971798452364, 184414.663266918)

(32.53792467306461, 9.99925264592533)

(62.158654646026676, 9.99999999995515)

(-43.77098469219225, 1820079562144.98)

(85.94499902320649, -10)

(92.22818433038607, -10)

(56.77306723987409, 9.99999999885243)

(-25.818333964763628, 23928983.0940163)

(80.11061266653972, 10)

(89.98418957782194, 10)

(-7.866687624342887, 478.467125102297)

(52.28507773476348, 9.99999998392814)

(70.23703575525752, 9.9999999999997)

(66.19784520064208, -9.99999999999624)

(84.14980322115518, -10)

(-30.75531355651429, -494691177.955843)

(44.20669662729629, 9.99999842138155)

(72.03223155730883, 9.9999999999999)

(-39.7316432015658, -137572077896.305)

(98.06257068705283, 10)

(-13.700546488853144, -16537.6992325216)

(74.27622630987297, -9.99999999999998)

(76.07142211192428, -9.99999999999999)

(67.99304100269339, -9.99999999999877)

(-41.9757224936161, 575446698904.945)

(40.1675060865455, -9.99998571786786)

(10.55142387108372, -5.02055981989318)

(-19.983757234576586, -706024.296983838)

(-29.857680266296285, -284219007.33675)

(-15.944510259776571, 63162.9911014025)

(18.1767240959622, 9.54571562397436)

(32.089125907984986, -9.99906566549406)

(50.04108298224914, -9.99999994123282)

(46.00189242822899, 9.99999941897102)

(14.138626591426524, -8.14746298249291)

(-33.89703035194544, 3484129389.91502)

(10.10336567636967, 4.49669129113124)

(88.18899377577063, 10)

(54.08027353680247, 9.99999999436783)

(78.31541686448841, 10)

(-24.023072934052593, 8044625.65903659)

(2.01140565955222, 6.59530490421583)

(36.12831564350242, 9.99987966451883)

(-3.832370401199318, -28.8430254409776)

(24.01078116227525, -9.95852971985115)

(100.30656543961697, -10)

(28.0499407408494, 9.99340729146942)

(58.1194640914118, -9.999999999486)

(8.312684683773794, 2.34204802358243)

(-2.019992833843614, -7.44137548093109)

(41.962701878961276, -9.9999945892181)

(37.47471243167369, -9.99994035791684)

(94.02338013243738, -10)

(-35.69229667571486, 10722041118.6583)

(6.065125203071009, -0.619949559421381)

(-37.93637862588157, -44086472939.6451)

(63.95385044807795, 9.99999999998503)


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=4.24636798025675x_{1} = 4.24636798025675
x2=−4.72759136513997x_{2} = -4.72759136513997
x3=30.2939313939915x_{3} = 30.2939313939915
x4=22.2156262736786x_{4} = 22.2156262736786
x5=−28.0624142679307x_{5} = -28.0624142679307
x6=15.9331666622884x_{6} = 15.9331666622884
x7=−11.9054253078556x_{7} = -11.9054253078556
x8=48.2458871803189x_{8} = 48.2458871803189
x9=−21.779003635354x_{9} = -21.779003635354
x10=85.9449990232065x_{10} = 85.9449990232065
x11=92.2281843303861x_{11} = 92.2281843303861
x12=66.1978452006421x_{12} = 66.1978452006421
x13=84.1498032211552x_{13} = 84.1498032211552
x14=−30.7553135565143x_{14} = -30.7553135565143
x15=−39.7316432015658x_{15} = -39.7316432015658
x16=−13.7005464888531x_{16} = -13.7005464888531
x17=74.276226309873x_{17} = 74.276226309873
x18=76.0714221119243x_{18} = 76.0714221119243
x19=67.9930410026934x_{19} = 67.9930410026934
x20=40.1675060865455x_{20} = 40.1675060865455
x21=10.5514238710837x_{21} = 10.5514238710837
x22=−19.9837572345766x_{22} = -19.9837572345766
x23=−29.8576802662963x_{23} = -29.8576802662963
x24=32.089125907985x_{24} = 32.089125907985
x25=50.0410829822491x_{25} = 50.0410829822491
x26=14.1386265914265x_{26} = 14.1386265914265
x27=−3.83237040119932x_{27} = -3.83237040119932
x28=24.0107811622753x_{28} = 24.0107811622753
x29=100.306565439617x_{29} = 100.306565439617
x30=58.1194640914118x_{30} = 58.1194640914118
x31=−2.01999283384361x_{31} = -2.01999283384361
x32=41.9627018789613x_{32} = 41.9627018789613
x33=37.4747124316737x_{33} = 37.4747124316737
x34=94.0233801324374x_{34} = 94.0233801324374
x35=6.06512520307101x_{35} = 6.06512520307101
x36=−37.9363786258816x_{36} = -37.9363786258816
Puntos máximos de la función:
x36=19.9717417744427x_{36} = 19.9717417744427
x36=6142.48683619382x_{36} = 6142.48683619382
x36=96.2673748850015x_{36} = 96.2673748850015
x36=26.2547527780997x_{36} = 26.2547527780997
x36=−17.7397179845236x_{36} = -17.7397179845236
x36=32.5379246730646x_{36} = 32.5379246730646
x36=62.1586546460267x_{36} = 62.1586546460267
x36=−43.7709846921923x_{36} = -43.7709846921923
x36=56.7730672398741x_{36} = 56.7730672398741
x36=−25.8183339647636x_{36} = -25.8183339647636
x36=80.1106126665397x_{36} = 80.1106126665397
x36=89.9841895778219x_{36} = 89.9841895778219
x36=−7.86668762434289x_{36} = -7.86668762434289
x36=52.2850777347635x_{36} = 52.2850777347635
x36=70.2370357552575x_{36} = 70.2370357552575
x36=44.2066966272963x_{36} = 44.2066966272963
x36=72.0322315573088x_{36} = 72.0322315573088
x36=98.0625706870528x_{36} = 98.0625706870528
x36=−41.9757224936161x_{36} = -41.9757224936161
x36=−15.9445102597766x_{36} = -15.9445102597766
x36=18.1767240959622x_{36} = 18.1767240959622
x36=46.001892428229x_{36} = 46.001892428229
x36=−33.8970303519454x_{36} = -33.8970303519454
x36=10.1033656763697x_{36} = 10.1033656763697
x36=88.1889937757706x_{36} = 88.1889937757706
x36=54.0802735368025x_{36} = 54.0802735368025
x36=78.3154168644884x_{36} = 78.3154168644884
x36=−24.0230729340526x_{36} = -24.0230729340526
x36=2.01140565955222x_{36} = 2.01140565955222
x36=36.1283156435024x_{36} = 36.1283156435024
x36=28.0499407408494x_{36} = 28.0499407408494
x36=8.31268468377379x_{36} = 8.31268468377379
x36=−35.6922966757149x_{36} = -35.6922966757149
x36=63.953850448078x_{36} = 63.953850448078
Decrece en los intervalos
[100.306565439617,∞)\left[100.306565439617, \infty\right)
Crece en los intervalos
(−∞,−39.7316432015658]\left(-\infty, -39.7316432015658\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
7x(−x2(x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−16im⁡(x−x8))im⁡(x−x8)+(−x((log⁡(xsign⁡(x))+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))+16re⁡(x−x8))(x2re⁡(x−x8)−10))cos⁡(7x)sign⁡(10−x2−x8)4(10−x2−x8)−49sin⁡(7x)∣10−x2−x8∣−(−xx2−x8(x2(x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−16im⁡(x−x8))im⁡(x−x8)+(x((log⁡(xsign⁡(x))+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))−16re⁡(x−x8))(x2re⁡(x−x8)−10))(log⁡(x)+x−16x)sign⁡(x2−x8−10)x2−x8−10+8x(x2(x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−16im⁡(x−x8))im⁡(x−x8)+(x((log⁡(xsign⁡(x))+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))−16re⁡(x−x8))(x2re⁡(x−x8)−10))ddx(−sign⁡(x2−x8−10))−(−x3(x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−16im⁡(x−x8))((log⁡(∣x∣)+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−x2(x((log⁡(xsign⁡(x))+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))−16re⁡(x−x8))(x((log⁡(∣x∣)+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))−16re⁡(x−x8))+16x2(x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−16im⁡(x−x8))im⁡(x−x8)+x2(−x2(((log⁡(∣x∣)+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))arg⁡(x)+((log⁡(∣x∣)+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))(log⁡(xsign⁡(x))+1)+8(2xδ(x)sign⁡(x)−1)im⁡(x−x8)x)+16x((log⁡(xsign⁡(x))+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))+16x((log⁡(∣x∣)+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))−128im⁡(x−x8))im⁡(x−x8)+(x2re⁡(x−x8)−10)(x2((−(log⁡(∣x∣)+1)re⁡(x−x8)+im⁡(x−x8)arg⁡(x))(log⁡(xsign⁡(x))+1)+((log⁡(∣x∣)+1)im⁡(x−x8)+re⁡(x−x8)arg⁡(x))arg⁡(x)−8(2xδ(x)sign⁡(x)−1)re⁡(x−x8)x)+16x((log⁡(xsign⁡(x))+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))+16x((log⁡(∣x∣)+1)re⁡(x−x8)−im⁡(x−x8)arg⁡(x))−128re⁡(x−x8)))sign⁡(x2−x8−10))sin⁡(7x)64(10−x2−x8)=0\frac{7 x \left(- x^{2} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(- x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) + 16 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - 10\right)\right) \cos{\left(7 x \right)} \operatorname{sign}{\left(10 - x^{2 - \frac{x}{8}} \right)}}{4 \left(10 - x^{2 - \frac{x}{8}}\right)} - 49 \sin{\left(7 x \right)} \left|{10 - x^{2 - \frac{x}{8}}}\right| - \frac{\left(- \frac{x x^{2 - \frac{x}{8}} \left(x^{2} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - 10\right)\right) \left(\log{\left(x \right)} + \frac{x - 16}{x}\right) \operatorname{sign}{\left(x^{2 - \frac{x}{8}} - 10 \right)}}{x^{2 - \frac{x}{8}} - 10} + 8 x \left(x^{2} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - 10\right)\right) \frac{d}{d x} \left(- \operatorname{sign}{\left(x^{2 - \frac{x}{8}} - 10 \right)}\right) - \left(- x^{3} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - x^{2} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(x \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) + 16 x^{2} \left(x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 16 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + x^{2} \left(- x^{2} \left(\left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) \arg{\left(x \right)} + \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) \left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) + \frac{8 \left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}}{x}\right) + 16 x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) + 16 x \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 128 \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - 10\right) \left(x^{2} \left(\left(- \left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) \left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) + \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) \arg{\left(x \right)} - \frac{8 \left(\frac{2 x \delta\left(x\right)}{\operatorname{sign}{\left(x \right)}} - 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}}{x}\right) + 16 x \left(\left(\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) + 16 x \left(\left(\log{\left(\left|{x}\right| \right)} + 1\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} - \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}\right) - 128 \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right)\right) \operatorname{sign}{\left(x^{2 - \frac{x}{8}} - 10 \right)}\right) \sin{\left(7 x \right)}}{64 \left(10 - x^{2 - \frac{x}{8}}\right)} = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(sin⁡(7x)∣10−x−x8+2∣)=⟨−10,10⟩\lim_{x \to -\infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−10,10⟩y = \left\langle -10, 10\right\rangle
lim⁡x→∞(sin⁡(7x)∣10−x−x8+2∣)=⟨−10,10⟩\lim_{x \to \infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−10,10⟩y = \left\langle -10, 10\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(10 - x^(2 - x/8))*sin(7*x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(sin⁡(7x)∣10−x−x8+2∣x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(sin⁡(7x)∣10−x−x8+2∣x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
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:
sin⁡(7x)∣10−x−x8+2∣=−sin⁡(7x)∣(−x)x8+2−10∣\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = - \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|
- No
sin⁡(7x)∣10−x−x8+2∣=sin⁡(7x)∣(−x)x8+2−10∣\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = absolute(10-x^(2-(x/8)))*sin(7*x)
    © Sr Examen – Калькулятор