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¿Cómo usar?
- Gráfico de la función y =:
-
(x-1)/(x+2)
-
-1-x
-
y=2x^2+x+1
-
-exp(-x)+(-cos(x*sqrt(3)/2)-sin(x*sqrt(3)/2))*exp(x/2)
-
Expresiones idénticas
- absolute(diez -x^(dos -(x/ ocho)))*sin(siete *x)
- absolute(10 menos x en el grado (2 menos (x dividir por 8))) multiplicar por seno de (7 multiplicar por x)
- absolute(diez menos x en el grado (dos menos (x dividir por ocho))) multiplicar por seno de (siete multiplicar por x)
- absolute(10-x(2-(x/8)))*sin(7*x)
- absolute10-x2-x/8*sin7*x
- absolute(10-x^(2-(x/8)))sin(7x)
- absolute(10-x(2-(x/8)))sin(7x)
- absolute10-x2-x/8sin7x
- absolute10-x^2-x/8sin7x
- absolute(10-x^(2-(x dividir por 8)))*sin(7*x)
-
Expresiones semejantes
- absolute(10+x^(2-(x/8)))*sin(7*x)
- absolute(10-x^(2+(x/8)))*sin(7*x)
-
Expresiones con funciones
- absolute
- absolute|2x-3/absolutex+1|
- absolute(2x)
- absolute(x-3)/(x^2-3x)
- absolute(sin(x))/sin(x)
- absolute(cosx-1)
- Seno sin
- sin(x)+x
- sin(x)*sin(3*x)
- sin(x)/sin(x+pi/4)
- sinx+cos^2x
- sin(x)*cos(x)^(2)
Gráfico de la función y = absolute(10-x^(2-(x/8)))*sin(7*x)
Solución
Ha introducido
[src]
| x|
| 2 - -|
| 8|
f(x) = |10 - x |*sin(7*x)
$$f{\left(x \right)} = \sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|$$
f = sin(7*x)*Abs(10 - x^(-x/8 + 2))
Gráfico de la función
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:
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -4.03919055461545$$
$$x_{2} = -26.030339129744$$
$$x_{3} = 60.1390593687189$$
$$x_{4} = 83.4766047953859$$
$$x_{5} = 87.9645943005142$$
$$x_{6} = -19.7471538225644$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = 74.0518268346165$$
$$x_{9} = 8.0783811092309$$
$$x_{10} = -41.738302397693$$
$$x_{11} = -21.9911485751286$$
$$x_{12} = 64.1782499233343$$
$$x_{13} = -15.707963267949$$
$$x_{14} = -9.87357691128221$$
$$x_{15} = 72.2566310325652$$
$$x_{16} = 38.1479107935903$$
$$x_{17} = 17.9519580205131$$
$$x_{18} = 20.1959527730772$$
$$x_{19} = -1.79519580205131$$
$$x_{20} = 100.082165964361$$
$$x_{21} = 16.1567622184618$$
$$x_{22} = 63.2806520223087$$
$$x_{23} = 12.1175716638463$$
$$x_{24} = -31.8647254864108$$
$$x_{25} = 30.0695296843594$$
$$x_{26} = 26.030339129744$$
$$x_{27} = 61.0366572697446$$
$$x_{28} = -5.83438635666676$$
$$x_{29} = 6.28318530717959$$
$$x_{30} = -23.7863443771799$$
$$x_{31} = 92.0037848551297$$
$$x_{32} = 54.3046730120521$$
$$x_{33} = 46.2262919028212$$
$$x_{34} = 65.9734457253857$$
$$x_{35} = 0$$
$$x_{36} = -17.9519580205131$$
$$x_{37} = 96.0429754097451$$
$$x_{38} = 82.1302079438475$$
$$x_{39} = 39.9431065956417$$
$$x_{40} = 48.0214877048726$$
$$x_{41} = 70.0126362800011$$
$$x_{42} = 86.1693984984629$$
$$x_{43} = -43.9822971502571$$
$$x_{44} = 34.1087202389749$$
$$x_{45} = -45.7774929523084$$
$$x_{46} = 52.060678259488$$
$$x_{47} = 43.9822971502571$$
$$x_{48} = 90.2085890530783$$
$$x_{49} = -39.9431065956417$$
$$x_{50} = -13.9127674658977$$
$$x_{51} = 68.2174404779498$$
$$x_{52} = 4.03919055461545$$
$$x_{53} = 76.2958215871807$$
$$x_{54} = 24.2351433276927$$
$$x_{55} = 56.0998688141035$$
$$x_{56} = -8.0783811092309$$
$$x_{57} = -35.9039160410262$$
$$x_{58} = -10.7711748123079$$
$$x_{59} = 32.3135244369236$$
$$x_{60} = 28.2743338823081$$
$$x_{61} = 2.24399475256414$$
$$x_{62} = 61.9342551707702$$
$$x_{63} = 10.7711748123079$$
$$x_{64} = 21.9911485751286$$
$$x_{65} = 78.091017389232$$
$$x_{66} = -27.8255349317953$$
$$x_{67} = 98.2869701623092$$
$$x_{68} = 50.2654824574367$$
$$x_{69} = 13.015169564872$$
$$x_{70} = 94.2477796076938$$
$$x_{71} = 42.1871013482058$$
$$x_{72} = -24.2351433276927$$
$$x_{73} = -30.5183286348723$$
o sea hay que resolver la ecuación:
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución numérica
$$x_{1} = -4.03919055461545$$
$$x_{2} = -26.030339129744$$
$$x_{3} = 60.1390593687189$$
$$x_{4} = 83.4766047953859$$
$$x_{5} = 87.9645943005142$$
$$x_{6} = -19.7471538225644$$
$$x_{7} = -37.6991118430775$$
$$x_{8} = 74.0518268346165$$
$$x_{9} = 8.0783811092309$$
$$x_{10} = -41.738302397693$$
$$x_{11} = -21.9911485751286$$
$$x_{12} = 64.1782499233343$$
$$x_{13} = -15.707963267949$$
$$x_{14} = -9.87357691128221$$
$$x_{15} = 72.2566310325652$$
$$x_{16} = 38.1479107935903$$
$$x_{17} = 17.9519580205131$$
$$x_{18} = 20.1959527730772$$
$$x_{19} = -1.79519580205131$$
$$x_{20} = 100.082165964361$$
$$x_{21} = 16.1567622184618$$
$$x_{22} = 63.2806520223087$$
$$x_{23} = 12.1175716638463$$
$$x_{24} = -31.8647254864108$$
$$x_{25} = 30.0695296843594$$
$$x_{26} = 26.030339129744$$
$$x_{27} = 61.0366572697446$$
$$x_{28} = -5.83438635666676$$
$$x_{29} = 6.28318530717959$$
$$x_{30} = -23.7863443771799$$
$$x_{31} = 92.0037848551297$$
$$x_{32} = 54.3046730120521$$
$$x_{33} = 46.2262919028212$$
$$x_{34} = 65.9734457253857$$
$$x_{35} = 0$$
$$x_{36} = -17.9519580205131$$
$$x_{37} = 96.0429754097451$$
$$x_{38} = 82.1302079438475$$
$$x_{39} = 39.9431065956417$$
$$x_{40} = 48.0214877048726$$
$$x_{41} = 70.0126362800011$$
$$x_{42} = 86.1693984984629$$
$$x_{43} = -43.9822971502571$$
$$x_{44} = 34.1087202389749$$
$$x_{45} = -45.7774929523084$$
$$x_{46} = 52.060678259488$$
$$x_{47} = 43.9822971502571$$
$$x_{48} = 90.2085890530783$$
$$x_{49} = -39.9431065956417$$
$$x_{50} = -13.9127674658977$$
$$x_{51} = 68.2174404779498$$
$$x_{52} = 4.03919055461545$$
$$x_{53} = 76.2958215871807$$
$$x_{54} = 24.2351433276927$$
$$x_{55} = 56.0998688141035$$
$$x_{56} = -8.0783811092309$$
$$x_{57} = -35.9039160410262$$
$$x_{58} = -10.7711748123079$$
$$x_{59} = 32.3135244369236$$
$$x_{60} = 28.2743338823081$$
$$x_{61} = 2.24399475256414$$
$$x_{62} = 61.9342551707702$$
$$x_{63} = 10.7711748123079$$
$$x_{64} = 21.9911485751286$$
$$x_{65} = 78.091017389232$$
$$x_{66} = -27.8255349317953$$
$$x_{67} = 98.2869701623092$$
$$x_{68} = 50.2654824574367$$
$$x_{69} = 13.015169564872$$
$$x_{70} = 94.2477796076938$$
$$x_{71} = 42.1871013482058$$
$$x_{72} = -24.2351433276927$$
$$x_{73} = -30.5183286348723$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$7 \cos{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| + \frac{\left(- x^{2} \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} - \frac{\operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + \frac{\operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(- x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + 10\right)\right) \sin{\left(7 x \right)} \operatorname{sign}{\left(10 - x^{2 - \frac{x}{8}} \right)}}{10 - x^{2 - \frac{x}{8}}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 4.24636798025675$$
$$x_{2} = 19.9717417744427$$
$$x_{3} = 6142.48683619382$$
$$x_{4} = -4.72759136513997$$
$$x_{5} = 30.2939313939915$$
$$x_{6} = 96.2673748850015$$
$$x_{7} = 22.2156262736786$$
$$x_{8} = -28.0624142679307$$
$$x_{9} = 15.9331666622884$$
$$x_{10} = 26.2547527780997$$
$$x_{11} = -11.9054253078556$$
$$x_{12} = 48.2458871803189$$
$$x_{13} = -21.779003635354$$
$$x_{14} = -17.7397179845236$$
$$x_{15} = 32.5379246730646$$
$$x_{16} = 62.1586546460267$$
$$x_{17} = -43.7709846921923$$
$$x_{18} = 85.9449990232065$$
$$x_{19} = 92.2281843303861$$
$$x_{20} = 56.7730672398741$$
$$x_{21} = -25.8183339647636$$
$$x_{22} = 80.1106126665397$$
$$x_{23} = 89.9841895778219$$
$$x_{24} = -7.86668762434289$$
$$x_{25} = 52.2850777347635$$
$$x_{26} = 70.2370357552575$$
$$x_{27} = 66.1978452006421$$
$$x_{28} = 84.1498032211552$$
$$x_{29} = -30.7553135565143$$
$$x_{30} = 44.2066966272963$$
$$x_{31} = 72.0322315573088$$
$$x_{32} = -39.7316432015658$$
$$x_{33} = 98.0625706870528$$
$$x_{34} = -13.7005464888531$$
$$x_{35} = 74.276226309873$$
$$x_{36} = 76.0714221119243$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = -41.9757224936161$$
$$x_{39} = 40.1675060865455$$
$$x_{40} = 10.5514238710837$$
$$x_{41} = -19.9837572345766$$
$$x_{42} = -29.8576802662963$$
$$x_{43} = -15.9445102597766$$
$$x_{44} = 18.1767240959622$$
$$x_{45} = 32.089125907985$$
$$x_{46} = 50.0410829822491$$
$$x_{47} = 46.001892428229$$
$$x_{48} = 14.1386265914265$$
$$x_{49} = -33.8970303519454$$
$$x_{50} = 10.1033656763697$$
$$x_{51} = 88.1889937757706$$
$$x_{52} = 54.0802735368025$$
$$x_{53} = 78.3154168644884$$
$$x_{54} = -24.0230729340526$$
$$x_{55} = 2.01140565955222$$
$$x_{56} = 36.1283156435024$$
$$x_{57} = -3.83237040119932$$
$$x_{58} = 24.0107811622753$$
$$x_{59} = 100.306565439617$$
$$x_{60} = 28.0499407408494$$
$$x_{61} = 58.1194640914118$$
$$x_{62} = 8.31268468377379$$
$$x_{63} = -2.01999283384361$$
$$x_{64} = 41.9627018789613$$
$$x_{65} = 37.4747124316737$$
$$x_{66} = 94.0233801324374$$
$$x_{67} = -35.6922966757149$$
$$x_{68} = 6.06512520307101$$
$$x_{69} = -37.9363786258816$$
$$x_{70} = 63.953850448078$$
Signos de extremos en los puntos:
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:
$$x_{1} = 4.24636798025675$$
$$x_{2} = -4.72759136513997$$
$$x_{3} = 30.2939313939915$$
$$x_{4} = 22.2156262736786$$
$$x_{5} = -28.0624142679307$$
$$x_{6} = 15.9331666622884$$
$$x_{7} = -11.9054253078556$$
$$x_{8} = 48.2458871803189$$
$$x_{9} = -21.779003635354$$
$$x_{10} = 85.9449990232065$$
$$x_{11} = 92.2281843303861$$
$$x_{12} = 66.1978452006421$$
$$x_{13} = 84.1498032211552$$
$$x_{14} = -30.7553135565143$$
$$x_{15} = -39.7316432015658$$
$$x_{16} = -13.7005464888531$$
$$x_{17} = 74.276226309873$$
$$x_{18} = 76.0714221119243$$
$$x_{19} = 67.9930410026934$$
$$x_{20} = 40.1675060865455$$
$$x_{21} = 10.5514238710837$$
$$x_{22} = -19.9837572345766$$
$$x_{23} = -29.8576802662963$$
$$x_{24} = 32.089125907985$$
$$x_{25} = 50.0410829822491$$
$$x_{26} = 14.1386265914265$$
$$x_{27} = -3.83237040119932$$
$$x_{28} = 24.0107811622753$$
$$x_{29} = 100.306565439617$$
$$x_{30} = 58.1194640914118$$
$$x_{31} = -2.01999283384361$$
$$x_{32} = 41.9627018789613$$
$$x_{33} = 37.4747124316737$$
$$x_{34} = 94.0233801324374$$
$$x_{35} = 6.06512520307101$$
$$x_{36} = -37.9363786258816$$
Puntos máximos de la función:
$$x_{36} = 19.9717417744427$$
$$x_{36} = 6142.48683619382$$
$$x_{36} = 96.2673748850015$$
$$x_{36} = 26.2547527780997$$
$$x_{36} = -17.7397179845236$$
$$x_{36} = 32.5379246730646$$
$$x_{36} = 62.1586546460267$$
$$x_{36} = -43.7709846921923$$
$$x_{36} = 56.7730672398741$$
$$x_{36} = -25.8183339647636$$
$$x_{36} = 80.1106126665397$$
$$x_{36} = 89.9841895778219$$
$$x_{36} = -7.86668762434289$$
$$x_{36} = 52.2850777347635$$
$$x_{36} = 70.2370357552575$$
$$x_{36} = 44.2066966272963$$
$$x_{36} = 72.0322315573088$$
$$x_{36} = 98.0625706870528$$
$$x_{36} = -41.9757224936161$$
$$x_{36} = -15.9445102597766$$
$$x_{36} = 18.1767240959622$$
$$x_{36} = 46.001892428229$$
$$x_{36} = -33.8970303519454$$
$$x_{36} = 10.1033656763697$$
$$x_{36} = 88.1889937757706$$
$$x_{36} = 54.0802735368025$$
$$x_{36} = 78.3154168644884$$
$$x_{36} = -24.0230729340526$$
$$x_{36} = 2.01140565955222$$
$$x_{36} = 36.1283156435024$$
$$x_{36} = 28.0499407408494$$
$$x_{36} = 8.31268468377379$$
$$x_{36} = -35.6922966757149$$
$$x_{36} = 63.953850448078$$
Decrece en los intervalos
$$\left[100.306565439617, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -39.7316432015658\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada
$$7 \cos{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| + \frac{\left(- x^{2} \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} - \frac{\operatorname{re}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{im}{\left(x^{- \frac{x}{8}}\right)}\right) \operatorname{im}{\left(x^{- \frac{x}{8}}\right)} + \left(- x^{2} \left(\left(- \frac{\log{\left(\frac{x}{\operatorname{sign}{\left(x \right)}} \right)}}{8} - \frac{1}{8}\right) \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + \frac{\operatorname{im}{\left(x^{- \frac{x}{8}}\right)} \arg{\left(x \right)}}{8}\right) - 2 x \operatorname{re}{\left(x^{- \frac{x}{8}}\right)}\right) \left(- x^{2} \operatorname{re}{\left(x^{- \frac{x}{8}}\right)} + 10\right)\right) \sin{\left(7 x \right)} \operatorname{sign}{\left(10 - x^{2 - \frac{x}{8}} \right)}}{10 - x^{2 - \frac{x}{8}}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 4.24636798025675$$
$$x_{2} = 19.9717417744427$$
$$x_{3} = 6142.48683619382$$
$$x_{4} = -4.72759136513997$$
$$x_{5} = 30.2939313939915$$
$$x_{6} = 96.2673748850015$$
$$x_{7} = 22.2156262736786$$
$$x_{8} = -28.0624142679307$$
$$x_{9} = 15.9331666622884$$
$$x_{10} = 26.2547527780997$$
$$x_{11} = -11.9054253078556$$
$$x_{12} = 48.2458871803189$$
$$x_{13} = -21.779003635354$$
$$x_{14} = -17.7397179845236$$
$$x_{15} = 32.5379246730646$$
$$x_{16} = 62.1586546460267$$
$$x_{17} = -43.7709846921923$$
$$x_{18} = 85.9449990232065$$
$$x_{19} = 92.2281843303861$$
$$x_{20} = 56.7730672398741$$
$$x_{21} = -25.8183339647636$$
$$x_{22} = 80.1106126665397$$
$$x_{23} = 89.9841895778219$$
$$x_{24} = -7.86668762434289$$
$$x_{25} = 52.2850777347635$$
$$x_{26} = 70.2370357552575$$
$$x_{27} = 66.1978452006421$$
$$x_{28} = 84.1498032211552$$
$$x_{29} = -30.7553135565143$$
$$x_{30} = 44.2066966272963$$
$$x_{31} = 72.0322315573088$$
$$x_{32} = -39.7316432015658$$
$$x_{33} = 98.0625706870528$$
$$x_{34} = -13.7005464888531$$
$$x_{35} = 74.276226309873$$
$$x_{36} = 76.0714221119243$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = -41.9757224936161$$
$$x_{39} = 40.1675060865455$$
$$x_{40} = 10.5514238710837$$
$$x_{41} = -19.9837572345766$$
$$x_{42} = -29.8576802662963$$
$$x_{43} = -15.9445102597766$$
$$x_{44} = 18.1767240959622$$
$$x_{45} = 32.089125907985$$
$$x_{46} = 50.0410829822491$$
$$x_{47} = 46.001892428229$$
$$x_{48} = 14.1386265914265$$
$$x_{49} = -33.8970303519454$$
$$x_{50} = 10.1033656763697$$
$$x_{51} = 88.1889937757706$$
$$x_{52} = 54.0802735368025$$
$$x_{53} = 78.3154168644884$$
$$x_{54} = -24.0230729340526$$
$$x_{55} = 2.01140565955222$$
$$x_{56} = 36.1283156435024$$
$$x_{57} = -3.83237040119932$$
$$x_{58} = 24.0107811622753$$
$$x_{59} = 100.306565439617$$
$$x_{60} = 28.0499407408494$$
$$x_{61} = 58.1194640914118$$
$$x_{62} = 8.31268468377379$$
$$x_{63} = -2.01999283384361$$
$$x_{64} = 41.9627018789613$$
$$x_{65} = 37.4747124316737$$
$$x_{66} = 94.0233801324374$$
$$x_{67} = -35.6922966757149$$
$$x_{68} = 6.06512520307101$$
$$x_{69} = -37.9363786258816$$
$$x_{70} = 63.953850448078$$
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:
$$x_{1} = 4.24636798025675$$
$$x_{2} = -4.72759136513997$$
$$x_{3} = 30.2939313939915$$
$$x_{4} = 22.2156262736786$$
$$x_{5} = -28.0624142679307$$
$$x_{6} = 15.9331666622884$$
$$x_{7} = -11.9054253078556$$
$$x_{8} = 48.2458871803189$$
$$x_{9} = -21.779003635354$$
$$x_{10} = 85.9449990232065$$
$$x_{11} = 92.2281843303861$$
$$x_{12} = 66.1978452006421$$
$$x_{13} = 84.1498032211552$$
$$x_{14} = -30.7553135565143$$
$$x_{15} = -39.7316432015658$$
$$x_{16} = -13.7005464888531$$
$$x_{17} = 74.276226309873$$
$$x_{18} = 76.0714221119243$$
$$x_{19} = 67.9930410026934$$
$$x_{20} = 40.1675060865455$$
$$x_{21} = 10.5514238710837$$
$$x_{22} = -19.9837572345766$$
$$x_{23} = -29.8576802662963$$
$$x_{24} = 32.089125907985$$
$$x_{25} = 50.0410829822491$$
$$x_{26} = 14.1386265914265$$
$$x_{27} = -3.83237040119932$$
$$x_{28} = 24.0107811622753$$
$$x_{29} = 100.306565439617$$
$$x_{30} = 58.1194640914118$$
$$x_{31} = -2.01999283384361$$
$$x_{32} = 41.9627018789613$$
$$x_{33} = 37.4747124316737$$
$$x_{34} = 94.0233801324374$$
$$x_{35} = 6.06512520307101$$
$$x_{36} = -37.9363786258816$$
Puntos máximos de la función:
$$x_{36} = 19.9717417744427$$
$$x_{36} = 6142.48683619382$$
$$x_{36} = 96.2673748850015$$
$$x_{36} = 26.2547527780997$$
$$x_{36} = -17.7397179845236$$
$$x_{36} = 32.5379246730646$$
$$x_{36} = 62.1586546460267$$
$$x_{36} = -43.7709846921923$$
$$x_{36} = 56.7730672398741$$
$$x_{36} = -25.8183339647636$$
$$x_{36} = 80.1106126665397$$
$$x_{36} = 89.9841895778219$$
$$x_{36} = -7.86668762434289$$
$$x_{36} = 52.2850777347635$$
$$x_{36} = 70.2370357552575$$
$$x_{36} = 44.2066966272963$$
$$x_{36} = 72.0322315573088$$
$$x_{36} = 98.0625706870528$$
$$x_{36} = -41.9757224936161$$
$$x_{36} = -15.9445102597766$$
$$x_{36} = 18.1767240959622$$
$$x_{36} = 46.001892428229$$
$$x_{36} = -33.8970303519454$$
$$x_{36} = 10.1033656763697$$
$$x_{36} = 88.1889937757706$$
$$x_{36} = 54.0802735368025$$
$$x_{36} = 78.3154168644884$$
$$x_{36} = -24.0230729340526$$
$$x_{36} = 2.01140565955222$$
$$x_{36} = 36.1283156435024$$
$$x_{36} = 28.0499407408494$$
$$x_{36} = 8.31268468377379$$
$$x_{36} = -35.6922966757149$$
$$x_{36} = 63.953850448078$$
Decrece en los intervalos
$$\left[100.306565439617, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, -39.7316432015658\right]$$
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$\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
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(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:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
segunda derivada
$$\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
$$\lim_{x \to -\infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -10, 10\right\rangle$$
$$\lim_{x \to \infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -10, 10\right\rangle$$
$$\lim_{x \to -\infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \left\langle -10, 10\right\rangle$$
$$\lim_{x \to \infty}\left(\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|\right) = \left\langle -10, 10\right\rangle$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \left\langle -10, 10\right\rangle$$
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
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{x \to \infty}\left(\frac{\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right|}{x}\right) = 0$$
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:
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = - \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|$$
- No
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = - \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|$$
- No
$$\sin{\left(7 x \right)} \left|{10 - x^{- \frac{x}{8} + 2}}\right| = \sin{\left(7 x \right)} \left|{\left(- x\right)^{\frac{x}{8} + 2} - 10}\right|$$
- No
es decir, función
no es
par ni impar
Gráfico