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Trazado el gráfico de la función/ sqrt(x-1)/(x(x-2)(x-4)(x-6))

Gráfico de la función y = sqrt(x-1)/(x(x-2)(x-4)(x-6))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
                 _______        
               \/ x - 1         
f(x) = -------------------------
       x*(x - 2)*(x - 4)*(x - 6)
f(x)=x−1x(x−2)(x−4)(x−6)f{\left(x \right)} = \frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)} 
f = sqrt(x - 1)/((((x*(x - 2))*(x - 4))*(x - 6)))
Gráfico de la función
02468-8-6-4-2-10105-5
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
x1=0x_{1} = 0
x2=2x_{2} = 2
x3=4x_{3} = 4
x4=6x_{4} = 6
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:
x−1x(x−2)(x−4)(x−6)=0\frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=1x_{1} = 1
Solución numérica
x1=−10463.3520231334x_{1} = -10463.3520231334
x2=−18355.8192081777x_{2} = -18355.8192081777
x3=−10858.1352691136x_{3} = -10858.1352691136
x4=10418.4460670948x_{4} = 10418.4460670948
x5=4092.27301132531x_{5} = 4092.27301132531
x6=−15988.557495318x_{6} = -15988.557495318
x7=6863.54106929506x_{7} = 6863.54106929506
x8=15943.5730944369x_{8} = 15943.5730944369
x9=11997.3909563043x_{9} = 11997.3909563043
x10=−17566.7589971481x_{10} = -17566.7589971481
x11=−2541.05574791508x_{11} = -2541.05574791508
x12=−19539.3681093536x_{12} = -19539.3681093536
x13=13181.3856980523x_{13} = 13181.3856980523
x14=−10068.5379312492x_{14} = -10068.5379312492
x15=−19144.8568733011x_{15} = -19144.8568733011
x16=−13226.3430210557x_{16} = -13226.3430210557
x17=−5721.68041642362x_{17} = -5721.68041642362
x18=12786.7374039534x_{18} = 12786.7374039534
x19=13970.6394351944x_{19} = 13970.6394351944
x20=−20328.3768703791x_{20} = -20328.3768703791
x21=9628.80657458026x_{21} = 9628.80657458026
x22=12392.0730165096x_{22} = 12392.0730165096
x23=−11252.890949987x_{23} = -11252.890949987
x24=3695.10777751089x_{24} = 3695.10777751089
x25=−9673.68916977333x_{25} = -9673.68916977333
x26=−3340.95974714954x_{26} = -3340.95974714954
x27=−13620.9815192031x_{27} = -13620.9815192031
x28=2898.52935941839x_{28} = 2898.52935941839
x29=17916.2955322612x_{29} = 17916.2955322612
x30=14365.2472213818x_{30} = 14365.2472213818
x31=−14804.8182828537x_{31} = -14804.8182828537
x32=−2941.8021254212x_{32} = -2941.8021254212
x33=−5325.80598005326x_{33} = -5325.80598005326
x34=−15593.9872157644x_{34} = -15593.9872157644
x35=−9278.8012548172x_{35} = -9278.8012548172
x36=6468.19172768099x_{36} = 6468.19172768099
x37=−14410.2180637099x_{37} = -14410.2180637099
x38=−6908.26867253397x_{38} = -6908.26867253397
x39=−19933.8746841156x_{39} = -19933.8746841156
x40=−16383.1192341825x_{40} = -16383.1192341825
x41=−4533.25966811153x_{41} = -4533.25966811153
x42=16338.1320419569x_{42} = 16338.1320419569
x43=−6512.87964715932x_{43} = -6512.87964715932
x44=4488.95354451896x_{44} = 4488.95354451896
x45=−8093.84440311863x_{45} = -8093.84440311863
x46=−8883.86889313524x_{46} = -8883.86889313524
x47=9233.93265012983x_{47} = 9233.93265012983
x48=−7303.54827820532x_{48} = -7303.54827820532
x49=−12831.6893655994x_{49} = -12831.6893655994
x50=8839.01619570758x_{50} = 8839.01619570758
x51=−8488.88579054538x_{51} = -8488.88579054538
x52=15549.0058212758x_{52} = 15549.0058212758
x53=14759.8436400939x_{53} = 14759.8436400939
x54=10023.6429659865x_{54} = 10023.6429659865
x55=−6117.35951234089x_{55} = -6117.35951234089
x56=8444.05128452171x_{56} = 8444.05128452171
x57=11207.9663931036x_{57} = 11207.9663931036
x58=−17961.2921077183x_{58} = -17961.2921077183
x59=3297.28347966006x_{59} = 3297.28347966006
x60=18310.8206573651x_{60} = 18310.8206573651
x61=13576.0192953367x_{61} = 13576.0192953367
x62=−12437.0190967089x_{62} = -12437.0190967089
x63=5281.29539464981x_{63} = 5281.29539464981
x64=15154.4295752189x_{64} = 15154.4295752189
x65=−14015.6061507218x_{65} = -14015.6061507218
x66=16732.6832502719x_{66} = 16732.6832502719
x67=−11647.621896795x_{67} = -11647.621896795
x68=−12042.3305654038x_{68} = -12042.3305654038
x69=7258.78730287627x_{69} = 7258.78730287627
x70=−15199.4077255852x_{70} = -15199.4077255852
x71=19099.854732456x_{71} = 19099.854732456
x72=5677.09823025008x_{72} = 5677.09823025008
x73=7653.94630137329x_{73} = 7653.94630137329
x74=−4136.42930203729x_{74} = -4136.42930203729
x75=−17172.2194596259x_{75} = -17172.2194596259
x76=−16777.6730388327x_{76} = -16777.6730388327
x77=11602.6894300542x_{77} = 11602.6894300542
x78=6072.71929150701x_{78} = 6072.71929150701
x79=17521.7645318927x_{79} = 17521.7645318927
x80=−3739.06298804957x_{80} = -3739.06298804957
x81=8049.03083262451x_{81} = 8049.03083262451
x82=−7698.73561010356x_{82} = -7698.73561010356
x83=−18750.3406800699x_{83} = -18750.3406800699
x84=−4929.68774390662x_{84} = -4929.68774390662
x85=17127.227251982x_{85} = 17127.227251982
x86=18705.3402774955x_{86} = 18705.3402774955
x87=4885.26692970721x_{87} = 4885.26692970721
x88=10813.2195037302x_{88} = 10813.2195037302
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 - 1)/((((x*(x - 2))*(x - 4))*(x - 6))).
−1(−6)(−4)(−2)0\frac{\sqrt{-1}}{\left(-6\right) \left(-4\right) \left(-2\right) 0}
Resultado:
f(0)=∞~f{\left(0 \right)} = \tilde{\infty}
signof no cruza Y
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
1x1x−61x−41x−22x−1+x−1(−x(x−2)(x−4)−(x−6)(x(x−2)+(x−4)(2x−2)))x2(x−6)2(x−4)2(x−2)2=0\frac{\frac{1}{x} \frac{1}{x - 6} \frac{1}{x - 4} \frac{1}{x - 2}}{2 \sqrt{x - 1}} + \frac{\sqrt{x - 1} \left(- x \left(x - 2\right) \left(x - 4\right) - \left(x - 6\right) \left(x \left(x - 2\right) + \left(x - 4\right) \left(2 x - 2\right)\right)\right)}{x^{2} \left(x - 6\right)^{2} \left(x - 4\right)^{2} \left(x - 2\right)^{2}} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177x_{1} = - \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}
x2=−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177x_{2} = \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}
Signos de extremos en los puntos:
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              /             /          _______                                                /              /          _______                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /                                                                                                /                                                                                   /                                         294*3 /   ---- + ---------                                                                                                                                                                                                                                                                                                                                                                       
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(-- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  -            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ----------------------------------------------------------------------------, --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------)
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        /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83                |  25          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |  11          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |3          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |17          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | 
      \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------    |- -- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  -            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|- -- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  -            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  -            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|-- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  -            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- | 
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                                                                                   /                                                                                   /                                         294*3 /   ---- + ---------     |         /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |         /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |      /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |       /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | 
                                                                                 \/                                                                                  \/                                              \/    2744      6174       |       \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |       \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |    \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |     \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | 
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              /             /          _______                                                /              /          _______                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /                                                                                                /                                                                                   /                                         294*3 /   ---- + ---------                                                                                                                                                                                                                                                                                                                                                                       
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(-- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  +            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ----------------------------------------------------------------------------, --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------)
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        /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83                |  25          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |  11          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |3          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | |17          /   51        /  177    \/ 51393                  83                            /   102        /  177    \/ 51393                  83                                                   432                                      | 
      \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------    |- -- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  +            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|- -- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  +            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  +            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- |*|-- +       /    -- + 2*3 /   ---- + ---------  + ---------------------------  +            /    --- - 2*3 /   ---- + ---------  - --------------------------- + ---------------------------------------------------------------------------- | 
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                                                                                   /                                                                                   /                                         294*3 /   ---- + ---------     |         /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |         /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |      /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | |       /                                         294*3 /   ---- + ---------            /                                          294*3 /   ---- + ---------               /   51        /  177    \/ 51393                  83              | 
                                                                                 \/                                                                                  \/                                              \/    2744      6174       |       \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |       \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |    \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | |     \/                                              \/    2744      6174             /                                               \/    2744      6174      343*      /    -- + 2*3 /   ---- + ---------  + ---------------------------  | 
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                                                                                                                                                                                                                                                |                                                                                    /                                                                                   /                                         294*3 /   ---- + ---------   | |                                                                                    /                                                                                   /                                         294*3 /   ---- + ---------   | |                                                                                 /                                                                                   /                                         294*3 /   ---- + ---------   | |                                                                                  /                                                                                   /                                         294*3 /   ---- + ---------   | 
                                                                                                                                                                                                                                                \                                                                                  \/                                                                                  \/                                              \/    2744      6174     / \                                                                                  \/                                                                                  \/                                              \/    2744      6174     / \                                                                               \/                                                                                  \/                                              \/    2744      6174     / \                                                                                \/                                                                                  \/                                              \/    2744      6174     /


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=−−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177x_{1} = - \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}
Puntos máximos de la función:
x1=−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177x_{1} = \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}
Decrece en los intervalos
[−−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177,−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177]\left[- \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}, \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}\right]
Crece en los intervalos
(−∞,−−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177]∪[−2513936174+17727443−83294513936174+17727443+43234383294513936174+17727443+2513936174+17727443+5149+10249+83294513936174+17727443+2513936174+17727443+5149+177,∞)\left(-\infty, - \sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}\right] \cup \left[\sqrt{- 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} - \frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + \frac{432}{343 \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}}} + \frac{102}{49}} + \sqrt{\frac{83}{294 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}}} + 2 \sqrt[3]{\frac{\sqrt{51393}}{6174} + \frac{177}{2744}} + \frac{51}{49}} + \frac{17}{7}, \infty\right)
Asíntotas verticales
Hay:
x1=0x_{1} = 0
x2=2x_{2} = 2
x3=4x_{3} = 4
x4=6x_{4} = 6
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(x−1x(x−2)(x−4)(x−6))=0\lim_{x \to -\infty}\left(\frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=0y = 0
lim⁡x→∞(x−1x(x−2)(x−4)(x−6))=0\lim_{x \to \infty}\left(\frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)}\right) = 0
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=0y = 0
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función sqrt(x - 1)/((((x*(x - 2))*(x - 4))*(x - 6))), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(1x(x−6)(x−4)(x−2)x−1x)=0\lim_{x \to -\infty}\left(\frac{\frac{1}{x \left(x - 6\right) \left(x - 4\right) \left(x - 2\right)} \sqrt{x - 1}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(1x(x−6)(x−4)(x−2)x−1x)=0\lim_{x \to \infty}\left(\frac{\frac{1}{x \left(x - 6\right) \left(x - 4\right) \left(x - 2\right)} \sqrt{x - 1}}{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:
x−1x(x−2)(x−4)(x−6)=−−x−1x(−x−6)(−x−4)(−x−2)\frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)} = - \frac{\sqrt{- x - 1}}{x \left(- x - 6\right) \left(- x - 4\right) \left(- x - 2\right)}
- No
x−1x(x−2)(x−4)(x−6)=−x−1x(−x−6)(−x−4)(−x−2)\frac{\sqrt{x - 1}}{x \left(x - 2\right) \left(x - 4\right) \left(x - 6\right)} = \frac{\sqrt{- x - 1}}{x \left(- x - 6\right) \left(- x - 4\right) \left(- x - 2\right)}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор