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- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
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- Desigualdades:
-
(x+4)(x-8)>0
-
(x+4)*(x-8)>0
-
(x-1)^2>0
-
(x-1)^2*(x-4)<=0
-
Expresiones idénticas
- (logx^(uno / dos)(cos(x))+ uno)/(dos x^2+ cero . tres)> cero
- ( logaritmo de x en el grado (1 dividir por 2)( coseno de (x)) más 1) dividir por (2x al cuadrado más 0.3) más 0
- ( logaritmo de x en el grado (uno dividir por dos)( coseno de (x)) más uno) dividir por (dos x al cuadrado más cero . tres) más cero
- (logx(1/2)(cos(x))+1)/(2x2+0.3)>0
- logx1/2cosx+1/2x2+0.3>0
- (logx^(1/2)(cos(x))+1)/(2x²+0.3)>0
- (logx en el grado (1/2)(cos(x))+1)/(2x en el grado 2+0.3)>0
- logx^1/2cosx+1/2x^2+0.3>0
- (logx^(1 dividir por 2)(cos(x))+1) dividir por (2x^2+0.3)>0
-
Expresiones semejantes
- (logx^(1/2)(cos(x))+1)/(2x^2-0.3)>0
- (logx^(1/2)(cos(x))-1)/(2x^2+0.3)>0
- (logx^(1/2)(cosx)+1)/(2x^2+0.3)>0
-
Expresiones con funciones
- logx
- logx(6-x)>2
- logx(21-4*x)>2
- logx(3x+1)>logx(x+2)
- logx/x-3(7)<logx/3(7)
- logx(x^2+3x-3)>1
- Coseno cos
- cosx<√2/2
- cosx<1/2
- cosx/2>-1/2
- cosx>√3/2
- cosx>=x^2+1
(logx^(1/2)(cos(x))+1)/(2x^2+0.3)>0 desigualdades
Solución
Ha introducido
[src]
________
\/ log(x) *cos(x) + 1
--------------------- > 0
2 3
2*x + --
10
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0$$
(sqrt(log(x))*cos(x) + 1)/(2*x^2 + 3/10) > 0
Solución detallada
Se da la desigualdad:
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} = 0$$
Resolvemos:
$$x_{1} = 71.1912792889667$$
$$x_{2} = 98.474533286571$$
$$x_{3} = 39.81790749774$$
$$x_{4} = 21.0304855439734$$
$$x_{5} = 16.6398016669406$$
$$x_{6} = -14.5888124902477 + 0.226872717278656 i$$
$$x_{7} = 92.1875094576666$$
$$x_{8} = 10.281291113331$$
$$x_{9} = -39.7038117619331 + 0.17233651300255 i$$
$$x_{10} = -96.2321309612412 + 0.137179335755008 i$$
$$x_{11} = -45.9837737712157 + 0.165738764495262 i$$
$$x_{12} = 52.3629208376902$$
$$x_{13} = -8.30976228954732 + 0.265285357278091 i$$
$$x_{14} = 73.3238866173867$$
$$x_{15} = 33.5494926868552$$
$$x_{16} = 2.89542674062072$$
$$x_{17} = 41.8676121416725$$
$$x_{18} = 96.3054969471318$$
$$x_{19} = -2.00403434136006 + 0.381685209669179 i$$
$$x_{20} = 46.0893682722708$$
$$x_{21} = -33.4242689303608 - 0.180502407081655 i$$
$$x_{22} = 85.900110905374$$
$$x_{23} = 67.0348489150335$$
$$x_{24} = 48.1617912315399$$
$$x_{25} = -20.8667854490919 + 0.205372682871723 i$$
$$x_{26} = 35.5707249305613$$
$$x_{27} = 77.4690706575254$$
$$x_{28} = -27.1452347681677 + 0.191019151516423 i$$
$$x_{29} = -64.8254962012094 + 0.151548289135052 i$$
$$x_{30} = -71.1065236432573 + 0.148006153381578 i$$
$$x_{31} = -83.6690686014435 + 0.142043989123022 i$$
$$x_{32} = -89.9505434161105 - 0.139497269580281 i$$
$$x_{33} = -77.3877222898321 + 0.144862032629662 i$$
$$x_{34} = 79.612267055827$$
$$x_{35} = -77.3877222898321 - 0.144862032629662 i$$
$$x_{36} = 60.7449902944826$$
$$x_{37} = 90.0262672782923$$
$$x_{38} = 3.6362645418106$$
$$x_{39} = -33.4242689303608 + 0.180502407081655 i$$
$$x_{40} = 83.7474330794998$$
$$x_{41} = 27.2858437418209$$
$$x_{42} = -52.2640794943649 + 0.160251249342434 i$$
$$x_{43} = 54.4540818737093$$
$$x_{44} = 58.6379866203864$$
$$x_{45} = -58.5446692207647 + 0.155585268948379 i$$
$$x_{46} = 14.7922764129932$$
$$x_{47} = -45.9837737712157 - 0.165738764495262 i$$
$$x_{48} = 64.9141910839444$$
$$x_{49} = 8.6039855648616$$
$$x_{50} = 22.9616469753377$$
$$x_{51} = -89.9505434161105 + 0.139497269580281 i$$
$$x_{52} = 29.2696879165931$$
Descartamos las soluciones complejas:
$$x_{1} = 71.1912792889667$$
$$x_{2} = 98.474533286571$$
$$x_{3} = 39.81790749774$$
$$x_{4} = 21.0304855439734$$
$$x_{5} = 16.6398016669406$$
$$x_{6} = 92.1875094576666$$
$$x_{7} = 10.281291113331$$
$$x_{8} = 52.3629208376902$$
$$x_{9} = 73.3238866173867$$
$$x_{10} = 33.5494926868552$$
$$x_{11} = 2.89542674062072$$
$$x_{12} = 41.8676121416725$$
$$x_{13} = 96.3054969471318$$
$$x_{14} = 46.0893682722708$$
$$x_{15} = 85.900110905374$$
$$x_{16} = 67.0348489150335$$
$$x_{17} = 48.1617912315399$$
$$x_{18} = 35.5707249305613$$
$$x_{19} = 77.4690706575254$$
$$x_{20} = 79.612267055827$$
$$x_{21} = 60.7449902944826$$
$$x_{22} = 90.0262672782923$$
$$x_{23} = 3.6362645418106$$
$$x_{24} = 83.7474330794998$$
$$x_{25} = 27.2858437418209$$
$$x_{26} = 54.4540818737093$$
$$x_{27} = 58.6379866203864$$
$$x_{28} = 14.7922764129932$$
$$x_{29} = 64.9141910839444$$
$$x_{30} = 8.6039855648616$$
$$x_{31} = 22.9616469753377$$
$$x_{32} = 29.2696879165931$$
Las raíces dadas
$$x_{11} = 2.89542674062072$$
$$x_{23} = 3.6362645418106$$
$$x_{30} = 8.6039855648616$$
$$x_{7} = 10.281291113331$$
$$x_{28} = 14.7922764129932$$
$$x_{5} = 16.6398016669406$$
$$x_{4} = 21.0304855439734$$
$$x_{31} = 22.9616469753377$$
$$x_{25} = 27.2858437418209$$
$$x_{32} = 29.2696879165931$$
$$x_{10} = 33.5494926868552$$
$$x_{18} = 35.5707249305613$$
$$x_{3} = 39.81790749774$$
$$x_{12} = 41.8676121416725$$
$$x_{14} = 46.0893682722708$$
$$x_{17} = 48.1617912315399$$
$$x_{8} = 52.3629208376902$$
$$x_{26} = 54.4540818737093$$
$$x_{27} = 58.6379866203864$$
$$x_{21} = 60.7449902944826$$
$$x_{29} = 64.9141910839444$$
$$x_{16} = 67.0348489150335$$
$$x_{1} = 71.1912792889667$$
$$x_{9} = 73.3238866173867$$
$$x_{19} = 77.4690706575254$$
$$x_{20} = 79.612267055827$$
$$x_{24} = 83.7474330794998$$
$$x_{15} = 85.900110905374$$
$$x_{22} = 90.0262672782923$$
$$x_{6} = 92.1875094576666$$
$$x_{13} = 96.3054969471318$$
$$x_{2} = 98.474533286571$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{11}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{11} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2.89542674062072$$
=
$$2.79542674062072$$
lo sustituimos en la expresión
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0$$
$$\frac{\sqrt{\log{\left(2.79542674062072 \right)}} \cos{\left(2.79542674062072 \right)} + 1}{\frac{3}{10} + 2 \cdot 2.79542674062072^{2}} > 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < 2.89542674062072$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < 2.89542674062072$$
$$x > 3.6362645418106 \wedge x < 8.6039855648616$$
$$x > 10.281291113331 \wedge x < 14.7922764129932$$
$$x > 16.6398016669406 \wedge x < 21.0304855439734$$
$$x > 22.9616469753377 \wedge x < 27.2858437418209$$
$$x > 29.2696879165931 \wedge x < 33.5494926868552$$
$$x > 35.5707249305613 \wedge x < 39.81790749774$$
$$x > 41.8676121416725 \wedge x < 46.0893682722708$$
$$x > 48.1617912315399 \wedge x < 52.3629208376902$$
$$x > 54.4540818737093 \wedge x < 58.6379866203864$$
$$x > 60.7449902944826 \wedge x < 64.9141910839444$$
$$x > 67.0348489150335 \wedge x < 71.1912792889667$$
$$x > 73.3238866173867 \wedge x < 77.4690706575254$$
$$x > 79.612267055827 \wedge x < 83.7474330794998$$
$$x > 85.900110905374 \wedge x < 90.0262672782923$$
$$x > 92.1875094576666 \wedge x < 96.3054969471318$$
$$x > 98.474533286571$$
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} = 0$$
Resolvemos:
$$x_{1} = 71.1912792889667$$
$$x_{2} = 98.474533286571$$
$$x_{3} = 39.81790749774$$
$$x_{4} = 21.0304855439734$$
$$x_{5} = 16.6398016669406$$
$$x_{6} = -14.5888124902477 + 0.226872717278656 i$$
$$x_{7} = 92.1875094576666$$
$$x_{8} = 10.281291113331$$
$$x_{9} = -39.7038117619331 + 0.17233651300255 i$$
$$x_{10} = -96.2321309612412 + 0.137179335755008 i$$
$$x_{11} = -45.9837737712157 + 0.165738764495262 i$$
$$x_{12} = 52.3629208376902$$
$$x_{13} = -8.30976228954732 + 0.265285357278091 i$$
$$x_{14} = 73.3238866173867$$
$$x_{15} = 33.5494926868552$$
$$x_{16} = 2.89542674062072$$
$$x_{17} = 41.8676121416725$$
$$x_{18} = 96.3054969471318$$
$$x_{19} = -2.00403434136006 + 0.381685209669179 i$$
$$x_{20} = 46.0893682722708$$
$$x_{21} = -33.4242689303608 - 0.180502407081655 i$$
$$x_{22} = 85.900110905374$$
$$x_{23} = 67.0348489150335$$
$$x_{24} = 48.1617912315399$$
$$x_{25} = -20.8667854490919 + 0.205372682871723 i$$
$$x_{26} = 35.5707249305613$$
$$x_{27} = 77.4690706575254$$
$$x_{28} = -27.1452347681677 + 0.191019151516423 i$$
$$x_{29} = -64.8254962012094 + 0.151548289135052 i$$
$$x_{30} = -71.1065236432573 + 0.148006153381578 i$$
$$x_{31} = -83.6690686014435 + 0.142043989123022 i$$
$$x_{32} = -89.9505434161105 - 0.139497269580281 i$$
$$x_{33} = -77.3877222898321 + 0.144862032629662 i$$
$$x_{34} = 79.612267055827$$
$$x_{35} = -77.3877222898321 - 0.144862032629662 i$$
$$x_{36} = 60.7449902944826$$
$$x_{37} = 90.0262672782923$$
$$x_{38} = 3.6362645418106$$
$$x_{39} = -33.4242689303608 + 0.180502407081655 i$$
$$x_{40} = 83.7474330794998$$
$$x_{41} = 27.2858437418209$$
$$x_{42} = -52.2640794943649 + 0.160251249342434 i$$
$$x_{43} = 54.4540818737093$$
$$x_{44} = 58.6379866203864$$
$$x_{45} = -58.5446692207647 + 0.155585268948379 i$$
$$x_{46} = 14.7922764129932$$
$$x_{47} = -45.9837737712157 - 0.165738764495262 i$$
$$x_{48} = 64.9141910839444$$
$$x_{49} = 8.6039855648616$$
$$x_{50} = 22.9616469753377$$
$$x_{51} = -89.9505434161105 + 0.139497269580281 i$$
$$x_{52} = 29.2696879165931$$
Descartamos las soluciones complejas:
$$x_{1} = 71.1912792889667$$
$$x_{2} = 98.474533286571$$
$$x_{3} = 39.81790749774$$
$$x_{4} = 21.0304855439734$$
$$x_{5} = 16.6398016669406$$
$$x_{6} = 92.1875094576666$$
$$x_{7} = 10.281291113331$$
$$x_{8} = 52.3629208376902$$
$$x_{9} = 73.3238866173867$$
$$x_{10} = 33.5494926868552$$
$$x_{11} = 2.89542674062072$$
$$x_{12} = 41.8676121416725$$
$$x_{13} = 96.3054969471318$$
$$x_{14} = 46.0893682722708$$
$$x_{15} = 85.900110905374$$
$$x_{16} = 67.0348489150335$$
$$x_{17} = 48.1617912315399$$
$$x_{18} = 35.5707249305613$$
$$x_{19} = 77.4690706575254$$
$$x_{20} = 79.612267055827$$
$$x_{21} = 60.7449902944826$$
$$x_{22} = 90.0262672782923$$
$$x_{23} = 3.6362645418106$$
$$x_{24} = 83.7474330794998$$
$$x_{25} = 27.2858437418209$$
$$x_{26} = 54.4540818737093$$
$$x_{27} = 58.6379866203864$$
$$x_{28} = 14.7922764129932$$
$$x_{29} = 64.9141910839444$$
$$x_{30} = 8.6039855648616$$
$$x_{31} = 22.9616469753377$$
$$x_{32} = 29.2696879165931$$
Las raíces dadas
$$x_{11} = 2.89542674062072$$
$$x_{23} = 3.6362645418106$$
$$x_{30} = 8.6039855648616$$
$$x_{7} = 10.281291113331$$
$$x_{28} = 14.7922764129932$$
$$x_{5} = 16.6398016669406$$
$$x_{4} = 21.0304855439734$$
$$x_{31} = 22.9616469753377$$
$$x_{25} = 27.2858437418209$$
$$x_{32} = 29.2696879165931$$
$$x_{10} = 33.5494926868552$$
$$x_{18} = 35.5707249305613$$
$$x_{3} = 39.81790749774$$
$$x_{12} = 41.8676121416725$$
$$x_{14} = 46.0893682722708$$
$$x_{17} = 48.1617912315399$$
$$x_{8} = 52.3629208376902$$
$$x_{26} = 54.4540818737093$$
$$x_{27} = 58.6379866203864$$
$$x_{21} = 60.7449902944826$$
$$x_{29} = 64.9141910839444$$
$$x_{16} = 67.0348489150335$$
$$x_{1} = 71.1912792889667$$
$$x_{9} = 73.3238866173867$$
$$x_{19} = 77.4690706575254$$
$$x_{20} = 79.612267055827$$
$$x_{24} = 83.7474330794998$$
$$x_{15} = 85.900110905374$$
$$x_{22} = 90.0262672782923$$
$$x_{6} = 92.1875094576666$$
$$x_{13} = 96.3054969471318$$
$$x_{2} = 98.474533286571$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{11}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{11} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 2.89542674062072$$
=
$$2.79542674062072$$
lo sustituimos en la expresión
$$\frac{\sqrt{\log{\left(x \right)}} \cos{\left(x \right)} + 1}{2 x^{2} + \frac{3}{10}} > 0$$
$$\frac{\sqrt{\log{\left(2.79542674062072 \right)}} \cos{\left(2.79542674062072 \right)} + 1}{\frac{3}{10} + 2 \cdot 2.79542674062072^{2}} > 0$$
0.00290341311615150 > 0
significa que una de las soluciones de nuestra ecuación será con:
$$x < 2.89542674062072$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x11 x23 x30 x7 x28 x5 x4 x31 x25 x32 x10 x18 x3 x12 x14 x17 x8 x26 x27 x21 x29 x16 x1 x9 x19 x20 x24 x15 x22 x6 x13 x2Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < 2.89542674062072$$
$$x > 3.6362645418106 \wedge x < 8.6039855648616$$
$$x > 10.281291113331 \wedge x < 14.7922764129932$$
$$x > 16.6398016669406 \wedge x < 21.0304855439734$$
$$x > 22.9616469753377 \wedge x < 27.2858437418209$$
$$x > 29.2696879165931 \wedge x < 33.5494926868552$$
$$x > 35.5707249305613 \wedge x < 39.81790749774$$
$$x > 41.8676121416725 \wedge x < 46.0893682722708$$
$$x > 48.1617912315399 \wedge x < 52.3629208376902$$
$$x > 54.4540818737093 \wedge x < 58.6379866203864$$
$$x > 60.7449902944826 \wedge x < 64.9141910839444$$
$$x > 67.0348489150335 \wedge x < 71.1912792889667$$
$$x > 73.3238866173867 \wedge x < 77.4690706575254$$
$$x > 79.612267055827 \wedge x < 83.7474330794998$$
$$x > 85.900110905374 \wedge x < 90.0262672782923$$
$$x > 92.1875094576666 \wedge x < 96.3054969471318$$
$$x > 98.474533286571$$
Solución de la desigualdad en el gráfico