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- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
y=(x+1)^3
-
y=2x
-
2*x^3-3*x
-
3-x^2
-
Expresiones idénticas
- cos(dos *n)/(- tres +sqrt(n))
- coseno de (2 multiplicar por n) dividir por ( menos 3 más raíz cuadrada de (n))
- coseno de (dos multiplicar por n) dividir por ( menos tres más raíz cuadrada de (n))
- cos(2*n)/(-3+√(n))
- cos(2n)/(-3+sqrt(n))
- cos2n/-3+sqrtn
- cos(2*n) dividir por (-3+sqrt(n))
-
Expresiones semejantes
- cos(2*n)/(3+sqrt(n))
- cos(2*n)/(-3-sqrt(n))
-
Expresiones con funciones
- Coseno cos
- cos[x]/x^2
- cos(x-pi/3)-1
- cos(x)/(1+cos^2*2x)
- cos(1)/((3*x))
- cos(sqrt(x))+1
- Raíz cuadrada sqrt
- sqrt(x^2+4*x+4)
- sqrt(x^2+1)-sqrt(x^2-1)
- sqrt(x^2-6*x+11)
- sqrt[x^2+10x+26]-2
- sqrt(9*x)^2+5
Gráfico de la función y = cos(2*n)/(-3+sqrt(n))
Solución
Ha introducido
[src]
cos(2*n)
f(n) = ----------
___
-3 + \/ n
$$f{\left(n \right)} = \frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3}$$
f = cos(2*n)/(sqrt(n) - 3)
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$n_{1} = 9$$
$$n_{1} = 9$$
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje N con f = 0
o sea hay que resolver la ecuación:
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje N:
Solución analítica
$$n_{1} = \frac{\pi}{4}$$
$$n_{2} = \frac{3 \pi}{4}$$
Solución numérica
$$n_{1} = -46.3384916404494$$
$$n_{2} = 107.59954838545$$
$$n_{3} = -93.4623814442964$$
$$n_{4} = 2.35619449019234$$
$$n_{5} = 19.6349540849362$$
$$n_{6} = 5.49778714378214$$
$$n_{7} = -5.49778714378214$$
$$n_{8} = -63.6172512351933$$
$$n_{9} = 99.7455667514759$$
$$n_{10} = 33.7721210260903$$
$$n_{11} = 38.484510006475$$
$$n_{12} = 96.6039740978861$$
$$n_{13} = 66.7588438887831$$
$$n_{14} = -71.4712328691678$$
$$n_{15} = -49.4800842940392$$
$$n_{16} = -76.1836218495525$$
$$n_{17} = -25.9181393921158$$
$$n_{18} = -7.06858347057703$$
$$n_{19} = 27.4889357189107$$
$$n_{20} = 62.0464549083984$$
$$n_{21} = 91.8915851175014$$
$$n_{22} = 25.9181393921158$$
$$n_{23} = -2.35619449019234$$
$$n_{24} = 24.3473430653209$$
$$n_{25} = 76.1836218495525$$
$$n_{26} = -19.6349540849362$$
$$n_{27} = -54.1924732744239$$
$$n_{28} = 82.4668071567321$$
$$n_{29} = -13.3517687777566$$
$$n_{30} = 77.7544181763474$$
$$n_{31} = -77.7544181763474$$
$$n_{32} = 46.3384916404494$$
$$n_{33} = 16.4933614313464$$
$$n_{34} = -11.7809724509617$$
$$n_{35} = -3.92699081698724$$
$$n_{36} = -36.9137136796801$$
$$n_{37} = 22.776546738526$$
$$n_{38} = -27.4889357189107$$
$$n_{39} = -90.3207887907066$$
$$n_{40} = -57.3340659280137$$
$$n_{41} = -82.4668071567321$$
$$n_{42} = 74.6128255227576$$
$$n_{43} = -24.3473430653209$$
$$n_{44} = -40.0553063332699$$
$$n_{45} = -18.0641577581413$$
$$n_{46} = 18.0641577581413$$
$$n_{47} = 60.4756585816035$$
$$n_{48} = 11.7809724509617$$
$$n_{49} = 69.9004365423729$$
$$n_{50} = -35.3429173528852$$
$$n_{51} = -16.4933614313464$$
$$n_{52} = -99.7455667514759$$
$$n_{53} = 88.7499924639117$$
$$n_{54} = 55.7632696012188$$
$$n_{55} = -69.9004365423729$$
$$n_{56} = 47.9092879672443$$
$$n_{57} = -41.6261026600648$$
$$n_{58} = -79.3252145031423$$
$$n_{59} = -85.6083998103219$$
$$n_{60} = 54.1924732744239$$
$$n_{61} = -62.0464549083984$$
$$n_{62} = 40.0553063332699$$
$$n_{63} = -60.4756585816035$$
$$n_{64} = 41.6261026600648$$
$$n_{65} = 90.3207887907066$$
$$n_{66} = -91.8915851175014$$
$$n_{67} = -55.7632696012188$$
$$n_{68} = 3.92699081698724$$
$$n_{69} = 32.2013246992954$$
$$n_{70} = 57.3340659280137$$
$$n_{71} = -32.2013246992954$$
$$n_{72} = 30.6305283725005$$
$$n_{73} = 49.4800842940392$$
$$n_{74} = 85.6083998103219$$
$$n_{75} = -47.9092879672443$$
$$n_{76} = -84.037603483527$$
$$n_{77} = 98.174770424681$$
$$n_{78} = 52.621676947629$$
$$n_{79} = 44.7676953136546$$
$$n_{80} = 63.6172512351933$$
$$n_{81} = -98.174770424681$$
$$n_{82} = -68.329640215578$$
$$n_{83} = -10.2101761241668$$
$$n_{84} = 68.329640215578$$
$$n_{85} = -33.7721210260903$$
$$n_{86} = 10.2101761241668$$
$$n_{87} = 84.037603483527$$
o sea hay que resolver la ecuación:
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje N:
Solución analítica
$$n_{1} = \frac{\pi}{4}$$
$$n_{2} = \frac{3 \pi}{4}$$
Solución numérica
$$n_{1} = -46.3384916404494$$
$$n_{2} = 107.59954838545$$
$$n_{3} = -93.4623814442964$$
$$n_{4} = 2.35619449019234$$
$$n_{5} = 19.6349540849362$$
$$n_{6} = 5.49778714378214$$
$$n_{7} = -5.49778714378214$$
$$n_{8} = -63.6172512351933$$
$$n_{9} = 99.7455667514759$$
$$n_{10} = 33.7721210260903$$
$$n_{11} = 38.484510006475$$
$$n_{12} = 96.6039740978861$$
$$n_{13} = 66.7588438887831$$
$$n_{14} = -71.4712328691678$$
$$n_{15} = -49.4800842940392$$
$$n_{16} = -76.1836218495525$$
$$n_{17} = -25.9181393921158$$
$$n_{18} = -7.06858347057703$$
$$n_{19} = 27.4889357189107$$
$$n_{20} = 62.0464549083984$$
$$n_{21} = 91.8915851175014$$
$$n_{22} = 25.9181393921158$$
$$n_{23} = -2.35619449019234$$
$$n_{24} = 24.3473430653209$$
$$n_{25} = 76.1836218495525$$
$$n_{26} = -19.6349540849362$$
$$n_{27} = -54.1924732744239$$
$$n_{28} = 82.4668071567321$$
$$n_{29} = -13.3517687777566$$
$$n_{30} = 77.7544181763474$$
$$n_{31} = -77.7544181763474$$
$$n_{32} = 46.3384916404494$$
$$n_{33} = 16.4933614313464$$
$$n_{34} = -11.7809724509617$$
$$n_{35} = -3.92699081698724$$
$$n_{36} = -36.9137136796801$$
$$n_{37} = 22.776546738526$$
$$n_{38} = -27.4889357189107$$
$$n_{39} = -90.3207887907066$$
$$n_{40} = -57.3340659280137$$
$$n_{41} = -82.4668071567321$$
$$n_{42} = 74.6128255227576$$
$$n_{43} = -24.3473430653209$$
$$n_{44} = -40.0553063332699$$
$$n_{45} = -18.0641577581413$$
$$n_{46} = 18.0641577581413$$
$$n_{47} = 60.4756585816035$$
$$n_{48} = 11.7809724509617$$
$$n_{49} = 69.9004365423729$$
$$n_{50} = -35.3429173528852$$
$$n_{51} = -16.4933614313464$$
$$n_{52} = -99.7455667514759$$
$$n_{53} = 88.7499924639117$$
$$n_{54} = 55.7632696012188$$
$$n_{55} = -69.9004365423729$$
$$n_{56} = 47.9092879672443$$
$$n_{57} = -41.6261026600648$$
$$n_{58} = -79.3252145031423$$
$$n_{59} = -85.6083998103219$$
$$n_{60} = 54.1924732744239$$
$$n_{61} = -62.0464549083984$$
$$n_{62} = 40.0553063332699$$
$$n_{63} = -60.4756585816035$$
$$n_{64} = 41.6261026600648$$
$$n_{65} = 90.3207887907066$$
$$n_{66} = -91.8915851175014$$
$$n_{67} = -55.7632696012188$$
$$n_{68} = 3.92699081698724$$
$$n_{69} = 32.2013246992954$$
$$n_{70} = 57.3340659280137$$
$$n_{71} = -32.2013246992954$$
$$n_{72} = 30.6305283725005$$
$$n_{73} = 49.4800842940392$$
$$n_{74} = 85.6083998103219$$
$$n_{75} = -47.9092879672443$$
$$n_{76} = -84.037603483527$$
$$n_{77} = 98.174770424681$$
$$n_{78} = 52.621676947629$$
$$n_{79} = 44.7676953136546$$
$$n_{80} = 63.6172512351933$$
$$n_{81} = -98.174770424681$$
$$n_{82} = -68.329640215578$$
$$n_{83} = -10.2101761241668$$
$$n_{84} = 68.329640215578$$
$$n_{85} = -33.7721210260903$$
$$n_{86} = 10.2101761241668$$
$$n_{87} = 84.037603483527$$
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d n} f{\left(n \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d n} f{\left(n \right)} = $$
primera derivada
$$- \frac{2 \sin{\left(2 n \right)}}{\sqrt{n} - 3} - \frac{\cos{\left(2 n \right)}}{2 \sqrt{n} \left(\sqrt{n} - 3\right)^{2}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$n_{1} = 70.6830851309004$$
$$n_{2} = 78.5374102453155$$
$$n_{3} = 6.38629728547638$$
$$n_{4} = 45.5481531883468$$
$$n_{5} = 8.11731854421992$$
$$n_{6} = 157.078586474577$$
$$n_{7} = 36.1214064737428$$
$$n_{8} = 64.399549605123$$
$$n_{9} = 94.2458601360682$$
$$n_{10} = 20.4021161735597$$
$$n_{11} = 14.0931253451482$$
$$n_{12} = 23.5480443722197$$
$$n_{13} = 42.4060353800282$$
$$n_{14} = 43.9771068533672$$
$$n_{15} = 89.5333463755868$$
$$n_{16} = 73.824825840124$$
$$n_{17} = 100.529190612205$$
$$n_{18} = 95.8166948550549$$
$$n_{19} = 15.6750948155792$$
$$n_{20} = 48.6901828315696$$
$$n_{21} = 28.264185022968$$
$$n_{22} = 81.679118212623$$
$$n_{23} = 65.970441227173$$
$$n_{24} = 10.8706173948531$$
$$n_{25} = 1.62737987261952$$
$$n_{26} = 92.6750238793872$$
$$n_{27} = 67.5413273993203$$
$$n_{28} = 56.5449898533705$$
$$n_{29} = 34.5501304145796$$
$$n_{30} = 12.5007461644164$$
$$n_{31} = 51.8321444303151$$
$$n_{32} = 86.391661509481$$
$$n_{33} = 80.1082655876698$$
$$n_{34} = 29.8358370323357$$
$$n_{35} = 72.2539574476408$$
$$n_{36} = 26.6923716914806$$
$$n_{37} = 50.2611711248153$$
$$n_{38} = 59.6868367202835$$
$$n_{39} = 58.1159176268788$$
$$n_{40} = 21.9753550261319$$
$$n_{41} = 87.9625049203305$$
$$n_{42} = 37.6926268971637$$
$$n_{43} = 3.19902956050771$$
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:
$$n_{1} = 70.6830851309004$$
$$n_{2} = 6.38629728547638$$
$$n_{3} = 45.5481531883468$$
$$n_{4} = 36.1214064737428$$
$$n_{5} = 64.399549605123$$
$$n_{6} = 20.4021161735597$$
$$n_{7} = 14.0931253451482$$
$$n_{8} = 23.5480443722197$$
$$n_{9} = 42.4060353800282$$
$$n_{10} = 89.5333463755868$$
$$n_{11} = 73.824825840124$$
$$n_{12} = 95.8166948550549$$
$$n_{13} = 48.6901828315696$$
$$n_{14} = 10.8706173948531$$
$$n_{15} = 92.6750238793872$$
$$n_{16} = 67.5413273993203$$
$$n_{17} = 51.8321444303151$$
$$n_{18} = 86.391661509481$$
$$n_{19} = 80.1082655876698$$
$$n_{20} = 29.8358370323357$$
$$n_{21} = 26.6923716914806$$
$$n_{22} = 58.1159176268788$$
$$n_{23} = 3.19902956050771$$
Puntos máximos de la función:
$$n_{23} = 78.5374102453155$$
$$n_{23} = 8.11731854421992$$
$$n_{23} = 157.078586474577$$
$$n_{23} = 94.2458601360682$$
$$n_{23} = 43.9771068533672$$
$$n_{23} = 100.529190612205$$
$$n_{23} = 15.6750948155792$$
$$n_{23} = 28.264185022968$$
$$n_{23} = 81.679118212623$$
$$n_{23} = 65.970441227173$$
$$n_{23} = 1.62737987261952$$
$$n_{23} = 56.5449898533705$$
$$n_{23} = 34.5501304145796$$
$$n_{23} = 12.5007461644164$$
$$n_{23} = 72.2539574476408$$
$$n_{23} = 50.2611711248153$$
$$n_{23} = 59.6868367202835$$
$$n_{23} = 21.9753550261319$$
$$n_{23} = 87.9625049203305$$
$$n_{23} = 37.6926268971637$$
Decrece en los intervalos
$$\left[95.8166948550549, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, 3.19902956050771\right]$$
$$\frac{d}{d n} f{\left(n \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d n} f{\left(n \right)} = $$
primera derivada
$$- \frac{2 \sin{\left(2 n \right)}}{\sqrt{n} - 3} - \frac{\cos{\left(2 n \right)}}{2 \sqrt{n} \left(\sqrt{n} - 3\right)^{2}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$n_{1} = 70.6830851309004$$
$$n_{2} = 78.5374102453155$$
$$n_{3} = 6.38629728547638$$
$$n_{4} = 45.5481531883468$$
$$n_{5} = 8.11731854421992$$
$$n_{6} = 157.078586474577$$
$$n_{7} = 36.1214064737428$$
$$n_{8} = 64.399549605123$$
$$n_{9} = 94.2458601360682$$
$$n_{10} = 20.4021161735597$$
$$n_{11} = 14.0931253451482$$
$$n_{12} = 23.5480443722197$$
$$n_{13} = 42.4060353800282$$
$$n_{14} = 43.9771068533672$$
$$n_{15} = 89.5333463755868$$
$$n_{16} = 73.824825840124$$
$$n_{17} = 100.529190612205$$
$$n_{18} = 95.8166948550549$$
$$n_{19} = 15.6750948155792$$
$$n_{20} = 48.6901828315696$$
$$n_{21} = 28.264185022968$$
$$n_{22} = 81.679118212623$$
$$n_{23} = 65.970441227173$$
$$n_{24} = 10.8706173948531$$
$$n_{25} = 1.62737987261952$$
$$n_{26} = 92.6750238793872$$
$$n_{27} = 67.5413273993203$$
$$n_{28} = 56.5449898533705$$
$$n_{29} = 34.5501304145796$$
$$n_{30} = 12.5007461644164$$
$$n_{31} = 51.8321444303151$$
$$n_{32} = 86.391661509481$$
$$n_{33} = 80.1082655876698$$
$$n_{34} = 29.8358370323357$$
$$n_{35} = 72.2539574476408$$
$$n_{36} = 26.6923716914806$$
$$n_{37} = 50.2611711248153$$
$$n_{38} = 59.6868367202835$$
$$n_{39} = 58.1159176268788$$
$$n_{40} = 21.9753550261319$$
$$n_{41} = 87.9625049203305$$
$$n_{42} = 37.6926268971637$$
$$n_{43} = 3.19902956050771$$
Signos de extremos en los puntos:
(70.68308513090037, -0.184931586955847)
(78.5374102453155, 0.170584382074242)
(6.386297285476382, -2.06986010438309)
(45.54815318834676, -0.266729245366475)
(8.11731854421992, 5.72850394577009)
(157.07858647457732, 0.104897446700594)
(36.12140647374277, -0.332182201552589)
(64.39954960512303, -0.199003804276507)
(94.24586013606816, 0.149073949643014)
(20.40211617355971, -0.658813774348403)
(14.093125345148245, -1.32097609370413)
(23.548044372219653, -0.5395638118)
(42.40603538002821, -0.28472170644289)
(43.97710685336724, 0.275351670297758)
(89.53334637558676, -0.154744619633328)
(73.82482584012402, -0.178820079873054)
(100.5291906122048, 0.142318996948088)
(95.81669485505493, -0.147304729437117)
(15.675094815579234, 1.04030694221653)
(48.690182831569594, -0.251382828360378)
(28.264185022968018, 0.431614108436005)
(81.67911821262301, 0.165625615652143)
(65.97044122717296, 0.195224364503229)
(10.87061739485307, -3.26172302109014)
(1.6273798726195188, 0.576231816234792)
(92.67502387938723, -0.150901538460956)
(67.54132739932027, -0.191628085281248)
(56.54498985337054, 0.221250560972295)
(34.550130414579556, 0.347433316663596)
(12.500746164416444, 1.85087050855428)
(51.83214443031513, -0.238118028297417)
(86.39166150948098, -0.158862066056694)
(80.1082655876698, -0.168056277736239)
(29.835837032335686, -0.406067557494453)
(72.25395744764081, 0.181807887500748)
(26.692371691480556, -0.461466103450614)
(50.261171124815284, 0.244518902248487)
(59.68683672028347, 0.211602753119934)
(58.115917626878776, -0.216286551435883)
(21.975355026131936, 0.592195969897178)
(87.96250492033055, 0.156767123143844)
(37.69262689716375, 0.318502152699087)
(3.1990295605077073, -0.820039136349884)
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:
$$n_{1} = 70.6830851309004$$
$$n_{2} = 6.38629728547638$$
$$n_{3} = 45.5481531883468$$
$$n_{4} = 36.1214064737428$$
$$n_{5} = 64.399549605123$$
$$n_{6} = 20.4021161735597$$
$$n_{7} = 14.0931253451482$$
$$n_{8} = 23.5480443722197$$
$$n_{9} = 42.4060353800282$$
$$n_{10} = 89.5333463755868$$
$$n_{11} = 73.824825840124$$
$$n_{12} = 95.8166948550549$$
$$n_{13} = 48.6901828315696$$
$$n_{14} = 10.8706173948531$$
$$n_{15} = 92.6750238793872$$
$$n_{16} = 67.5413273993203$$
$$n_{17} = 51.8321444303151$$
$$n_{18} = 86.391661509481$$
$$n_{19} = 80.1082655876698$$
$$n_{20} = 29.8358370323357$$
$$n_{21} = 26.6923716914806$$
$$n_{22} = 58.1159176268788$$
$$n_{23} = 3.19902956050771$$
Puntos máximos de la función:
$$n_{23} = 78.5374102453155$$
$$n_{23} = 8.11731854421992$$
$$n_{23} = 157.078586474577$$
$$n_{23} = 94.2458601360682$$
$$n_{23} = 43.9771068533672$$
$$n_{23} = 100.529190612205$$
$$n_{23} = 15.6750948155792$$
$$n_{23} = 28.264185022968$$
$$n_{23} = 81.679118212623$$
$$n_{23} = 65.970441227173$$
$$n_{23} = 1.62737987261952$$
$$n_{23} = 56.5449898533705$$
$$n_{23} = 34.5501304145796$$
$$n_{23} = 12.5007461644164$$
$$n_{23} = 72.2539574476408$$
$$n_{23} = 50.2611711248153$$
$$n_{23} = 59.6868367202835$$
$$n_{23} = 21.9753550261319$$
$$n_{23} = 87.9625049203305$$
$$n_{23} = 37.6926268971637$$
Decrece en los intervalos
$$\left[95.8166948550549, \infty\right)$$
Crece en los intervalos
$$\left(-\infty, 3.19902956050771\right]$$
Asíntotas verticales
Hay:
$$n_{1} = 9$$
$$n_{1} = 9$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con n->+oo y n->-oo
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 0$$
$$\lim_{n \to \infty}\left(\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = 0$$
$$\lim_{n \to \infty}\left(\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3}\right) = 0$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = 0$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(2*n)/(-3 + sqrt(n)), dividida por n con n->+oo y n ->-oo
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(2 n \right)}}{n \left(\sqrt{n} - 3\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{n \to \infty}\left(\frac{\cos{\left(2 n \right)}}{n \left(\sqrt{n} - 3\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(2 n \right)}}{n \left(\sqrt{n} - 3\right)}\right) = 0$$
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
$$\lim_{n \to \infty}\left(\frac{\cos{\left(2 n \right)}}{n \left(\sqrt{n} - 3\right)}\right) = 0$$
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(-n) и f = -f(-n).
Pues, comprobamos:
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = \frac{\cos{\left(2 n \right)}}{\sqrt{- n} - 3}$$
- No
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = - \frac{\cos{\left(2 n \right)}}{\sqrt{- n} - 3}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = \frac{\cos{\left(2 n \right)}}{\sqrt{- n} - 3}$$
- No
$$\frac{\cos{\left(2 n \right)}}{\sqrt{n} - 3} = - \frac{\cos{\left(2 n \right)}}{\sqrt{- n} - 3}$$
- No
es decir, función
no es
par ni impar