Sr Examen
Otras calculadoras
- Gráfico de la función implícita
- Derivadas paso a paso
- Integrales paso a paso
- Gráfico de la función paramétrica
- Gráfico en coordenadas polares
- Superficie especificada paramétricamente
- Superficie dada por la ecuación
- Curva en el espacio especificada paramétricamente
- Superficie de una figura limitada con líneas
- Puntos de cruce de las funciones
-
¿Cómo usar?
- Gráfico de la función y =:
-
-sqrt(-1+x^2)
-
(e^x)*sin(x)
-
-exp(-2*x)-exp(3*x)
-
-exp(-3*x)-exp(2*x)
-
Expresiones idénticas
- (sinx+tgx)/(dos *x*ctgx)
- ( seno de x más tgx) dividir por (2 multiplicar por x multiplicar por ctgx)
- ( seno de x más tgx) dividir por (dos multiplicar por x multiplicar por ctgx)
- (sinx+tgx)/(2xctgx)
- sinx+tgx/2xctgx
- (sinx+tgx) dividir por (2*x*ctgx)
-
Expresiones semejantes
- (sinx-tgx)/(2*x*ctgx)
Gráfico de la función y = (sinx+tgx)/(2*x*ctgx)
Solución
Ha introducido
[src]
sin(x) + tan(x)
f(x) = ---------------
2*x*cot(x)
$$f{\left(x \right)} = \frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}$$
f = (sin(x) + tan(x))/(((2*x)*cot(x)))
Gráfico de la función
Dominio de definición de la función
Puntos en los que la función no está definida exactamente:
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
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:
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = - \pi$$
$$x_{2} = \pi$$
$$x_{3} = 2 \pi$$
Solución numérica
$$x_{1} = -91.1080860717611$$
$$x_{2} = -25.1327416534355$$
$$x_{3} = -31.41592673575$$
$$x_{4} = -18.849554936845$$
$$x_{5} = -81.6814090386147$$
$$x_{6} = -62.8318521658186$$
$$x_{7} = 31.4159239820201$$
$$x_{8} = -62.8318540332717$$
$$x_{9} = 12.5663700981581$$
$$x_{10} = 47.1209763081767$$
$$x_{11} = 40.8389774408875$$
$$x_{12} = -84.8261831073356$$
$$x_{13} = 34.5566546899828$$
$$x_{14} = 43.9822971695215$$
$$x_{15} = -9.42567821453527$$
$$x_{16} = -40.8376695273069$$
$$x_{17} = -21.9911796982577$$
$$x_{18} = 47.1270880348955$$
$$x_{19} = 81.6814092182089$$
$$x_{20} = -65.9735393758622$$
$$x_{21} = -75.3982238987855$$
$$x_{22} = 25.132742193978$$
$$x_{23} = 94.247779609352$$
$$x_{24} = -15.7080841076436$$
$$x_{25} = -47.1257220786859$$
$$x_{26} = -56.5486706799278$$
$$x_{27} = -59.6904319845233$$
$$x_{28} = 9.42658199496347$$
$$x_{29} = -3.14326707194023$$
$$x_{30} = 62.8318526701909$$
$$x_{31} = 91.1095039335036$$
$$x_{32} = -75.3982155408245$$
$$x_{33} = -87.9645943582203$$
$$x_{34} = -18.8495568079986$$
$$x_{35} = 15.7088922765864$$
$$x_{36} = 65.9735389843344$$
$$x_{37} = 75.3982213788012$$
$$x_{38} = -53.4080340967238$$
$$x_{39} = 25.1327403244751$$
$$x_{40} = 75.3982241638922$$
$$x_{41} = 100.530964745217$$
$$x_{42} = 97.3913416584044$$
$$x_{43} = -72.2558000971762$$
$$x_{44} = 21.9911796938987$$
$$x_{45} = 18.849558891133$$
$$x_{46} = 84.8213388084006$$
$$x_{47} = 28.2742637865287$$
$$x_{48} = 59.6912473597501$$
$$x_{49} = -94.247779428311$$
$$x_{50} = -37.6991118774179$$
$$x_{51} = -84.8200753771042$$
$$x_{52} = 56.5486675835781$$
$$x_{53} = -12.5663701515109$$
$$x_{54} = -43.9822971744317$$
$$x_{55} = 62.8318564649026$$
$$x_{56} = 37.6991120547296$$
$$x_{57} = -28.2734476034419$$
$$x_{58} = -34.5557272431001$$
$$x_{59} = 34.5611202441731$$
$$x_{60} = -6.28318509237865$$
$$x_{61} = 18.849555492068$$
$$x_{62} = -69.1150388295625$$
$$x_{63} = -12.5663731336943$$
$$x_{64} = -56.5486673390634$$
$$x_{65} = 12.5663704177689$$
$$x_{66} = 69.1150375370464$$
$$x_{67} = 78.5390028929786$$
$$x_{68} = -69.1150357551256$$
$$x_{69} = 87.9645943361683$$
$$x_{70} = 6.28318528394097$$
$$x_{71} = 91.1033742827819$$
$$x_{72} = 53.4089756107496$$
$$x_{73} = 72.2566119315779$$
$$x_{74} = 31.4159269876038$$
$$x_{75} = -50.2654822658225$$
$$x_{76} = -25.1327382847962$$
$$x_{77} = 50.2654824463177$$
$$x_{78} = -40.8437719191275$$
$$x_{79} = -31.4159219217159$$
$$x_{80} = 81.68140841851$$
$$x_{81} = -97.3903823516316$$
$$x_{82} = 69.1150394191749$$
$$x_{83} = -100.530964509946$$
$$x_{84} = -78.5380926204531$$
o sea hay que resolver la ecuación:
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = 0$$
Resolvermos esta ecuación
Puntos de cruce con el eje X:
Solución analítica
$$x_{1} = - \pi$$
$$x_{2} = \pi$$
$$x_{3} = 2 \pi$$
Solución numérica
$$x_{1} = -91.1080860717611$$
$$x_{2} = -25.1327416534355$$
$$x_{3} = -31.41592673575$$
$$x_{4} = -18.849554936845$$
$$x_{5} = -81.6814090386147$$
$$x_{6} = -62.8318521658186$$
$$x_{7} = 31.4159239820201$$
$$x_{8} = -62.8318540332717$$
$$x_{9} = 12.5663700981581$$
$$x_{10} = 47.1209763081767$$
$$x_{11} = 40.8389774408875$$
$$x_{12} = -84.8261831073356$$
$$x_{13} = 34.5566546899828$$
$$x_{14} = 43.9822971695215$$
$$x_{15} = -9.42567821453527$$
$$x_{16} = -40.8376695273069$$
$$x_{17} = -21.9911796982577$$
$$x_{18} = 47.1270880348955$$
$$x_{19} = 81.6814092182089$$
$$x_{20} = -65.9735393758622$$
$$x_{21} = -75.3982238987855$$
$$x_{22} = 25.132742193978$$
$$x_{23} = 94.247779609352$$
$$x_{24} = -15.7080841076436$$
$$x_{25} = -47.1257220786859$$
$$x_{26} = -56.5486706799278$$
$$x_{27} = -59.6904319845233$$
$$x_{28} = 9.42658199496347$$
$$x_{29} = -3.14326707194023$$
$$x_{30} = 62.8318526701909$$
$$x_{31} = 91.1095039335036$$
$$x_{32} = -75.3982155408245$$
$$x_{33} = -87.9645943582203$$
$$x_{34} = -18.8495568079986$$
$$x_{35} = 15.7088922765864$$
$$x_{36} = 65.9735389843344$$
$$x_{37} = 75.3982213788012$$
$$x_{38} = -53.4080340967238$$
$$x_{39} = 25.1327403244751$$
$$x_{40} = 75.3982241638922$$
$$x_{41} = 100.530964745217$$
$$x_{42} = 97.3913416584044$$
$$x_{43} = -72.2558000971762$$
$$x_{44} = 21.9911796938987$$
$$x_{45} = 18.849558891133$$
$$x_{46} = 84.8213388084006$$
$$x_{47} = 28.2742637865287$$
$$x_{48} = 59.6912473597501$$
$$x_{49} = -94.247779428311$$
$$x_{50} = -37.6991118774179$$
$$x_{51} = -84.8200753771042$$
$$x_{52} = 56.5486675835781$$
$$x_{53} = -12.5663701515109$$
$$x_{54} = -43.9822971744317$$
$$x_{55} = 62.8318564649026$$
$$x_{56} = 37.6991120547296$$
$$x_{57} = -28.2734476034419$$
$$x_{58} = -34.5557272431001$$
$$x_{59} = 34.5611202441731$$
$$x_{60} = -6.28318509237865$$
$$x_{61} = 18.849555492068$$
$$x_{62} = -69.1150388295625$$
$$x_{63} = -12.5663731336943$$
$$x_{64} = -56.5486673390634$$
$$x_{65} = 12.5663704177689$$
$$x_{66} = 69.1150375370464$$
$$x_{67} = 78.5390028929786$$
$$x_{68} = -69.1150357551256$$
$$x_{69} = 87.9645943361683$$
$$x_{70} = 6.28318528394097$$
$$x_{71} = 91.1033742827819$$
$$x_{72} = 53.4089756107496$$
$$x_{73} = 72.2566119315779$$
$$x_{74} = 31.4159269876038$$
$$x_{75} = -50.2654822658225$$
$$x_{76} = -25.1327382847962$$
$$x_{77} = 50.2654824463177$$
$$x_{78} = -40.8437719191275$$
$$x_{79} = -31.4159219217159$$
$$x_{80} = 81.68140841851$$
$$x_{81} = -97.3903823516316$$
$$x_{82} = 69.1150394191749$$
$$x_{83} = -100.530964509946$$
$$x_{84} = -78.5380926204531$$
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
$$\frac{1}{2 x \cot{\left(x \right)}} \left(\cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right) + \frac{\left(- 2 x \left(- \cot^{2}{\left(x \right)} - 1\right) - 2 \cot{\left(x \right)}\right) \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{4 x^{2} \cot^{2}{\left(x \right)}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 34.5574417217695$$
$$x_{2} = -100.530964914873$$
$$x_{3} = -40.8403379519905$$
$$x_{4} = -3.14175093489092$$
$$x_{5} = -25.1327412287183$$
$$x_{6} = -75.398223686155$$
$$x_{7} = -50.2654824574367$$
$$x_{8} = 81.6814089933346$$
$$x_{9} = 50.2654824574367$$
$$x_{10} = -43.9822971502571$$
$$x_{11} = 21.991151641644$$
$$x_{12} = -37.6991118430775$$
$$x_{13} = -72.2565554808085$$
$$x_{14} = 25.1327412287183$$
$$x_{15} = -9.42485781925051$$
$$x_{16} = 72.2566292955242$$
$$x_{17} = -78.5396461911396$$
$$x_{18} = -18.8495559215388$$
$$x_{19} = 59.6903504740077$$
$$x_{20} = 84.8228398927363$$
$$x_{21} = -15.7079741591662$$
$$x_{22} = -56.5486677646163$$
$$x_{23} = 18.8495559215388$$
$$x_{24} = -6.28318530717959$$
$$x_{25} = -21.99115164051$$
$$x_{26} = -47.1240716887076$$
$$x_{27} = 12.5663706143592$$
$$x_{28} = -97.3894633954265$$
$$x_{29} = -40.8410747688973$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = -62.8318530717959$$
$$x_{32} = 15.7080473943606$$
$$x_{33} = 78.5397437779814$$
$$x_{34} = 69.1150383789755$$
$$x_{35} = 6.28318530717959$$
$$x_{36} = 53.4072667518135$$
$$x_{37} = 37.6991118430775$$
$$x_{38} = -31.4159265358979$$
$$x_{39} = 100.530964914873$$
$$x_{40} = -84.8226545167245$$
$$x_{41} = -53.4071612202693$$
$$x_{42} = 94.2477796076938$$
$$x_{43} = -34.5573403476478$$
$$x_{44} = 9.42495587951317$$
$$x_{45} = -91.1063775106345$$
$$x_{46} = -12.5663706143592$$
$$x_{47} = 65.97345482794$$
$$x_{48} = -94.2477796076938$$
$$x_{49} = 28.274327526925$$
$$x_{50} = 40.8405347827156$$
$$x_{51} = 43.9822971502571$$
$$x_{52} = 75.398223686155$$
$$x_{53} = -59.6902758155797$$
$$x_{54} = 91.1058606234583$$
$$x_{55} = 62.8318530717959$$
$$x_{56} = -28.2742529777451$$
$$x_{57} = 97.389573015133$$
$$x_{58} = -84.8233930037709$$
$$x_{59} = 87.9645943005142$$
$$x_{60} = 91.1066053663186$$
$$x_{61} = -65.9734547229338$$
$$x_{62} = 47.1235460529235$$
$$x_{63} = -81.6814089933346$$
$$x_{64} = -87.9645943005142$$
$$x_{65} = -69.1150383789755$$
$$x_{66} = 31.4159265358979$$
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:
$$x_{1} = 81.6814089933346$$
$$x_{2} = 50.2654824574367$$
$$x_{3} = 25.1327412287183$$
$$x_{4} = 18.8495559215388$$
$$x_{5} = 12.5663706143592$$
$$x_{6} = 56.5486677646163$$
$$x_{7} = 69.1150383789755$$
$$x_{8} = 6.28318530717959$$
$$x_{9} = 37.6991118430775$$
$$x_{10} = 100.530964914873$$
$$x_{11} = 94.2477796076938$$
$$x_{12} = 43.9822971502571$$
$$x_{13} = 75.398223686155$$
$$x_{14} = 62.8318530717959$$
$$x_{15} = 87.9645943005142$$
$$x_{16} = 31.4159265358979$$
Puntos máximos de la función:
$$x_{16} = -100.530964914873$$
$$x_{16} = -25.1327412287183$$
$$x_{16} = -75.398223686155$$
$$x_{16} = -50.2654824574367$$
$$x_{16} = -43.9822971502571$$
$$x_{16} = -37.6991118430775$$
$$x_{16} = -18.8495559215388$$
$$x_{16} = -56.5486677646163$$
$$x_{16} = -6.28318530717959$$
$$x_{16} = -62.8318530717959$$
$$x_{16} = -31.4159265358979$$
$$x_{16} = -12.5663706143592$$
$$x_{16} = -94.2477796076938$$
$$x_{16} = -81.6814089933346$$
$$x_{16} = -87.9645943005142$$
$$x_{16} = -69.1150383789755$$
Decrece en los intervalos
$$\left[100.530964914873, \infty\right)$$
Crece en los intervalos
$$\left[-6.28318530717959, 6.28318530717959\right]$$
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(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
$$\frac{1}{2 x \cot{\left(x \right)}} \left(\cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right) + \frac{\left(- 2 x \left(- \cot^{2}{\left(x \right)} - 1\right) - 2 \cot{\left(x \right)}\right) \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{4 x^{2} \cot^{2}{\left(x \right)}} = 0$$
Resolvermos esta ecuación
Raíces de esta ecuación
$$x_{1} = 34.5574417217695$$
$$x_{2} = -100.530964914873$$
$$x_{3} = -40.8403379519905$$
$$x_{4} = -3.14175093489092$$
$$x_{5} = -25.1327412287183$$
$$x_{6} = -75.398223686155$$
$$x_{7} = -50.2654824574367$$
$$x_{8} = 81.6814089933346$$
$$x_{9} = 50.2654824574367$$
$$x_{10} = -43.9822971502571$$
$$x_{11} = 21.991151641644$$
$$x_{12} = -37.6991118430775$$
$$x_{13} = -72.2565554808085$$
$$x_{14} = 25.1327412287183$$
$$x_{15} = -9.42485781925051$$
$$x_{16} = 72.2566292955242$$
$$x_{17} = -78.5396461911396$$
$$x_{18} = -18.8495559215388$$
$$x_{19} = 59.6903504740077$$
$$x_{20} = 84.8228398927363$$
$$x_{21} = -15.7079741591662$$
$$x_{22} = -56.5486677646163$$
$$x_{23} = 18.8495559215388$$
$$x_{24} = -6.28318530717959$$
$$x_{25} = -21.99115164051$$
$$x_{26} = -47.1240716887076$$
$$x_{27} = 12.5663706143592$$
$$x_{28} = -97.3894633954265$$
$$x_{29} = -40.8410747688973$$
$$x_{30} = 56.5486677646163$$
$$x_{31} = -62.8318530717959$$
$$x_{32} = 15.7080473943606$$
$$x_{33} = 78.5397437779814$$
$$x_{34} = 69.1150383789755$$
$$x_{35} = 6.28318530717959$$
$$x_{36} = 53.4072667518135$$
$$x_{37} = 37.6991118430775$$
$$x_{38} = -31.4159265358979$$
$$x_{39} = 100.530964914873$$
$$x_{40} = -84.8226545167245$$
$$x_{41} = -53.4071612202693$$
$$x_{42} = 94.2477796076938$$
$$x_{43} = -34.5573403476478$$
$$x_{44} = 9.42495587951317$$
$$x_{45} = -91.1063775106345$$
$$x_{46} = -12.5663706143592$$
$$x_{47} = 65.97345482794$$
$$x_{48} = -94.2477796076938$$
$$x_{49} = 28.274327526925$$
$$x_{50} = 40.8405347827156$$
$$x_{51} = 43.9822971502571$$
$$x_{52} = 75.398223686155$$
$$x_{53} = -59.6902758155797$$
$$x_{54} = 91.1058606234583$$
$$x_{55} = 62.8318530717959$$
$$x_{56} = -28.2742529777451$$
$$x_{57} = 97.389573015133$$
$$x_{58} = -84.8233930037709$$
$$x_{59} = 87.9645943005142$$
$$x_{60} = 91.1066053663186$$
$$x_{61} = -65.9734547229338$$
$$x_{62} = 47.1235460529235$$
$$x_{63} = -81.6814089933346$$
$$x_{64} = -87.9645943005142$$
$$x_{65} = -69.1150383789755$$
$$x_{66} = 31.4159265358979$$
Signos de extremos en los puntos:
(34.557441721769464, 2.60544241909504e-19)
(-100.53096491487338, -1.52764277031079e-31)
(-40.8403379519905, -1.10499008809096e-16)
(-3.141750934890923, -4.99443894134616e-17)
(-25.132741228718345, -3.81910692577698e-32)
(-75.39822368615503, -1.14573207773309e-31)
(-50.26548245743669, -7.63821385155396e-32)
(81.68140899333463, 1.88255223925939e-31)
(50.26548245743669, 7.63821385155396e-32)
(-43.982297150257104, -6.68343712010972e-32)
(21.991151641643985, 1.00525924381744e-24)
(-37.69911184307752, -5.72866038866547e-32)
(-72.25655548080847, -1.1273039336493e-19)
(25.132741228718345, 3.81910692577698e-32)
(-9.424857819250505, -1.07882095276346e-18)
(72.25662929552416, 3.15009033747855e-26)
(-78.53964619113955, -2.66786990270092e-18)
(-18.84955592153876, -2.86433019433274e-32)
(59.690350474007744, 2.75475304481601e-19)
(84.82283989273634, 2.01766630804503e-18)
(-15.707974159166167, -2.23936882398876e-22)
(-56.548667764616276, -8.59299058299821e-32)
(18.84955592153876, 2.86433019433274e-32)
(-6.283185307179586, -9.54776731444245e-33)
(-21.991151640509973, -1.00376583622348e-24)
(-47.12407168870756, -5.806085316048e-18)
(12.566370614359172, 1.90955346288849e-32)
(-97.38946339542655, -1.77073058979625e-19)
(-40.84107476889726, -1.15060815318006e-16)
(56.548667764616276, 8.59299058299821e-32)
(-62.83185307179586, -9.54776731444245e-32)
(15.708047394360637, 7.97163235164562e-19)
(78.53974377798144, 8.82433229843939e-20)
(69.11503837897546, 2.81541104661861e-31)
(6.283185307179586, 9.54776731444245e-33)
(53.40726675181354, 6.3138091250563e-18)
(37.69911184307752, 5.72866038866547e-32)
(-31.41592653589793, -4.77388365722123e-32)
(100.53096491487338, 1.52764277031079e-31)
(-84.82265451672453, -4.27954673616227e-17)
(-53.40716122026933, -2.57359145580604e-19)
(94.2477796076938, 1.24937720620631e-31)
(-34.55734034764782, -7.40075829164777e-18)
(9.424955879513174, 2.65795427218555e-17)
(-91.10637751063449, -3.61815017326727e-18)
(-12.566370614359172, -1.90955346288849e-32)
(65.97345482794003, 2.60149754277779e-23)
(-94.2477796076938, -1.24937720620631e-31)
(28.274327526924953, 1.44249900139147e-23)
(40.840534782715636, 5.07830496843494e-18)
(43.982297150257104, 6.68343712010972e-32)
(75.39822368615503, 1.14573207773309e-31)
(-59.69027581557969, -2.35408833715755e-22)
(91.10586062345827, 3.11189662741211e-17)
(62.83185307179586, 9.54776731444245e-32)
(-28.274252977745054, -3.78827011247992e-19)
(97.38957301513302, 4.169491411353e-18)
(-84.82339300377086, -6.91378946352496e-17)
(87.96459430051421, 1.33668742402194e-31)
(91.10660536631859, 8.41022481934631e-17)
(-65.97345472293381, -2.48351882236391e-23)
(47.12354605292351, 7.40760077486107e-17)
(-81.68140899333463, -1.88255223925939e-31)
(-87.96459430051421, -1.33668742402194e-31)
(-69.11503837897546, -2.81541104661861e-31)
(31.41592653589793, 4.77388365722123e-32)
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:
$$x_{1} = 81.6814089933346$$
$$x_{2} = 50.2654824574367$$
$$x_{3} = 25.1327412287183$$
$$x_{4} = 18.8495559215388$$
$$x_{5} = 12.5663706143592$$
$$x_{6} = 56.5486677646163$$
$$x_{7} = 69.1150383789755$$
$$x_{8} = 6.28318530717959$$
$$x_{9} = 37.6991118430775$$
$$x_{10} = 100.530964914873$$
$$x_{11} = 94.2477796076938$$
$$x_{12} = 43.9822971502571$$
$$x_{13} = 75.398223686155$$
$$x_{14} = 62.8318530717959$$
$$x_{15} = 87.9645943005142$$
$$x_{16} = 31.4159265358979$$
Puntos máximos de la función:
$$x_{16} = -100.530964914873$$
$$x_{16} = -25.1327412287183$$
$$x_{16} = -75.398223686155$$
$$x_{16} = -50.2654824574367$$
$$x_{16} = -43.9822971502571$$
$$x_{16} = -37.6991118430775$$
$$x_{16} = -18.8495559215388$$
$$x_{16} = -56.5486677646163$$
$$x_{16} = -6.28318530717959$$
$$x_{16} = -62.8318530717959$$
$$x_{16} = -31.4159265358979$$
$$x_{16} = -12.5663706143592$$
$$x_{16} = -94.2477796076938$$
$$x_{16} = -81.6814089933346$$
$$x_{16} = -87.9645943005142$$
$$x_{16} = -69.1150383789755$$
Decrece en los intervalos
$$\left[100.530964914873, \infty\right)$$
Crece en los intervalos
$$\left[-6.28318530717959, 6.28318530717959\right]$$
Asíntotas verticales
Hay:
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
$$x_{1} = 0$$
$$x_{2} = 1.5707963267949$$
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
$$y = \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
$$y = \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}\right)$$
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (sin(x) + tan(x))/(((2*x)*cot(x))), dividida por x con x->+oo y x ->-oo
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{2 x \cot{\left(x \right)}} \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{x}\right)$$
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\frac{1}{2 x \cot{\left(x \right)}} \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
$$y = x \lim_{x \to -\infty}\left(\frac{\frac{1}{2 x \cot{\left(x \right)}} \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{x}\right)$$
True
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
$$y = x \lim_{x \to \infty}\left(\frac{\frac{1}{2 x \cot{\left(x \right)}} \left(\sin{\left(x \right)} + \tan{\left(x \right)}\right)}{x}\right)$$
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:
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = \frac{- \sin{\left(x \right)} - \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}$$
- No
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = - \frac{- \sin{\left(x \right)} - \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}$$
- No
es decir, función
no es
par ni impar
Pues, comprobamos:
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = \frac{- \sin{\left(x \right)} - \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}$$
- No
$$\frac{\sin{\left(x \right)} + \tan{\left(x \right)}}{2 x \cot{\left(x \right)}} = - \frac{- \sin{\left(x \right)} - \tan{\left(x \right)}}{2 x \cot{\left(x \right)}}$$
- No
es decir, función
no es
par ni impar