Determina el límite Lim 2 x² - 8 ______ x² - 16 Lim x² - 6x - 16 ______ 4x + 18 Lim x² + 6x + 9 ______ x² - 9 Lim 2 x² - 13x + 15 _________ x² - x - 20 Lim x² - 8x + 15 ________ x² - 7x + 12 Lim x² + 3x + 2 _________ x² - 1.
En resumen
<img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7B2x%5E%7B2%7D-8%7D%7Bx%5E%7B2%7D-16%7D%3D%5Cunderbrace%7B%5Cfrac%7B24%7D%7B0%7D%7D_%7Bindeterminado%7D" /> Hay que analizar los límites laterales : <img src="https://tex.z-dn.net/?
<img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%7D%20%5Cfrac%7B2x%5E%7B2%7D-8%7D%7Bx%5E%7B2%7D-16%7D%3D%5Cunderbrace%7B%5Cfrac%7B24%7D%7B0%7D%7D_%7Bindeterminado%7D" /> Hay que analizar los límites laterales : <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%204%5E%7B%2B%7D%7D%20%5Cdfrac%7B2x%5E%7B2%7D-8%7D%7Bx%5E%7B2%7D-16%7D%3D24%2A%5Cinfty%3D%5Cinfty%5C%5C%5Clim_%7Bx%20%5Cto%204%5E%7B-%7D%7D%20%5Cdfrac%7B2x%5E%7B2%7D-8%7D%7Bx%5E%7B2%7D-16%7D%3D24%2A-%5Cinfty%3D-%5Cinfty" />Como los límites laterales son distintos el límite es divergente.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20-2%7D%20%5Cdfrac%7Bx%5E%7B2%7D-6x-16%7D%7B4x%2B18%7D%3D%5Cdfrac%7B%28-2%29%5E%7B2%7D-6%28-2%29-16%7D%7B4%28-2%29%2B18%7D%3D%5Cfrac%7B4%2B12-16%7D%7B-8%2B18%7D%3D%5Cfrac%7B0%7D%7B10%7D%3D0" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%203%7D%20%5Cfrac%7Bx%5E%7B2%7D%2B6x%2B9%7D%7Bx%5E%7B2%7D-9%7D%3D%5Cfrac%7B3%5E%7B2%7D%2B6%283%29%2B9%7D%7B3%5E%7B2%7D-9%7D%3D%5Cunderbrace%7B%5Cfrac%7B36%7D%7B0%7D%7D_%7Bindeterminado%7D" />Hay que analizar los límites laterales : <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%2B6x%2B9%7D%7Bx%5E%7B2%7D-9%7D%3D%5Cfrac%7B%28x%2B3%29%5E%7B2%7D%7D%7B%28x-3%29%28x%2B3%29%7D%3D%5Cfrac%7B%28x%2B3%29%7D%7B%28x-3%29%7D%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%203%5E%7B%2B%7D%20%7D%20%5Cdfrac%7Bx%2B3%7D%7Bx-3%7D%3D6%2A%5Cinfty%3D%5Cinfty%5C%5C%5Clim_%7Bx%20%5Cto%203%5E%7B-%7D%20%7D%20%5Cdfrac%7Bx%2B3%7D%7Bx-3%7D%3D6%2A-%5Cinfty%3D-%5Cinfty" />Como los límites laterales son distintos el límite es divergente, no existe.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%202%7D%20%5Cdfrac%7B2x%5E%7B2%7D-13x%2B15%7D%7Bx%5E%7B2%7D-x-20%7D%3D%5Cdfrac%7B2%282%29%5E%7B2%7D-13%282%29%2B15%7D%7B%282%29%5E%7B2%7D-%282%29-20%7D%20%3D%5Cfrac%7B8-26%2B15%7D%7B4-2-20%7D%3D%5Cfrac%7B-3%7D%7B-18%7D%3D%5Cfrac%7B1%7D%7B6%7D" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20-1%7D%20%5Cdfrac%7Bx%5E%7B2%7D-8x%2B15%7D%7Bx%5E%7B2%7D-7x%2B12%7D%3D%5Cdfrac%7B%28-1%29%5E%7B2%7D-8%28-1%29%2B15%7D%7B%28-1%29%5E%7B2%7D-7%28-1%29%2B12%7D%3D%5Cfrac%7B1%2B8%2B15%7D%7B1%2B7%2B12%7D%3D%5Cfrac%7B24%7D%7B20%7D%3D%5Cfrac%7B6%7D%7B5%7D" /> = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <img src="https://tex.z-dn.net/?f=%5Cunderbrace%7B%5Clim_%7Bx%20%5Cto%20-1%7D%20%5Cfrac%7Bx%5E%7B2%7D%2B3x%2B2%7D%7Bx%5E%7B2%7D-1%7D%7D_%7Baplicar%20L%27Hopital%7D%3D%5Clim_%7Bx%20%5Cto%20-1%7D%20%5Cfrac%7B2x%2B3%7D%7B2x%7D%3D%5Cfrac%7B2%28-1%29%2B3%7D%7B2%28-1%29%7D%3D%5Cfrac%7B-4%2B3%7D%7B-2%7D%3D%5Cfrac%7B1%7D%7B2%7D" />.
1) <img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%7D%5Cfrac%7B2x%5E2-8%7D%7Bx%5E2-16%7D" />
la función no está definida en cuando <img src="https://tex.z-dn.net/?f=x%5Cto%204%20" /> entonces analizar loa límites laterales
<img src="https://tex.z-dn.net/?f=%5Cmathrm%7B%5Clarge%7Bl%C3%ADmite%20%5C%20por%5C%20izquierda%3A%7D%7D" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E-%7D%5Cfrac%7B2x%5E2-8%7D%7Bx%5E2-16%7D%3D%5Cfrac%7B%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E-%7D%5Coverbrace%7B2x%5E2-8%7D%5E%7B24%7D%7D%7B%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E-%7D%5Cunderbrace%7Bx%5E2-16%7D_%7B-0%7D%7D%3D-%20%5Cinfty" />
es <img src="https://tex.z-dn.net/?f=%28-%5Cinfty%29" /> porque cuando <img src="https://tex.z-dn.net/?f=%20x%5Cto%204%5E-%20" /> <img src="https://tex.z-dn.net/?f=%20x%5E2-16%3C0" />
<img src="https://tex.z-dn.net/?f=%5Cmathrm%7B%5Clarge%7Bl%C3%ADmite%5C%20por%20%5C%20derecha%3A%7D%7D" />
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E%2B%7D%5Cfrac%7B2x%5E2-8%7D%7Bx%5E2-16%7D%3D%5Cfrac%7B%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E%2B%7D%5Coverbrace%7B2x%5E2-8%7D%5E%7B24%7D%7D%7B%5Cdisplaystyle%5Clim_%7Bx%5Cto%204%5E%2B%7D%5Cunderbrace%7Bx%5E2-16%7D_%7B%2B0%7D%7D%3D%2B%E2%88%9E" />
es <img src="https://tex.z-dn.net/?f=%28%2B%5Cinfty%29" /> porque cuando [img = 10] [img = 11]0" alt = " x ^ 2 - 16>0" align = "absmiddle" class = "latex - formula">
como [img = 12]
entonces no existe el límite.
[img = 13]
2)[img = 14]
analizando el límite cuando [img = 15]
[img = 16]
entonces [img = 17]
[img = 18]
3)[img = 19]
la función no está definida en [img = 20]
entonces analizar los límites laterales :
[img = 21]
[img = 22]
es [img = 23] porque cuando [img = 24] [img = 25]
[img = 26]
[img = 27]
es [img = 28] porque cuando [img = 29] [img = 30]0" alt = " x ^ 2 - 9>0" align = "absmiddle" class = "latex - formula">
como [img = 31]
entonces no existe el límite.
[img = 32]
4)[img = 33]
[img = 34]
5)[img = 35]
[img = 36]
6)[img = 37]
aplicando regla de L'Hopital, derivando arriba y abajo
[img = 38].
1. Lim 4x - 5 = 4(1) - 5 = 4 - 5 = - 1 x - >1 2. - Lim (3x + 1) / (2x - 5) = 3(3) + 1 / 2(3) - 5 = 10 / 1 = 10 x - >3 3. - Lim 5x ^ 2 + 4x = x(5x + 4) = 2(5(2) + 4) = 2(14) = 28 x - >2.
Respuesta : 〖lim〗┬(x→ - ∞)〖f(x) = ∞〗 〖lim〗┬(x→∞)〖f(x) = 2〗 〖lim〗┬(x→〖 - 1〗 ^ - )〖f(x) = 1〗 〖lim〗┬(x→ - 1 ^ + )〖f(x) = 2〗 〖lim〗┬(x→1 ^ - )〖f(x)〗 = 1 〖lim〗┬(x→1 ^ + )〖f(x) = 2〗 Explicación :
Eso es infinito ya que no pueden haber dos infinidades ni una infinidad 455 + 3 nada con el infinito sigue siendo infinito.
El valor del limite lim √8 + t³ cuando t = 2 es 8 + √8Un limite : nos dice a que valor se aproxima una función cuando la variable de la misma tienda a otro valor (aunque no es igual)Tenemos el limite : Si evaluamos y no…