¿Quien puede resolver este limite ?

Es cero en el numerador 

El resultado es cero no es indeterminado

Hay diversas indeterminaciones, cuando es de la forma x/0 tiende a mas infinito o menos infinito dependiendo el caso, para el que expones el limite si existe y es 0, dado que no existe una indeterminación.

PD: El resultado se obtiene al sustituir el valor al cual tiende la variable "x"

 si , El numerador es cero, si se puede dividir cero entre algo, lo que no se puede es dividir algo entre cero.

Lim (x^2-4)/(x^2+4) = 0/8 = 0

x->2

El numerador es cero, si se puede dividir cero entre algo, lo que no se puede es dividir algo entre cero.

Lim (x^2-4)/(x^2+4) = 0/8 = 0

x->2

Lim (x^2-4)/(x^2+4) = 0/8 = 0

x->2, el numerador es cero ;)

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parte

I ante una fracción racional hallas el "conjunto restricción"

 igualando a cero el denominador. Y resuelves esa ecuación

x^2 + 4 = 0

x^2 = - 4

x = 2i

no existe restricción  dentro del os números reales

observación = no acemos restrcción al numerador, sólo al denominador

si el denominador es distinto de cero, podemos reemplazar libremente. SI además el numerador es cero entonces el resultado será cero

Parte II

supongamos que buscas determinar el límite de la siguiente función

Lim (x^2+4) / (x^2-4) cuando x -->2

primero hacemos la restricción

x^2 - 4 = 0x^2 = 4x1 = +2

x2 = - 2en estos dos valores se puede indefinir, por lo tanto no podemos hacer una reemplazo directo, pero igualmente puede ser alguno de esos valores, el valor del límite

como   x -->2  lo ideal es probar número menores a 2 muy cercanos a 2. Asimismo números mayores a 2 , muy cercanos a 2. Analizams a qué número tienden cuando los reemplazamos

con los números mayores, obtenemos el límite por la derecha:

Lim (1.7^2+4) / (1,7^2-4) cuando x -->2    = -6,207207207

Lim (1,8^2+4) / (1,8^2-4) cuando x -->2 = -9,526315789

Lim (1,9^2+4) / (1,9^2-4) cuando x -->2 = -19,51282051

para 1,99 el valor de la funcipon es -199,5012531

para 1,999 el valor de la función es -1999,500125

para 1,9999  el valor de la función es  19999,5

para 1,99999 = -199999,5

para x = 1,999999    el valor de la función es = - 1999999.5

con los números menores  obtenemos el límite por la izquierda

para,2,5 el valor de la función es 4,5555555

para 2,4 el valor será 5,45454545

para  2,3 el valor es 7,201550388

para 2,2 el valor es 10,52380952

para 2,1 el valor es de 20,51219512

para 2,11   el valor 18,69520017

para 2,111 el valor es de 18,53151838

para 2,1111 el valor 18,51531237

para 2,11111 el valor 18,51369338

para 2,111111111111 el vlor de la función es 18,51351353

al parecer el límite por la derecha tiende a 18,51

pero el límite por la izquierda no tiene a un número definido, sino a 1999....999

por ende no existe el límite por la izquierda

como no se cumple que seam iguales lel ímite por la derecha y el límite por la izquierda, concluimos que no existe el límite cuando x iende a 2 de la función dada

observación: de probar este método de acercamiento con el método anterior te hubiere dado el valor de lso 3 límites