Question

Question #a7396

Answer 1

`lim_(x->2)(x^2-x-2)^20/(x^3-12x+16)^10 =(3/2)^10=59049/1024`

Explanation:

`lim_(x->2)(x^2-x-2)^20/(x^3-12x+16)^10 = lim_(x->2)[(x+1)(x-2)]^20/[(x+4)(x-2)^2]^10`

`=lim_(x->2)((x+1)^20(x-2)^20)/((x+4)^10(x-2)^20)`

`=lim_(x->2)(x+1)^20/(x+4)^10`

`=3^20/6^10`

`=(3/2)^10`