Question #a7396

1 Answer
Oct 5, 2016

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