Question

lim as x approaches -2 of (x+2/ x^2+8 )

Answer 1

lim (x->-2) of (2/x^2+x+8)

The limit of a sum is the sum of the limits:
2 (lim(x->-2) 1/x^2)+lim(x->-2) x+8

The limit of a quotient is the quotient of the limits:
2/(lim(x->-2) x^2)+lim(x->-2) x+8

The limit of x as x approaches -2 is -2:
= 2/(lim(x->-2) x^2)+6

Using the power law, write lim(x->-2) x^2 as (lim(x->-2) x)^2:
= 2/(lim(x->-2) x)^2+6

The limit of x as x approaches -2 is -2:
= 13/2