If we are given p(x) = x^2 - 1, q(x) = x^3 - 1, and r(x) = x^4- 1 then how would you evaluate....?

Question

lim......q(x) .
x=>1......p(x)

Answer 1

as x->1, p(x) -> 0 and q(x) -> 0, so try factoring both.

p(x) = x^2 - 1 = (x+1)(x-1)
q(x) = x^3 - 1 = (x-1)(x^2+x+1).

So, q(x)/p(x) = (x^2+x+1) / (x+1).

Plug in x=1 to obtain the limit.

Answer 2

use l'hopital's rule