Question

Solve this limit approaching 1, algebraically: x^2-1/x^3-1
Please & thank you!

Answer 1

gimmick is to factor and cancel, then replace x by 1

Answer 2

Satellite's on it already!

Answer 3

Can you use L'Hopital on it?

Answer 4

\[\frac{x^2-1}{x^3-1}=\frac{(x-1)(x+1)}{(x-1)(x^2+x+1)}=\frac{x+1}{x^2+x+1}\]

Answer 5

replace x by 1 and unless i screwed the pooch on the algebra you get
\[\frac{2}{3}\]

Answer 6

Thank you soooo much, you just saved me from failing my test tomorrow :)

Answer 7

@mathboy usually these come before derivatives, so long before l'hopital

Answer 8

@nsl11
if you get
\[\frac{0}{0}\] look to factor and cancel

Answer 9

I got 2/3, thank you!

Answer 10

and it is not hard to factor if you have polynomials when you are given a 0. factor it out