Question

what is the limit of (x^3+1)/(x+1) as x approaches -1?

Answer 1

Have you learn L'Hopitals?

Answer 2

no? or at least I don't remember...

Answer 3

If you have, since you get 0/0, you can take the derivatives of the top and bottom separately. You will end up with (3x^2)/1, and as x approaches -1, you will get 3.

Answer 4

ah, they're not letting us use calculus yet... :/ just algebra

Answer 5

Oh ok. Well in that case, you could use the cube rule on the top.

Since the top is x^3 +1, you can expand that to (x + 1)(x^2 - x + 1).

Then, the x +1 on the top and bottom cancel, and you are left with the lim as x approaches -1 of (x^2 - x + 1), which you can see is 3.

Answer 6

ahhh, brilliant! I got it :)

Answer 7

When you have a sum of perfect cubes, then:

(a^3 + b^3) = (a + b)(a^2 - 2ab + b^2)

Answer 8

Ok, great!

Answer 9

BTW, it's not -2ab. It's just -ab.

Answer 10

yeah i gotcha.