what is the limit of (x^3+1)/(x+1) as x approaches -1?
Stacey Warren - Expert brainly.com
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Have you learn L'Hopitals?
no? or at least I don't remember...
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.
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ah, they're not letting us use calculus yet... :/ just algebra
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.
ahhh, brilliant! I got it :)
When you have a sum of perfect cubes, then:
(a^3 + b^3) = (a + b)(a^2 - 2ab + b^2)