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

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