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Different Way to Solve a Limit of an Indeterminate Equation

  • Thread starter chislam
  • Start date
  • #1
79
0
[tex]
lim_{x\rightarrow-2}\frac{x^3 + 8}{x+2}
[/tex]

Ok, I have solved this using synthetic division in which the limit was 12, however I was wondering if there was a way to solve this without using synthetic division (seeing as I hate the process of it).

I've solved plenty of other indeterminate equations by factoring out a polynomial and then being able to cancel out so that I can then plug in x, but I wasn't able to do so with this one.

I'm just curious if there are any other ways to solve this specific limit.

Thanks
 

Answers and Replies

  • #2
378
2
L'hospital rule (applies only when it is in forms like 0/0, inf/inf)

differentiate both num and den, and then sub in your -2
 
  • #3
79
0
Yeah I started reading up on that rule, but didn't understand it fully until your reply. So the derivative of the numerator is 3x^2 and the denominator is 1 so then just sub in the -2 and you get 12. Got it, thanks a lot for clearing up that rule for me.
 
  • #4
dynamicsolo
Homework Helper
1,648
4
Not that this is much different than using synthetic division, but the numerator is a sum of two cubes, which factors according to

[tex]a^3 + b^3 = (a + b) \cdot (a^2 - ab + b^2)[/tex] . So, in fact, this numerator can be factored and the (x + 2) term can be cancelled.
 
Last edited:

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