SOLUTION: Limx->1 {{{(x^8-1)/(x^7-1)}}} (Limit as x approaches 1)

Question 921458: Limx->1
(Limit as x approaches 1)

Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Limx->1
(Limit as x approaches 1)
------------
Find the derivatives on the NUM and the DEN.
-->
Limit = 8/7

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There is probably a theorem that tells you what the limit should be, but who wants to memorize theorems?
We know that

and
.
We can multiply and check, but we get the idea from what we remember.
We remember that
from geometric sequences sums,
or at least we can generalize from remembering from polynomials that
and .
So, for ,
,
and
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