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Limit of Quotients Question.?
Okay here is the problem.
lim x-->1 as (1/x - 1) / (x - 1)
My professor got to this point then lost me
(1 - X) / (X) / (X - 1) then he rearranged it to (1 - X) / X (X - 1)
How the heck did he manage that? Whoever can provide me the answer to that rearranging gets the point, but explaining out the whole problem will earn brownie points.
You don't have to explain in layman's terms, I grasp the concepts. I just don't understand the steps he took to solve this one.
Thanks
this might be easier to read
1 - X 1 - X
____ to _____
X X( X - 1)
____
X - 1
or not.. lol
Yes you answered the question by how did the prof rearrange it to that final state. He made it a simple fraction.
Ohhhh I see. I always thought that you could multiply that second denominator by the numerator not the first denominator. I'm not sure where I got that idea. A fundamental problem I must have developed in trig. Thanks
1 Answer
- Anonymous1 decade agoFavorite Answer
The professor combined the two terms in the numerator to one fraction to get:
1/x - 1
= 1/x - x/x, by getting common denominators (LCD = x)
= (1 - x)/x.
So:
lim (x-->1) (1/x - 1)/(x - 1)
= lim (x-->1) [(1 - x)/x]/(x - 1).
Then, bringing the x down into the denominator:
lim (x-->1) [(1 - x)/x]/(x - 1)
= lim (x-->1) (1 - x)/[x(x - 1)]
= lim (x-->1) [-(x - 1)]/[x(x - 1)]
= lim (x-->1) -1/x
= -1.
I hope this helps!