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Home Q & A Board Science-Related Homework Help Mathematics
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Rkamu Rkamu
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11 years ago
Starting with the function F(x) = (x^2 - 8)/(x+3), I took the derivative of it and got (x^2+6x+8)/(x+3)^2. Then I found the limit of that as x approached infinity, and it was 1. What does that answer tell me about F(x), the original function?

And please don't post any silly answers. Thanks.
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#1
11 years ago
You did the derivative and the limit correctly.
In the limit, the slope of F is 1 means that eventually, the function F  is increasing 1 unit for every unit of x.
So the graph of F will eventual look like   F approximately =  1*x +b
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#2
11 years ago
So, whenever you are looking for the limit as x approaches positive or negative infinity, you are basically searching for the end behavior.  Therefore, in your situation, because f(x) approaches 1 as x approaches infinity, this tells you that you have a horizontal tangent at y = 1.
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