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## Homework Statement

((x+2)/(x-1))^x, lim as x --> infinitiy

## Homework Equations

I think l'Hospital's Rule or something like that...Not sure where to begin with this one.

## The Attempt at a Solution

((x+2)/(x-1))^x is the same as saying ((x+2)^x)/((x-1)^x). Since the numerator and denominator appear to be +inf/+inf or 0/0 as x --> +inf or -inf respectively, I think it's okay to use l'Hospital's rule.

So I start with finding the derivative of the numerator first. y=(x+2)^x, so I take the natural log of both sides to get ln(y) = x*ln(x+2). I take the derivative of both sides, which gives y'/y = ln(x+2) + x/(x+2). I multiply both sides by y, which gives y'=((x+2)^x)*(ln(x+2) + x/(x+2)). Along the same logic, the derivative of the denominator is y'=((x-1)^x)*(ln(x-1) + x/(x-1)). Pairing the side computations together, you get (((x+2)^x)/((x-1)^x))*((ln(x+2) + x/(x+2))/(ln(x-1) + x/(x-1))). This doesn't really get me anywhere...

I know the answer is e^3, but I don't know why. Here's the online calculation tool I used to arrive at that answer.

EDIT

Nevermind, found a solution.

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