Calculus - limit with f(x) and g^2(x) in limit

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Homework Statement



See the bottom problem (#2)
See image - http://imageshack.us/photo/my-images/842/img7774y.jpg/

The Attempt at a Solution



Plugged in 2 for f(x) and -4^2 for g^2(x)

got 2/3,

Is this correct? All help appreciated! Mad at my Calc teacher because he never gave us an example of this in class.
 
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2/3 is correct! :smile:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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