Help understanding what limits are

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Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.
 
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azncocoluver said:

Homework Statement


http://www4c.wolframalpha.com/Calculate/MSP/MSP18091a03ad70feibdhb300005da572897hebg236?MSPStoreType=image/gif&s=52&w=143&h=42


Homework Equations


lim x->2+ (x^2 - 3x + 2) / (x^3 - 4x)


The Attempt at a Solution


I plugged in 2 for x and it was 0/0 so then I divided each term by the highest power, which is x^3 but I still got 0/0. The answer is 1/8 but I don't know how to get it.

Factor the numerator and denominator!
 
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Oh yeah! I totally forgot about that. Thank you!
 
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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