Finding lim f(x) as x->+/- infinity?

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Finding lim f(x) as x-->+/- infinity?

f(x)= x^(5/3)-5x^(2/3)

Need to find limit f(x) as x-->+infinity, and x-->-infinity?
 
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Which term dominates as x approaches +/- infinity?
 


Factor out x5/3: f(x)= x5/3(1- x-1) The limit of 1- x-1, as x goes to plus or minus infinity should be pretty easy. What does that tell 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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