Investigating Limits: What Happens When x Approaches a Constant or Zero?

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nycmathguy
Homework Statement
Investigate each limit.
Relevant Equations
See attachment of piecewise function.
Investigate each limit.

1. lim f(x) x→3

2. lim f(x) x→0

See attachment.
 

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Thread closed. This is nearly identical to your other thread with almost the same name. When you figure this one out, you'll be able to figure this one out.
 
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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