Limit of Function: Find Solution

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Homework Statement


Find the above limit

Homework Equations


##\lim_{t\rightarrow 0} \dfrac{\exp(-A/t)}{t^{n/2}}## with A>0

The Attempt at a Solution


I tried using the change of variable ##u=1/t^{n/2}##, and then next use LHopital rule, but i don't find the way..
 
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Have you tried taking the natural log of the expression? What about letting u = 1/t rather than the more complex expression?
 
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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