I have 3 questions which are bessel, half range expression and laplace transform

tonylim456
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the questions are together with this file and my solutions are also attached. hope someone can comment on my solutions. thanks a lot and i hope i won't get any warning any more.
 

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anyone please help~
 
Please help me. thanks
 
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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