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April 25th, 2016, 02:08 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Simplify the following as one equation:
Please be aware that "log" refers to the natural logarithm, base e, which is commonly written as "ln" in the following function: The task is to simplify the above Piecewise function into one equation that is defined and continuous for all real input x except at x=0. However, I am not sure how this is possible. For example, if I had this: I could simplify that down to just the Cos(x). However, I am not sure how to do this for the initial equation I specified above. There is an answer to this, though, and I'm not sure what it is. 
April 25th, 2016, 03:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
It can't be done. $\displaystyle \lim_{x>0}$ does not exist for either part.

April 25th, 2016, 03:48 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
This was kind of a trick question, but I was hoping there was an answer that didn't use i (the square root of negative 1). Look at this. As far as I can tell, this is what it actually does simplify to. Correct me and explain (an example would be the best form of explanation) if I'm wrong: = Re[x^i] (Where Re[a+bi] is a function that gives only the real part (a) of any complex output.) I do know that 0^i is undefined, so I'm not sure if I'm wrong with this. 

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