December 4th, 2017, 05:23 PM  #11 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 
yes, understood clearly. thanks guys. appreciate 
December 7th, 2017, 03:03 PM  #12 
Newbie Joined: Dec 2017 From: USA Posts: 2 Thanks: 0 
Hi! I know that this has nothing to do with your questions, yet... I would be tremendously grateful if you could possibly give an answer to my questions and help me with this. I have two questions: first of all, what is the limit of an exponential function as x approaches 0? Is it 1? Second one: how exactly could I calculate lim as h approaches 0 of (1+h/x)^(1/h), that somehow must equal e^(1/x)? I am trying to follow the demonstration of why the derivative of ln is the reciprocal function and one step that is unclear is that limit, that is also written as lim of h as it approaches 0 of (1+h)^(1/xh). I tried to make a conjecture using the binomial formula, but I could not find anything (I am honestly not brave to use it for 1/x as an exponent). The only thing I am aware of is that lim of x as it approaches 0 of (1+x)^(1/x)=e. Thank you very much! Hope you can help me. Fondly, ap calc student. 
December 7th, 2017, 03:13 PM  #13 
Senior Member Joined: Sep 2015 From: USA Posts: 2,495 Thanks: 1370 
this question should be spun off this thread to it's own

December 7th, 2017, 03:14 PM  #14  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,829 Thanks: 648 Math Focus: Yet to find out.  Quote:
 

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