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Hey, I am having some difficulties. So it's my understanding that the function ex comes around out of a desire to have a function whose derivative is equal to itself. Well we can show that if f(x)=ax, a>0, then f'(x) is equal to a multiple of itself using the limit definition of the derivativef'(x) = lim h-->0 (f(x+h)-f(x))/h = lim h-->0 (ax+h - ax)/h = lim h-->0 ax(ah-1)/h = ax ( lim h-->0 (ah-1)/h )So the goal is, if we can find a value a that makes (lim h--> 0 (ah-1)/h ) = 1, then f'(x) = f(x).My only issue is that when I actually take this limit, I don't understand how it can be anything other than 0. lim h-->0 (ah-1)/h ) = 0/0 so if we apply L'hopitals, we getlim h-->0 (h*ah-1)/(1) = [lim h--> 0 (h) * lim h-->0 (ah-1)]/lim h-->0 (1) = 0Right? What am I doing wrong in evaluating this limit? I mean I know I"m doing something wrong I just can't figure out what it is
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