is this accurate?
''me returning to my lim x--> c f(x)/g(x) to see that it has now been reduced to x --> c f('x)/g'(x)''
No, that is not accurate. The correct transformation when differentiating a limit is as follows:
If you have the function lim x→c f(x)/g(x), then differentiating it gives lim x→c f'(x)/g'(x). The prime notation (') indicates the derivative of a function.
Based on the given statement, it seems that there might be a misunderstanding or a typo.
Usually, when applying L'Hôpital's rule to evaluate the limit of a function, the original form is:
lim(x -> c) [f(x) / g(x)]
If both the numerator and denominator approach zero or infinity, we can take the derivative of the numerator and denominator separately and then evaluate the limit again:
lim(x -> c) [f'(x) / g'(x)]
It appears that in the statement, "x --> c f('x) / g'(x)" is mentioned, which deviates from the typical application of L'Hôpital's rule. Therefore, it is not accurate. It could be a typo or a misinterpretation of the concept.