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mcastillo356
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- Bernouili's work, french mathematician's work, l'Hôpital first rule...Need some more knowledge
Hi, PF
Got questions to start with: ¿some casual background about these Rules?; ¿are them two, as the textbook says?.
https://en.wikipedia.org/wiki/L'Hôpital's_rule (only one statement found)
Here goes the first, from "Calculus, 7th ed, R, Adams, C. Essex"
THEOREM 3 The first l'Hôpital Rule
Suppose the functions and are differentiable on the interval and there. Suppose also that
(i) and
(ii) (where is finite or or )
Then
Similar results hold if every occurrence of is replaced by or even where . The cases and are also allowed
PROOF We prove the case involving for finite . Define
and
Then and are continuous on the interval and differentiable on the interval for every in . By the Generalized Mean-Value Theorem (...) there exists a number in such that
.
Since , if , then neccesarily , so we have
Mean Value Theorem seems a limitless tool in Analysis. Question: ? Think so. At this point, doesn´t add worth information; it's a useless limit
Attemtp: Wikipedia isn't wrong; is straight, I guess; but incomprehensive for me. I understand what the textbook says, but need some kind of text comment on the aim of my textbook.Thanks. I think LaTeX is not well done, please PF, check it.
Edited at 6:39 AM Europe timing
Got questions to start with: ¿some casual background about these Rules?; ¿are them two, as the textbook says?.
https://en.wikipedia.org/wiki/L'Hôpital's_rule (only one statement found)
Here goes the first, from "Calculus, 7th ed, R, Adams, C. Essex"
THEOREM 3 The first l'Hôpital Rule
Suppose the functions
(i)
(ii)
Then
Similar results hold if every occurrence of
PROOF We prove the case involving
and
Then
Since
Mean Value Theorem seems a limitless tool in Analysis. Question:
Attemtp: Wikipedia isn't wrong; is straight, I guess; but incomprehensive for me. I understand what the textbook says, but need some kind of text comment on the aim of my textbook.Thanks. I think LaTeX is not well done, please PF, check it.
Edited at 6:39 AM Europe timing
Last edited: