id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
american_scientific_journal-3982	Corona-Corona, Gulmaro	About the Proof of the L’Hôpital's Rule	2018	6	.pdf	application/pdf	2684	184	76	− �𝑠𝑠(𝑥𝑥) − 𝑠𝑠(𝑎𝑎)� �𝑠𝑠(𝑥𝑥) − 𝑠𝑠(𝑎𝑎)�𝑠𝑠′(𝑎𝑎) 𝑥𝑥 − 𝑎𝑎 ⎠ ⎟ ⎞ = lim 𝑥𝑥→𝑎𝑎 ⎝ ⎜ ⎛ (𝑥𝑥 − 𝑎𝑎) 𝑠𝑠′(𝑎𝑎) − 𝑠𝑠(𝑥𝑥) 𝜀𝜀2 − (𝑏𝑏 − 𝑎𝑎)2 = 𝜀𝜀2 − 𝑏𝑏2 − 𝑎𝑎2 + 2𝑎𝑎𝑏𝑏, that is to say ‖𝑎𝑎, 𝑏𝑏‖2 − 𝜀𝜀2 < 2𝑎𝑎𝑏𝑏 then by the assumption about the norm and the observation 3, 𝑎𝑎𝑏𝑏 > 0, if and only if 𝑎𝑎𝑏𝑏 = |𝑎𝑎𝑏𝑏| = |𝑎𝑎||𝑏𝑏|	cache/american_scientific_journal-3982.pdf	txt/american_scientific_journal-3982.txt