This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: f ( x ) = l n x , then f ’ ( x ) = 1/ x . Thus, f ’ (1) = 1 . Now, we use this fact to express the number e as a limit. From the definition of a derivative as a limit, we have: THE NUMBER e AS A LIMIT (Section 3.6) 1 (1 ) (1) (1 ) (1) '(1) lim lim ln(1 ) ln1 1 lim lim ln(1 ) lim ln(1 ) h x x x x x f h f f x f f h x x x x x x → → → → → ++= = += = + = + As f ’ (1) = 1 , we have If we put n = 1/ x , then n → ∞ as x → + . So, an alternative expression for e is: 1 lim ln(1 ) 1 x x x → + = 1/ 1 lim ln(1 ) 1 ln(1 ) 1 lim lim(1 ) x x x x x x x x e e e e x → + + → → = = = = + THE NUMBER e AS A LIMIT (Section 3.6) 1 lim(1 ) x x e x → = + 1 lim 1 n n e n →∞ = +...
View
Full
Document
This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
 Fall '08
 Noohi
 Calculus, Derivative

Click to edit the document details