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 Document
Unformatted text preview: Indeterminate Forms and L'Hospital's Rule What We Want . or to equal both are ) ( lim and ) ( lim when ) ( ) ( lim form the of s expression analyze To ∞ → → → x g x f x g x f a x a x a x Examples lim and sin lim case in this , ) sin( lim . 1 x (x) x x x x x = = → → → lim and lim case in this , lim . 2 3 2 3 2 e x e x x x x x x ∞ = ∞ = ∞ → ∞ → ∞ → . type of form ate indetermin an have we second, In the . type of form ate indetermin an have we case, first In the ∞ ∞ Tool to Use: L'Hospital's Rule ). or is (or exists limit last the if lim lim Then lim lim or that lim lim that Suppose . at possibly except , near and able differenti are and Suppose ∞ ∞ ′ ′ = = ± ∞ = = = ≠ ′ → → → → → → (x) g (x) f g(x) f(x) g(x). f(x) g(x) f(x) a a (x) g g(x) f(x) a x a x a x a x a x a x Examples lim and sin lim case in this , ) sin( lim . 1 x (x) x x x x x = = → → → Both functions are differentiable and the derivative of the denominator is 1, never zero. Hence, L'Hospital's Rule can be used....
View
Full
Document
This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.
 Fall '09
 L. OLDEWURTEL

Click to edit the document details