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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....
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 Fall '09
 L. OLDEWURTEL
 lim, Limit of a function, Indeterminate form, case lim sin

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