Math141_Section4.5

# Math141_Section4.5 - Section 4.5 Indeterminate Forms and...

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Section 4.5 – Indeterminate Forms and L’Hospital’s Rule 1. L’Hospital’s Rule - Suppose f and g are differentiable and 0 ) ( x g Suppose that 0 ) ( lim = x f a x and 0 ) ( lim = x g a x = ) ( lim x f a x and = ) ( lim x g a x Then ) ( ) ( lim ) ( ) ( lim x g x f x g x f a x z x = Examples a) x z x e x 3 lim b) 2 ln lim x x x c) #16 x x x π sin ln lim 1

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d) #32 ) cot (csc lim 0 x x x - Note: This is not in the form for L’Hospital’s rule; algebraically
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Math141_Section4.5 - Section 4.5 Indeterminate Forms and...

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