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29 - L'hopital

# 29 - L'hopital - lim x → bx 2 4 x-tan 4 x x 3 is defined...

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Indeterminate Forms and L’Hopital’s Rule Suppose we want to find lim x 0 sin x x . If we substitute 0 for x, we get 0 0 . The limit may or may not exist. It’s indeterminate. (We can’t determine the limit.) Any limit of the form lim x a f ( x ) g ( x ) 0 0 is called an indeterminate form of type 0 0 . We call the form lim x a f ( x ) g ( x ) an indeterminate form of type . L’Hopital’s Rule: If lim x a f ( x ) 0 lim x a g ( x ) or if lim x a f ( x ) lim x a g ( x ) then lim x a f ( x ) g ( x ) lim x a f ( x ) g ( x ) Ex. lim x 0 sin x x

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Ex. lim x 0 e x - 1 sin(2 x ) Ex. lim x 1 1 - x ln x 1 cos( x ) Ex. lim x e x x 2 x
Ex. Determine the value of b for which

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Unformatted text preview: lim x → bx 2 + 4 x-tan 4 x x 3 is defined. Products Ex. lim x →-x 2 e x If we have lim x → a f ( x ) g ( x ) ⋅ , rewrite the limit as lim x → a f ( x ) 1 g ( x ) ±or ±lim x → a g ( x ) 1 f ( x ) . Do: 1. lim x → sin 2 x x cos x 2. lim x → 1 ln x x-1 2 3. lim x → 3 x csc 2 x 4. Determine the value of b for which lim x → bx + sin 5 x x 2 is defined....
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29 - L'hopital - lim x → bx 2 4 x-tan 4 x x 3 is defined...

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