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(Calc 2) 0 and Infinity in limits

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valleystudent84's version from 2016-10-13 16:28

Section

Question Answer
e^∞ =
e^-∞ = 0
(Lim >o+) #/x - =
(Lim >0-) #/x = -∞
Graph of lnx (End Directions)Left = -∞ _ Right = +∞
Graph of e^e (End Directions)Left = o _ Right = +∞
Ln(∞) =
Ln(-∞) = Undefined
(Lim >0+) 1/x =
(Lim >0-) 1/x = -∞
o^∞ = 0
0^-∞ =
∞/# =
#/∞ =0
(L'Hôpital) Bad forms (6)0*∞ _ 1^∞ _ ∞^0 _ 0^0 _ ∞ - ∞ _ # (does not apply when yields # other than 0
(L'Hôpital) Good Forms (6)0/0 _ ∞/∞ = ∞ _ (-∞)-(-∞) = -∞ _ ∞+∞ = ∞ _ 0^∞ = 0 _ o^-∞ = ∞
(Lim X >0-) 1/x = 1/-0 = ??-∞
1/0 ≠ 1/-0 Why?left is undefined _ Right is APPROACHING 0, not actually 0 value
When does L'Hôpital's rule NOT apply?When substitution yields a real # INCLUDING 1
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