Tabella dei Limiti PDF

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Alex Gotev – Dispense di Analisi 1 Tabella dei limiti lim x 0 sin x = 1 x x ∞ 1 x x0 = e lim x 0 pos 1 x lim  1 x  = ∞ a x −1 lim = ln a x x 0 a0   1 x = 1 lim x−1 negat  lim  1x  arctan x = 1 x arccos x 2 lim = 2 1− x x 1 x 0 x   x 0 tan x = 1 x x 1 = log  1x  log  e ⇒ ...

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Alex Gotev – Dispense di Analisi 1

Tabella dei limiti lim x0

 

lim 1 x∞

1 x lim 1−cos = 2 2 x0 x

sin x = 1 x 1 x

x

= e

lim x0 pos

1 x

lim  1 x  = ∞

lim x0

lim x0

a 0

lim x0

e x −1 = 1 x

lim

arcsin x = 1 x

lim

 

lim log 1

1 x

x 0

x0

= 1

lim x−1 negat

ln 1x  = 1 x

lim

arctan x = 1 x

lim

  1 x

x 1

x

1x −1 =  x tan x = 1 x arccos x 2 = 2 1− x 1 x = log 1x  log e

⇒ = asintotico a.. x3 6

ln 1x  ⇒ x x ln a

a x −1 ⇒ x ln a tanh x ⇒ x

1x k ⇒ 1k x x2 2

tan x ⇒ x

sinh x ⇒ x

arctan x ⇒ x x2 2

arcsin x ⇒ x

x3 6

Forme indeterminate 0 0

∞ ∞

0⋅∞

∞

1

bx

 

a lim 1 x x±∞

sin x− x ⇒

x

x−sin x ⇒

x0

x−∞

e −1 ⇒ x

cosh x−1 ⇒

lim

= ln e = 1

lim a x = 0

sin x ⇒ x

1−cos x ⇒

x0

x0

Tabella degli Asintotici (per x → 0)

loga 1x  ⇒

= ∞

lim  1x  = 1 lim

x∞

x ∞

1 x

1 x



log a  1x  1 = ln a x

lim ln 1

lim loga x = ∞

x

  1

x∞

x

= log e

1−cos x = 0 x

x

x0

a −1 = ln a x

x∞

x0

lim  1 x  = e

x

x0

1 x

1 x

x−1 pos

lim

  1

lim

0

0

∞

0

∞−∞

= ea b...