Limiti e Integrali notevoli

Limiti notevoli

_limx→0 ^{sen x}/_x = 1 → _limx→0 ^{sen f(x)}/_β(x) = 1

_limx→0 ^{tan x}/_x = 1 → _limx→0 ^{tan f(x)}/_β(x) = 1

_limx→0 ^{1 - cos x}/_x² = 1/2 → _limx→0 ^{1 - cos f(x)}/_[β(x)]² = 1/2

_limx→0 ln(1 + x)/x = 1 → _limx→0 ln(1 + β(x))/f(x) = 1

_limx→0 ^{ex - 1}/_x = 1 → _limx→0 ^{eβ(x) - 1}/_f(x) = 1

_limx→0 ^{ax - 1}/_x = ln(a) → _limx→0 ^{aβ(x) - 1}/_f(x) = ln(a)

_limx→0 log_a(1+x)/x = 1/log_a → _limx→0 ^arcsin(x)/_x = 1 → _limβ(x)→0 ^arcsin(f(x))/_β(x) = 1

_limx→0 ^arctan(x)/_x = 1 → _limf(x)→0 ^arctan(f(x))/_f(x) = 1

_limx→0 ^sinh(x)/_x = 1 → _limβ(x)→0 ^sinh(f(x))/_β(x) = 1

_limx→0 cosh(x) - 1/_x² = 1/2 → _limx→0 cosh(f(x)) - 1/_(β(x))² = 1/2

Altri limiti notevoli

lim_x→0 sen x / x = 1
lim_x→0 sen f(x) / β(x) = 1

lim_x→0 tan x / x = 1
lim_x→0 tan f(x) / β(x) = 1

lim_x→0 (1 − cos x) / x² = 1/2
lim_x→0 (1 − cos f(x)) / [β(x)]² = 1/2

lim_x→0 ln(1 + x) / x = 1
lim_x→0 ln(1 + β(x)) / β(x) = 1

lim_x→0 (e^x − 1) / x = 1
lim_x→0 (e^β(x) − 1) / β(x) = 1

lim_x→0 (a^x − 1) / x = ln(a)
lim_x→0 (a^β(x) − 1) / β(x) = ln(a)

lim_x→0 log_a(1 + x) / x = 1/ln a
lim_x→0 arcsin(x) / x = 1
lim_β(x)→0 arcsin(f(x)) / β(x) = 1

lim_x→0 arctan(x) / x = 1
lim_f(x)→0 arctan(f(x)) / f(x) = 1

lim_x→0 sinh(x) / x = 1
lim_β(x)→0 sinh(f(x)) / β(x) = 1

lim_x→0 (cosh(x) − 1) / x² = 1/2
lim_x→0 (cosh(f(x)) − 1) / (β(x))² = 1/2