2.2

Podstawowe granice wyrażeń nieoznaczonych

1.

lim

x→0

sin x

x

= 1

2.

lim

x→0

tg x

x

= 1

3.

lim

x→0

x

sin x

= 1

4.

lim

x→0

x

tg x

= 1

5.

lim

x→0

(1 + x)

1

x

= e

6.

lim

x→0

(1 + x)

a

x

= e

a

7.

lim

x→+/−∞

(1 +

1

x

)

x

= e

8.

lim

x→+/−∞

(1 +

a
x

)

x

= e

a

9.

lim

x→0

e

x

− 1

x

= ln e = 1

10.

lim

x→0

a

x

− 1

x

= ln a

11.

lim

x→0

ln(1 + x)

x

= 1

12.

lim

x→0

log

a

(1 + x)

x

=

1

ln a

5