Clasa a 11-a E Test evaluare. Limite de funcii 14. 2. 2012

Calculai:

1) ( )2lim 2 2x

x x x

+ =

................................................................................................................................................................................................................

2) ( )lim xx

arctg e+

=

................................................................................................................................................................................................................

3) lnlim1 lnx

xx

x+

= +

................................................................................................................................................................................................................

Fie ( ): , 1 2 3x xf f x = + + . Calculai.

4) ( )( )lim 2xf x

f x =+

................................................................................................................................................................................................................

5) ( )( )limxf x

f x =

................................................................................................................................................................................................................

6) ( )( )limx

arcctg f x

=

................................................................................................................................................................................................................

7) ( )1lim ln

x f x =

................................................................................................................................................................................................................

Fie ( ) [ ]{ }: , .2x xf f x

x

+ =

+ Atunci.

8) ( )limx

f x

=

................................................................................................................................................................................................................

9) Studiai existena limitei ( )1

limx

f x

.

10) ( )limx

f x

=

................................................................................................................................................................................................................

Fie ( ) 2: , 2 5 .f f x x x x = + + Atunci. 11) ( )lim

xf x

=

................................................................................................................................................................................................................

12) ( )limx

f x

=

................................................................................................................................................................................................................

13) ( )21lim 1xf xx

=

................................................................................................................................................................................................................

14) ( )2lim 1xf xx

=

+

................................................................................................................................................................................................................

Fie ( ): , sin .f f x x = Atunci.

15) ( )limx

f xx

=

................................................................................................................................................................................................................

16) ( )211

lim1x

f xx

+=

................................................................................................................................................................................................................

17) ( )( )0

ln 1limx

f xx

+=

................................................................................................................................................................................................................

18) ( )( )ln 2limx

f xx

+=