1 callculus

=1 2 (4) = 5 (4)

4. (2,0) 6. , (, ) 9. (2 = (1,1) 11.

= 5 +2 =+ 2,3) =

( ’( ) ( )=5 ( )= 2 +1 ; ( )= 2 (2 + 1) ( 2 +1 ( )( ) = [ ( )] ( )( ) = [ ( = (2

) () ( )= () 2 + 1 = [(2 + 1) ] = ) ( )= ( )= ( )] + 1)

=2 ( )= 2 +1 ( )=( )( ) ( )( )= 2 +1 = (2 2 ** (2 + 1)

+1 1 = ( )( ) [ ( )] ( ) + 1 (2 + 1) + 1)

( )( )= = : ( ) = (2 1) : ( ) = 12

[ ( )] ( ) = () 2 + 13

2.6 1.1) = (2 + 3) 1.3) = (3 4 ) 1.7) = 3 + 2 1.10) = ) ( 1.13) = ( 3) (2 + 1.15) = ( ) ) (

+ 1)

2. ( )= () ( )= ( ( 3. ( ) = ( ( )) 5, (2) = 6, (4) = 9

( )= 3 1 )) (2) = 4, (2) = (2)

() () ( )= [ ( () … () … ( )= ( )= : (1) (

() )] = ( )( ) = +2 ( ) )=4 3 +5

, () () () = ( )= () () () ( = () ()

= () () () ) ( )= ( ) () ()

( )= ( )= ( t 2 +3 1) 2.) 3.) =

= () )= ( ) =4 =2

2.7 4+ 1. 1.1) ( ) = 5 1.3) ( ) = 3 2 + 1.5) ( ) = (5 3)(7 1.7) ( ) = 3. (2) ( ) =

2 5 7 +) =3 2

4. = 16 4.1) 4.2) 2 4.3) 4.4) 5

3

** (L’ “= ( ( [ ( )] () : : :

’Hospital’s rule) () & () ”

- - , < < : ( )=2

() < ( ) () > ( ) 7 ( )>0 ( )<0 3 12 + 4

(, ) (, () () 8 () ( )=0

) () () () () ( )=0 (critical value) = ()

() : ( )=2 +3

( ): + + : () ( ): = : () 12 7

() ( )>0 ( )<0 ** ( ) = 0 : ( )= +3

=0 () () 24 20

() () () ()

= () () () ()

f [, ] () ( : : [0,2] 3 +2

[, ] ( )=0 ) ( )) = = ( )=

2.8 1. 1.1) ( ) = 3 2 1.3) ( ) = 8 1.5) ( ) = 2 2. 8 +7 2.1) ( ) =

8 4 +7 7

2.4) ( ) = 8 + 3. 2 3.1) ( ) = 3.4) ( ) = + 5 4

12 4 + 8 [0,5] 4 [-3,-1]

3. = 0 )

)

: :

x x

2.8 2. 200 4.

3 10

9. 11. 0.04x x

xp p=100- 600+22x

13. a w s= k