1 callculus

ครูมยุรี สินเจริญเลิศ

1. (lim () () ( )= ( a () ( ) = 2,

mit and continuity) () () a () = ( )=2 ( )=2

-X - >> = >> !! = > =( + =( + =(

Y : < : !! )( + + ) )( + ) )( + )

2.1 5. = () 1.) f(x) 2.) ( ) 3.) ( ) 6. = ( ) 1.) ( ) 2.) ( ) 3.) ( ) 4.) ( ) 5.) ( ) 6.) ( ) 7. 1.) (1 + ) 2.) () ( )= + 2

+1; 2 ; >2

, ( g ( )= 1. = 2. = 3. = 4. ( ) = () 5.-6. [ ( ) ± ( )] = 7. [ ( ) ( )] = 8. ( )= 0 () () 9. [ ( )] = [ 10. ( ) = (

f ( )= = 0 )] = ( )=

() =

)= ( )

2.1 1.3 ( )( 2) 1.6 () () 1.9 1.11 2.1 | | 2.3 | | 2.6 | |



3. ( )= 4 4.) ( ) 2.) (x) 4. ;< ( ) ; 0< 4.) 7.) 8; ( ) 2.) ( ) 5.) ( ) 8.)

1; <2 () 4 +6; 2 ( ) 3.) () <0 3.) () 2 () >2 () ( ) 6.) ()

(, ) ( )= ( ) -: - := ( )= ! ||

(, ) = () ) () == ( )= ( ) ;0 ; <0

: ( ) = | + 1| ±, 1. ( , ) 1. + 2. + 3. 2. [ , ) 3. ( , ] 4. [ , ] : ( )= 9

=1 = = ( )= ( ) ( )= ( ) 9 [ 3,3]

1.2) ( =4 1.4) ( =-1 2.1) k ( ( ,)

)= )=| | )= 7 2; 1 ; >1

1.[PAT1/54] () =3 2.[PAT/58] , ( )= +2 + 1+ + =

3 =3 <0 =0 +5 1 >0 0 15 + 30

3.[ANET/50] , ( )= ( 1) ++ [ 2,2] (

<0 1 0 >1 ()

- : () () ( )= ** ( ) = >> ( ) = >> () [ ,] - : () (, ) 1. ( ) 2. ( ) 3. ( ) = ( )

= () ) (, )

2. (Derivative) = () = = () = ( ) ( )= ( ) h

= () () AB =+ ) () )

=( (, ) slope= (, ) = (slope) : :

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

= = : :

+ + (, ) = = = (3,1) = 2 (1, 1)

2.3 1. 1.1) = 3 (3, 1.4) = =1 1.6) = (2,2) 2. = = 3 + 8 (1,11)

,0) 1

= () ( )= ( : r 1.) 2.)

() “ ” () ( + ) () v

1. 1.1) ( ) = 3 1.4) ( ) = 2 + 1 1.7) ( ) = 2. (2) 3 =1 3. (3) = 1 = () =

= ( ) (2,5) (3) = 5 =3

6. 6.1) 6.2) 8. PV

PV=6000 V = 100

11. 11.1) 11.2) h

r

1. ( ) = ) ( 2. = 0 = 16 3. [ ( )] = [ ( )] (3 ) 4. ( ± ) ( ) = ( ) (12 5

6 )± ( ) 5 + 2)

5. ( ) ( ) = ( ) [( + 1)(3 6. ( ) = ( ) ( [ (2 4 ) = x

) ( )+ ( ) ( ) 3 20)] ) () () ( )] 12

1. 3 +7 1.3) = 1.4) = 5 + + 2 1.8) = (4 )( + 1.10) = 1.12) = 1.16) = ( + )(3 +

+ 3) + 27)

1.19) = 2. 2.1) ( ) = 2 2.4) ( ) = =2 (4) = 3 ( 3.1) ( ) = ( ) 3.2) ( ) = ( )