บทที่12. แคลคูลัส < calculus > · 4 ข้อสอบpat 1 ( พ.ศ....

P 1

P 1

(( ))

1212..

>

Concept

1. . ( . )2. ( )3. ( )4. !!

( )

BByy PP11

+++

!! !

Ent , A-NET , PAT 1 7

3,000 ..

!!!

>_

: th.wikipedia.org

WWW.NISITTUTOR-ONLINE.COM 1

12. ( Calculus )


PAT 1 ( .. 2552 )( PAT 152 .. )1. A y = 1 x2 X

B y =4

x2 X x = c x = c

c A = B ( 2 ) (B)1. 2 2. 2 3. 22 4. 4

2. f(x) = x4 3x2 + 7f ( 3 ) (B)

1. ( 3,2 )( 2,3 ) 2. ( 3,2 )( 1,2 ) 3. ( 1,0 )( 2,3 ) 4. ( 1,0 )( 1,2 )


3. f(x) =

3x

1x

121

)4(f)h4(f)1(f)h1(flim

0h

( 2 ) (B)

1. 1 2.5

16 3.57 4.

51

( PAT 152 .. )

4. f(x) = 3x2+x5 f(0) = 1

1

1dx)x(f ( 2 ) (B)

1.35 2.

37 3.

32 4.

31


5. f , g h f(1) = g(1) = h(1) = 1 f(1) = g(1) = h(1) = 2 ( fg+h )(1) ( 4 ) (B)

1. 1 2. 2 3. 4 4. 6

6. y = 2x3 x

1 x = 1 ( 4 ) (B)

1. 13x 2y 11 = 0 2. 13x + 2y 15 = 03. 2x 13y + 11 = 0 4. 2x + 13y 15 = 0

( PAT 152 .. )

7. f(x) = x2 1 0dx)x(f1

0

f(1) ( 0.25 ) (B)


8. f(x) = ax2 + b x a b 0b

2f(1) = f(1) )9(f)4(f

( 12 ) (B)

9. y = f(x) x = 1 f(x) = 4 x f(1) + f(3) = 0 f ( 8 ) (B)

( PAT 153 .. )10. R f : R R g : R R

f(x) = 3 3/2x , g(1) = 8 g(1) =32 ( fog)(1) ( 2 ) (B)

1.31 2.

32 3. 1 4.

34


11. a b f

f(x) =

2x,1axx

2x,ba

2x,2x

2x3x

2

3

f a2 + b2 ( 53 ) (C)

12. R f : R R f(x) = 3 x + 5 x

f(1) = 5 )x(f

2)x(flim2

4x

( 6 ) (B)


13. R f : R R f(x) = 6x+ 4 x y = f(x) ( 2,19 ) 19 f(1) ( 7 ) (B)

( PAT 153 .. )14. a b f

f(x) =

5x,55x1,bax

1x1,1x1x3

f ( 1, ) ab ( 4 ) (B)

1.45 2.

47 3. 15 4. 10


15. x x3450x2+60,200x+10,000 200 ( 200 ) (C)

16. f(x) y = f(x) ( 1,2 ) 4

dx)x(f2

1

= 12 f(1) + f(1) ( 18 ) (B)

17. h(x) = f(x)g(x) y = f(x) ( x,y ) 2 2x y = f(x) 5 g

g(2) = g(2) = 5 h(2) ( 10 ) (B)


( PAT 153 )18. R

f : R R x = 1 g

1x

7x)x(f

1x1x

23x

)x(g

g x = 1 (gof )(1) ( 4 ) (B)1. 32 2. 2 3. 72 4. 27

19. a b f f(x) = x4 + 2x3 x2 + ax + b

Q(x) f(x) = (Q(x))2 1

0dx)x(f ( 3 ) (A)

1.3071 2.

3031 3.

3011 4.

301


20. ff( 2x+1 ) = 4x2 + 14x f( f( f( 2553 ))) ( 120 ) (A)

( PAT 154 .. )

21. 223

0x xxxxlim

( 1 ) (B)

1.21 2.

21 3. 1 4. 1


22. f f(x) = ax + b a b f(0) = 2 f ( 1,5 ) 2a + 3b ( 3 ) (B)

1. 12 2. 20 3. 42 4. 48

23. R g : RR g(x) = 3x21 x 2

3

f : R R ( fog )(x) = x x f

21 ( 4 ) (B)

1.21 2.

21 3. 8 4. 8


24. R f : R R g : R R x Rg(x) = x2 2x + 5 , ( gof )(x) = x6 + 2x4 2x3 + x2 2x + 5 f(0) = 0

(fog)(1) + (gof)(0) ( 1 ) (A)

25. y = f(x) 2x y + 3 = 0 ( 0,3 ) 2

0dx)x(f = 3

g(x) = 2x f(x) g(2) = 0 f(2) ( 8 ) (A)


26. f(x) =3x

3x

a

13x10x23x

a f x = 3 a ( 8 ) (B)

( PAT 154 .. )27. R

f : RR f(x) = 32

x x N f ( a,f(a) ) a 0

N Y 25 N ( 2 ) (B)

1. ( 2,7 ) 2. ( 1,4 ) 3. ( 2,4 ) 4. ( 3,5 )


28. A( 0,0 ) , B( 1,0 )

23,

21C ABC

f(x) = ax2 + bx + c a , b c A( 0,0 ) B( 1,0 ) AC BC f A( 0,0 ) B( 1,0 )

f AB ( 1 ) (B)

1.63 2.

33 3.

23 4.

332

29. f , g h a. ( fog )(x) = 3x 14 x

b. f

36x = x 2 x

c. h( 2x1 ) = 6g(x) + 12 x h(0) ( 3 ) (B)


30. R f : R R f(x) = 0 x

f(0) = 23 f(1) = 103 1

0dx)x(f ( 63 ) (B)

31. L ( 0,10 ) 1 L x x = 0 x = 6 51

L x x = 1 x = 3 ( 18 ) (B)


32. 330x 8x8xxlim

( 6 ) (B)

( PAT 155 .. )33. R

f : R R f(x) = 2x + 1 f(2) = 2 y = f(x) ( 1,3 ) ( 2 ) (B)

1. y = x21 +2 2. y =

25x

21

3. y =25x

21 4. y = x

21 +2


34. R f : RR , g : R R h : R R

f(x) =1x1ax

2 a

g(x) = ( x2+1 ) f(x)

h(x) =

)x(g)x(f

2x2x

h x = 2 2h(2) h(2) ( 4 ) (A)

1. 0.6 2. 0.8 3. 1 4. 3

35. R f : R R , g : R R h : R Rh(x) = x2 + 4 , g(x) = h( f(x)1 ) f(1) = g(1) = 1 f(1) ( 2 )

(A)1. 2 2. 1.5 3. 1 4. 0.5


36. R f : R R f(x) = 2x + 3 ( gof )(x) = 8x3 + 44x2 + 80x + 48

x 6

0dx))x(g(f ( 990 ) (A)

37. f(x) = x3 + ax + b a b L1 L2 x = a x = b

L1 L2 )1(f)h1(fh9lim

0h = 1

2

0dx)x(f ( 4 ) (A)


( PAT 155 .. )38. f(x) = x3 26x2 +bx 216 b

a1 , a2 , a3 f(x) = 0 f(1) ( 2 ) (A)

1. 211 2. 107 3. 101 4. 85

39. f(x) f(0) = 1 f(x+1) = f(x1) + x + 1 x

1

2dx)x(f ( 1 ) (A)

1. 3 2. 2 3.32 4.

31


40. 23x

x2x1lim

2

1x

( 3 ) (B)

1. 12 2. 0 3. 12 4.

41. R f : RR g : RR1. ( fg )(x) = 2x+3 x2. f g x3. f 2 x = 14. g(x) = 2 x

g ( 2.25 ) (A)


42. P(x) P(x2+3) = 3x4 + 24x2 +40

f(x) = dt)t(Px

0

)x(f)x(Plim2x

( 3 ) (A)

43. P(x) P(0) = 1

)2(P)2x(P)2h(P)2hx(P

h2hx3lim0h

= 1

P(12) ( 157 ) (A)


( PAT 156 .. )

44. C y = 34

x2x3 x 0

L C ( 1,1 ) L x( x1 ) = y 1 A B A B ( 2 ) (B)

1. 4 82 2. 8 82 3. 4 41 4. 8 41

45. f(x) =

4x,3kx

4x,12x3x4x2

8x22

k f x = 4 f(k+1) ( 24 ) (B)


46. ff(x) x ax3+bx a b

g(x) = ( x3+2x )f(x) f(1) = 18 , f(0) = 6 f(2) = f(1)+f(0) g(1) ( 354 ) (B)

47. f(x) x+1 f(x)

5+2i f(x) = 0 f(0) = 58

dx)x(f)x(f2

0 ( 168 ) (B)


( PAT 156 .. )48. a b

f(x) =

5x,bax5x2,1x

2x,baxx2

f a b ( 2 ) (C)1. 5 2. 8 3. 11 4. 12

49. dx6x7x2

2

2

=ba a b b 0

... a b 1 a + b ( 4 ) (B)

1. 33 2. 69 3. 102 4. 104


50. f(x) =64x3x

x436

3

x

() f ( 0,3 )

() f 134

( 3 ) (B)1. () () 2. () () 3. () () 4. () ()

51. f(x) = x2 + ax + b a b

f(1) = 2 ( fof )(0) = 10

2

1dx)x(f ( 12 ) (B)


52. R f : R R f(x) = 3 + 6x x

y = f(x) ( 2,22 ) 20 )x(flim4x

( 100 ) (B)

( PAT 157 .. )53. f

f(x) =

3x,11x6x

3x2,bx52

2x,ax

2

a , b f x = 2 )x(flim

3x

a+5b ( 2 ) (C)

1. 8 2. 18 3.588 4.

5102


54. b 1 dxxx

1xb

1 = 4

1+b+b2 ( 3 ) (B)1. 21 2. 31 3. 91 4. 111

55. f(x) = ax2 + bx + c a , b , c a 0

f(1) = 0 f x =31

F(, ) = dx)x(f

F( 0,t ) = F( 1,t ) + 1 t 1

() F(1,2) = F(2,3)+ 10

() 2x)x(f 3

2

x2x2x3

( 2 ) (A)1. () () 2. () () 3. () () 4. () ()


56. R a , b f : R R f(x) = a + bx + x3 x 5x y + 13 = 0 f x = 1

2

0dx)x(f ( 38 ) (C)

57. R

f : R R f(3) = 111 3x333)x(xflim

3x

= 2013

f(x) x x = 3 ( 634 ) (A)


( PAT 157 .. )58. a b

f(x) = ax +xb x 0

y = f(x) y = 1 ( 1,1 )

() f x = 1() )x)(fof(lim

1x= f( 2a2+2b2 )

( 1 ) (B)1. () () 2. () () 3. () () 4. () ()

59. f gf g

(fog)(x) = 5x 2 x fog dx)x(g = x2 4x + C C L y = f(x) x = 0 L ( 3 ) (B)

1. x + y 3 = 0 2. 2x + y 7 = 03. 3x + y 5 = 0 4. 5x + y 2 = 0


60. f(x) = 4x3 + bx2 + cx + d b , c d

2

2dx)x(f =

364

g(x) g(x) = f(x) g(1) = g(0) = g(0) g(x) = g(x) + g(x) ( 4 ) (B)

1. x4 4x3 + 12x2 6x = 0 2. x4 8x3 12x2 6x = 03. 3x4 16x3 + 48x2 24x = 0 4. 3x4 + 8x3 48x2 + 24x = 0

61. f f( 2x1 ) = 4x2 10x + a a

f(0) = 12

4

1dx)x(f ( 34.5 ) (B)


62. R f : R R , g : R R s : R R

f(x) = x + 1 x Rg(f(x)) = x2 + 2x 1 x R

s(x) = h

)x(g)hx(glim22

0h

x R

( sg )(1) ( 4 ) (B)

( PAT 158 .. )63. 0 90 f(x) = 12x 9x2 0 x 1

sin = a f(a)

sec1)1)(sin(sec

sin1)1)(sec(cot 22

( 4 ) (B)

1. 1+ 5 2. 5 3. 1 5 4. 0


64. f(x) = log

x1x1 1 x 1

dx)x(f = A

dxx1x2f 2 ( 3 ) (B)

1. A2 2. A2 3. 2A 4. 2A

65. aaax

1x51x5lim0x

= 80

a2 + a + 58 ( 4 ) (B)1. 64 2. 78 3. 130 4. 330


66. R f : RR

f(x+y) = f(x) + f(y) + 3x2y + 3xy2 x y x

)x(flim0x

= 2

f(1) + f(5) ( 35 ) (A)

67. f g

f(x) = 34

xxx2 x 0 , g(x) = ( 1+x2 )f(x) g(1) = 2

2

1

3 dx)x(gx ( 132 ) (B)


68. f f(x) =

0x,x

1x5bx1

0x,ba0x,a2e

2

x2

a b

f x = 0 15a + 30b ( 15 ) (C)


ANET , Entrance ( .. 2549 2552 )( ANET52 )1. a b

f(x) =

1x,xbxax

1x,)1x(23

2

x = 1

f(1) ( 2 ) (B)1. 6 2. 4 3. 0 4. 4

1. f(x) = x3 3x +6 P y = f(x) f P ( 2,6 ) ( 2 ) (B)

1. 1 2. 32 3.

32 4. 2


2. y = x34x xx [ 2,1 ] ( 5.75 ) (B)

( ANET51 )

3. I(a) =

a

a

2 dx)1x( a [ 0, )

[ 0, ) ( 4 ) (A)1. a [ I(a) 0 ] 2. a [ ( I(a) = 0 ) ( a = 0 ) ]3. a [ (a 2) ( I(a) 0 ) ] 4. a[ ( a 0 ) ( I(a) 0 ) ]


4. f ( 0, ) f(2) = 2f(1) f(x) = 27x 2x1

L y = f(x) ( 1,f(1) ) L ( 2 ) (B)1. ( 2,64 ) 2. ( 2,66 ) 3. ( 3,94 ) 4. ( 3,96 )

5. f [ 2,2 ] f(0) = 1 , f(1) = 0 f x = 1 x = 1 ( 1 ) (A). f(2) f(x) x [ 2,2 ]. f(2) f(x) x [ 2,2 ]

1. . . 2. . . 3. . . 4. . .


6. f f(x) =

0x:1x0x:bax

3

2

f(1) = 4 ( fof )

3 2

1 ( 1.5 ) (B)

7. f(x) =

1x:x21x:3x

3

f [ 4,0 ] ( 3 ) (B)


( ANET50 )

8. a , b f f(x) =

1xbx1x0baxx

0x1)1x(3

2

f [ 2,2 ] f

21 ( 0.125 ) (C)

1. 0 2. 0.25 3. 0.5 4. 0.75

9. f(x) = 1+xa g(x) = x2 + b ( fog )(0) =

21 f(1) = 2

gf( a+b ) ( 4 ) (B)

1.31 2.

41 3.

41 4.

31


10. y = x3 2x2 + 2x x x = 0 x = 4 ( 37.33 ) (B)

1. 16 2. 16.25 3. 16.5 4. 17

11.

21x xx321

x11lim ( 1 ) (B)

( ANET 49 )

12. f(x) =

1xx31x01x2

0xx 2

)x(flim 20x

+ )x1(flim0x

( 3 ) (A)

1. 0 2. 1 3. 2 4. 3


13. P(x) 1 , 2 , 3 P(x) = 0 P(4) = 5 P(1)( 4 ) (B)

1. 76 2.

65 3.

54 4.

35

14. y = f(x) ( x,y ) 2x + 2 f 3y = f(x) x x = 1 x = 0

( 2 ) (B)

1.37 2.

38 3. 9 4. 12


( Ent48 .. )

15. dxx42

2

2 ( 4 ) (B)

1. ( 3.1,3.2 ) 2. ( 3.2,3.3 ) 3. ( 6.1,6.2 ) 4. ( 6.2,6.3 )

16. f(x) =

0x00x1

.0x

lim ( fof )( x ) = 0 .0x

lim ( fof )( x ) = 1 ( 1 ) (B)

1. . . 2. . . 3. . . 4. . .

17. y = f(x) ( x,y ) 2x 4 f 10 y = f(x) x x = 0 x = 3 ( 1 ) (B)

1. 33 2. 36 3. 39 4. 42


( Ent47 .. )18. f(x) g(x)

f(g(x) ) =)x(g

1

f(g(0) ) = 5 f (g(2) ) ( 4 ) (B)

1. 1 2. 3 3. 5 4. 7

19. f(x) =

0x1x0x1x

g gof ( 4 ) (A)1. g(x) = 1 x ( ,1 ) [ 1, )2. g(x) = f 1(x) x ( ,1 ) [ 1, )

3. g(x) =

1x)1x(

1x)1x(2

2

4. g(x) = x3 x ( ,1 )[ 1, )


20. y = f(x) 3 x = 2 3x + y 7 = 0

( 1,4 ) g(x) = x2f(x) 2

1dx)x(g ( 2 ) (A)

1. 5 2. 7 3. 8 4. 10

21. f(x) =

2n2x1n21n1n2xn2nx

n = 0, 1, 2, ,9

20

0dx)x(f ( 1 ) (A)

1. 105 2. 115 3. 125 4. 135


( Ent47 .. )22. f(x) = 3x + 1 ( fog )(x) = 3x2 + 1

g(0) = 1 1

0dx)x(g ( 1.25 ) (B)

23. f(x) =

0x1

0xx1

g(x) =1x

1

. fog x = 0

. f

21 = g

21

( 1 ) (B)1. . . 2. . . 3. . . 4. . .


24. f(x) =41 x4

32 x3

21 x2 + 2x

31

f ( c ,f(c) ) c 0 a f X b ( 3 ) (A)

1. a = 1 , b = 2 2. a = 1 , b = 4 3. a = 2 , b = 2 4. a = 2 , b = 4

25. f h( x ) = x3 + 1 a ( hof )( a ) = 9 ,

( hof )( a ) = 0 ,( hof )( a ) = 1

( 2 ) (A)1. f a 1 2. f a 23. f a 1 4. f a 2


26. f f(0) = 1 = f(1)

f(0) = 1

1

1dx)x(f = 6 f(1) ( 3 ) (B)

1. 7 2. 1 3. 13 4. 15

( Ent46 .. )

27. f(x) = x4x 2 g(x) = 16x 2 a , b f(x) = g(x)

)x(g)x(flim

ax+

)x(g)x(flim

bx( 1 ) (B)

1.23 2.

65 3.

21 4.

31


28. g f(x) = xg(x) f(x) = 4x3 + 9x2

f(0) = 0

)1x(g)x(f

dxd x = 2 ( 1 ) (B)

1. 4 2. 2 3. 2 4. 4

29. a , b f(x) = x3 + ax2 + bx + 1

f(1) = 15 dx)x(f10 = 1255 f(1) ( 2 ) (B)

1. 9 2. 10 3. 11 4. 12


30. f(x) = x2 1

. 1

1 dx)x(f = 34

. y = f(x) x = 1 x = 1 34

( 3 ) (B)1. . . 2. . . 3. . . 4. . .

( Ent46 .. )

31. )x1)(x1()x1)(x1(x1x1x1lim 2230x

( 3 ) (A)

1. 0 2.41 3.

21 4. 1


32. f g x = 4

4xkx4

4x2x

4x)x(f)x(g

2k

f y = x+1 x = 4 k ( 2 ) (A)1. ( 3,1 ) 2. ( 2,0 ) 3. ( 1,1 ) 4. ( 0,2 )

33. f f(x) = 2x+1 f 21 x = 1

f ( 4 ) (B)

1. 1 2. 31 3. 0 4.

31


34. 50 51 2 52 4 53 6

90 100 ( 1 ) (A)

1. 16,000 2. 16,200 3. 16,400 4. 16,600

35. y = f(x) ( x,y ) x2 3x+2 2

0)x(f = 4

( x,y ) y = f(x) ( 1 ) (B)1. ( 0,4/3 ) 2. ( 0,4/3 ) 3. ( 1,13/4 ) 4. ( 1,13/4 )


36. A XY y = x2 7 x x = 0 x = aa A x A x

2a a ( 2 ) (A)1. 32 2. 33 3. 5 4. 7

( Ent45 .. )

37. a 0 , f(x) =

axx

1x

ax2x

x

g(x) = x2

ax

lim ( fog )( x ) )2a(a

11)x)(gof(limax

a ( 2 ) (A)

1. 1 2. 3 3. 5 4. 9


38. f(x) = x2 6x + c c a b f(x) = 0 3a + 2b= 20 f(C) ( 1 ) (B)

1. 38 2. 26 3. 26 4. 38

39. f( x ) = x2 2 x g( x ) = x2 + 1 ( gof )( 3 ) + ( fog )(3) ( 3 ) (B)1. 132 2. 84 3. 84 4. 132


40. f(x) = ax a 2x + y 6 = 0 f ( 1,4 )

f(0) = 8 1

0dx)x(f ( 2 ) (B)

1.422 2.

423 3.

442 4.

443

( Ent45 .. )41. a y = a2x2 +4ax +10 x = 0 x = 1

( 7 ) (A)


42. f(x) =

4xbx

4x1

4x2x

a)2x)(4x(

2

a , b

f x = 4

16baf ( 2 ) (B)

1. 16 2. 14 3. 14 4. 16

43. f(x) = 1x3 g ( fog )(x) = x2 + 1 x R f(1) + g(1) ( 1 ) (B)

1. 41/12 2. 35/12 3. 33/4 4. 39/4

44. g(x) = x2f(x) f(x) = 2x + 3

g(1) = 0 f(4) ( 3 ) (B)

1. 0 2. 11 3. 13 4. 28


45. y = f(x) x ( x,y ) 6x+2b b x = 0 x = 2

x = 0 x = 1 f x ( 2 ) (A)1. x = 2 2. x = 1 3. x = 0 4. x = 1

( Ent44 .. )46. x = a y = x2 x = 0 x = 8 a3 ( 128 )(B)


47.

1x2

1x1x

1)x(f g(x) = x3+x2

h(x) = f(x)g(x) ( 4 ) (B)1. h x = 1 0)x(hlim

1x

2. h x = 1 4)x(hlim

1x

3. h x = 1 0)x(hlim

1x

4. h x = 1 4)x(hlim

1x

48. g x 0 g(3) = 3 n g( xn+2x ) = 4x3+6x2+31 ( 2 ) (A)

1. 5 2. 6 3. 7 4. 8

49. f f(0) = 2 f x = 1 x = 1 f(4) ( 4 ) (B)

1. 28 2. 24 3. 24 4. 28


50. y = f(x) ( 1,0 ) ( x,y ) 3x2 4x + 2x2

( a,b ) x 2 = 0 a+b ( 4 ) (B)1. 3/2 2. 2 3. 7/2 4. 4

( Ent44 .. )

51. y =

45x2)1x( 2

161,

21 x

20

2

sin2 ( 0.1 ) (A)


52. f(x) = ax3 + bx a b f 2 x = 1 g(x) = x3 + f(x) g ( 4 ) (B)

1. ( 0,2 ) 2. ( 3,1 ) 3. ( 1,1 ) 4. ( 2,0 )

53. f(x) = ax3 + bx2 + 2x 2 a , b f (1) = 5 f (0) = 12 dx)x(f)x(f ( 1 ) (B)

1. cx10x9x5 23 2. cx10x9x5 23 3. cx10x9x5 23 4. cx10x9x5 23


54. f f [ 0,1 ] g(x) =1x

)x(f4

f(1) = f (1) = 1 f(0) = f (0) = 2 dx)x(g1

0 ( 3 ) (A)

1. 5/2 2. 1/2 3. 3/2 4. 7/2

( Ent43 .. )

55. f(x) = x3 x2 + g(x) f(2) = f(2) = 2 )2(fg

( 1 ) (B)

1. 2 2. 1 / 2 3. 0 4. 2


56. y = f(x) ( 0,1 ) ( 4,c ) c ( x,y ) 1x c ( 2 ) (B)

1. 4 / 3 2. 7 / 3 3. 8 4. 9

57. f(x) = ax3 4x2 + 1 a

1x0

1x)x(f

1x)x(f

)x(g

g(x) 1 a ( 2 ) (B)1. 0 2. 5 / 2 3. 8 / 3 4. 3

58. f(x) = x2 c c 4c y = f(x) x = 2 x = 1 24 c ( 9 ) (B)


( Ent43 .. )59. f(x) = x3 +cx2 9x c f 1

f ( 1 ) (C)1. ( 3,1 ) 2. ( ,3 )( 1, ) 3. ( 1,4 ) 4. ( ,1 )( 4, )

60. F f f(x) = 3x2 6x + 3 F(0) = 1 F [ 0,2 ] x = c F(c) ( 3 ) (B)

1. 1 2. 0 3. 1 4. 2

61. fg(x) = ( x+1 )f( x )

dx)x(g = x2 x + c )1(f ( 1 ) (B)

1. 3/4 2. 5/4 3. 3/2 4. 5/2


62.

0x0

1x01x

1xx

)x(f

2

2x)1x(f

lim)x(flim1x

20x

( 1 ) (A)

1. 4/3 2. 1 3. 0 4. 1/ 3

( Ent42 .. )63. u , v x x2x)x(v 2

)x(v)x(u)x(f u(3) = 9 , 3)3(u )3(f ( 5 ) (B)


64. f

223

x44x4xx)x(f

2x

f(2) = a , f( 2) = b a b ( 4 ) (B)1. a = 1 , b = 3 2. a = 1 , b = 3 3. a = 1 , b = 3 4. a = 1 , b = 3

65. f ( 0,2 ) f(x) = 3x212x + 9 f( 3 ) (B)

1. 2 2. 3 3. 6 4. 8

66. F(x) = f(g(x)) g(x) = x3 + 2x +2 dx)x(F = 5x3+2x+c )5(f ( 1 ) (B)

1. 6 2. 5 3. 4 4. 3


( Ent42 .. )67. f f(3) = 2 , f(3) = 5

g(x) =1x

)x(f2

g(3) ( 0.62 ) (C)

68. f(x) =

1xx1x1

1x1)1x(2

1xx2

1x23

2

. f x = 1. f x = 1

( 1 ) (C)1. . . 2. . . 3. . . 4. . .


69. a , b , c , d dcxbxaxxf 23)( f 2x = 1 f(1) = 4 f(0) = 1 f ( 2 ) (B)

1. x = 3 2. x =31 3. x =

31 4. x = 3

70. R 1

sindx)3x4(

= 0 cos2 ( 3 ) (B)

1. 0 23 2. 0

23

3. 1 21 4. 1 1


( Ent41 .. )

71. f(x) =

1x1x

x521x1

1x01x3

1

. )x(flim)x(flim1x1x

. f x = 1

( 2 ) (B)1. . . 2. . . 3. . . 4. . .

72. f 15)]([)( 3 xfxF 4)1()1( fF )1(F ( 2 ) (B)

1.21 2.

23 3. 8 4. 24


73. y = x2 3x + 2 x = 0 x = 2 x( 4 ) (B)

1.23 2.

61 3.

32 4.

65

74. f f(2) = 1 f(1) = 3 f(x) = 3 x f(0)( 1 ) (B)

1. 5 2. 6 3. 12 4. 15

( Ent41 )

75. 3

9)(

2

x

xxf ( 1 ) (C)

1. 0)(lim3

xfx

)(lim3

xfx

2. 0)(lim3

xfx

6)(lim3

xfx

2. 0)(lim3

xfx

6)(lim3

xfx

4. )(lim3

xfx

0)(lim3

xfx


76. 1)( xxf xxg )( ))(()( xfogxF 1x )2()( 1 F ( 3 ) (B)

1. 0 2. 1 3. 2 4. 4

77. )(

1)(

32

xg

xxf

3)2()2( fg )2(g ( 1 ) (C)

1. 11 2. 12 3. 13 4. 14

78. xxxdx

dy435 24 )1()1( yy )0(y ( 3 ) (B)

1. 0 2. 1 3. 2 4. 3

บทที่12. แคลคูลัส < calculus > · 4 ข้อสอบpat 1 ( พ.ศ....

Documents

2010 Skema Pat Sbp

Dst t2 pat

Formulaciòn PAT

Pat Iei Chimbo 2016

PM PAT 2015

Anato Pat Sajin

Pat 2012 paper_pdf_10581

Pix70 Nat Pat

Pat Fizik k2

AllTheThingsYouAre Pat

Pat y Norma Tecnica

Pat7-3. 2552

Guia Pat - Srt

PAT DRELM 2016

PAT Maruanum 2013

Pat Colectivo

1 Matriz Elaboración Del PAT-IEI 137

BM Pemahaman PAT 2015

Pat7 4. 2552

US Pat 7,150,778

Issaguide Pat(2009)

PAT 2015 MCC

Exam Sains Pat k1

Guia Simplificada Pat

Alfaro Pat Raca

Pat 2014 Horizontal

Pat Benatar

engdouglasmenezes.webnode.com.pt...DE Pat - Bra -CPTWTETRÔ Pat - CEAT Btesser Pat - Cic Leste Pat Norte Pat - Pat Cidade Tiradentes Pat Ermelino Warazzo Pat Guaiarnzes Pat - Santana

Pat Sains Ting 2

Tsg pat douthwaite

Pat S Khumpaisal 1

Lucidi Lez 2 Pat

PAT1 2552-2554

Modelo Pat 2015

khb t1 pat 2014