Math exam m4 6 2008

F TOP TEST CENTER F ก ( .4- .6) ก ก 2551 12

F F
12 ก ก 2551 F 16 ก 2551 10.30 . 12.30 .

( .4 .6)

ก
F F F กF F
1. F 4 F 50 F 50
2. FF ก ก ก , , ก ,F , ,
F F ( F ก F F ) ก F ก F
( ก F F F F ก F)
3. F F ก ก F F F ( F 2B )
ก F ก F F ก F
F F ก 3 ก F ก ก

ก F ก F F F F ( F F )
F F F ก ก
( ก F F F ก ก F กก ก F 1 ก F F F F )


1. F A = {1 , 2 , 3 , , 9} B = {3 , 4 , 5 , 6 , 7} 7. ก ก (3)5 ก F
C = {X | B ⊄ X F X ⊂ A} F C 1) 3 ก 5
ก ก 2) 3 ก 5
1) 8 2) 16 3) 3 ก 5
3) 495 4) 496 4) 3 ก 5
2. F A ก B ก Cก D F 8. ก 24x 2 = 36x 3 F
F F F F F ก F F
(ก) (A ∩ C) (B ∪ D) ก 1) [ 1 , 0] 2) [1 , 2]
( ) (C A) ∩ D F 3) [0 , 1] 4) [2 , 3]
1) ก 2 F 2) F (ก) ก F 9. F A = {1 , 2} F F ก
3) 2 F 4) F ( ) ก F A×A A ก F
3. Fก Fก F 1) 16 F 2) 256 F
12 16
ก 3) 2 F 4) 2 F
1) 2) 10. F 3 sin A = 4 cos A A
3) ก 2 F 4) F F F F กก F tan A + cot A
4. ก F F F F ก F
ก F 1) 1 2) 2
1) ก ก 3) 3 4) 4
2) กF ก 11. F B F cosec B + cot B = 0.5
กF F F cot B cosec B ก F
1) ก F 1) 1 2) 1
2) ก F 3) 2 4) 2
3) F ก F 12. ก F f(x) = 9 − x 2 g(x) = x 2 − 16
4) F ก F F F F F F ก F
5. ก กก F ก ก (ก) gof F F
1 22 ( ) fog F F
, , 1.4142... , 0.12345 , 1.69 , 3 − 27 , − 9
π 7 1) F (ก) ก F 2) ก 2 F
1) 1 2) 2 3) F ( ) ก F 4) 2 F
3) 3 4) Fก 13. 3 , 3 , 3 , 3 , ...
6. F a , b a*b = a+b 5 1) F
ก ก F * ก F 2)
1) 0 2) 5 3) F ก
3) 1 4) 5 4) F ก
F -1-


 5 + 16 n − 4 n  1) F (ก) ก F 2) ก 2 F
14. F lim   ก F 3) F ( ) ก F 4) 2 F
n →∞  n +3 n +2 
1) 4 2) 5 20. ก F
3) 2.5 4) 1.5 F
15. ก FA,B ก F P(A) = 0.6 12 a 20
P(B) = 0.7 P(A ∪ B) = 0.9 F P(A ∪ B′) X 150 b 150
F F S.D. 2 c 3
1) 0.5 2) 0.6 F a + b + c2 ก F
3) 0.7 4) 0.8 1) 173.5 2) 174.5
n n n  n  3) 175.5 4) 176.5
16. F n∈N F F   +   +   + ... + 
1 2 3  n −1

        21. F F ab = 0 F a = 0 b=0
ก F ก F
1) 2n 2) 2n 1 1) ab = 0 F a ≠ 0 b≠0
3) 2n 2 4) 2n 1 2) ab = 0 a=0 F b≠0
17. ก F 2 , 6 , 12 , 20 , 30 , 42 , 56 , 3) F ab ≠ 0 F a ≠ 0 b≠0
72 , 90 F F F ก F F 4) F ab ≠ 0 F a ≠ 0 b≠0
1) 7 2) 8 22. ก F F F
3) 9 4) 10 (ก) 1) ∼ p ∨ q () 1) p ∨ q
18. ก F x1 , x2 , x3 , x4 , x5 ก 2) ∼ r → ∼ q 2) ∼ q
F ก x1 + x2 = 10 , x2 + x3 = 13 p→r p
x3 + x4 = 17 x4 + x5 = 24 F F Q1 + Q3 1) F (ก) F
ก F 2) F ( ) F
1) 16 2) 17 3) 2 F
3) 18 4) F F 4) F 2 F
19. F 10 4
23. ก ≥1 ก F
ก F F x2
X=7, (Mode) = 4 , (Med) = 6 1) (− ∞ , 2] ∪ (0 , 2] 2) [ 2 , 2]
F F 3) [ 2 , 0) ∪ [2 , ∞) 4) [ 2 , 0) ∪ (0 , 2]
10 10 24. ก ก F F F
(ก) ∑ x i − 7 < ∑ x i − 6
i=1 i=1 (x2 x 2)2 + (x2 + 2x 3)2 = (5 x 2x2)2
10 10 1) (− ∞ , 5) 2) ( 5 , 1)
( ) ∑ ( x i − 7) 2 < ∑ ( x i − 4 ) 2
i=1 i=1 3) (1 , 7) 4) (7 , ∞)
ก F F F ก F
F -2-


25. F ก ก F a,b∈I 5 6
32. F A ก F 3×3 M11(A) =
F (15 , 22) = 15a + 22b b F a 8 9
F 1 2 1 3
1) 0 2) 1 M23(A) = M32(A) = F
7 8 4 6
3) 2 4) 3 F det A ก F
26. F A(1 , 2) , B(2 , 5) , C(3 , 1) D 1) 0 2) 1
F ∆ ABC F ก F 3) 2 4) 1
F D กก AB ก F 33. F a , b , c , d F F F
1) 3x + y 8 = 0 2) x 3y + 4 = 0 F ก 2x + ay = b
3) x + 3y 8 = 0 4) 3x y 4 = 0 x + cy = d ก
27. ก Fก F ก F ก F
y2 = 8x F 3x 4y + 9 = 0 F 1) 2b + d ≠ 0 2) 2a + c ≠ 0
1) x2 + y2 4y + 5 = 0 2) x2 + y2 4y 5 = 0 3) b + 2d ≠ 0 4) a + 2c ≠ 0
3) x2 + y2 4x + 5 = 0 4) x2 + y2 4x 5 = 0 34. F F
28. ก x2 y2 + 4x + 6y 5 = 0 ก (ก) i < i
1) F 2 F ก 2) ก ( ) 2i < 2
3) F 2 F กก 4) F ก F F F ก F
29. F f(x) = 2x + 1 g(x) = x2 F F k ∈ R 1) F (ก) ก F 2) ก 2 F
F (fog)(x) = (gof)(x) F F (f + g)(k) 3) F ( ) ก F 4) 2 F
ก F 35. F F F ก F
1) 1 2) 1 1
(1 + i) + (1 i) 2
ก F
3) 3 4) 9 1) 0.5 2) 2
30. ก F A = {1 , 2 , 3 , 4} B = {5 , 6 , 7 , 8} 3) 0.25 4) 4
F กF f ก A B F 36. F ∆ ABC F
ก F a=4,b=5,c=6 F F
1) 16 กF 2) 20 กF A,B C( ) ก F
3) 24 กF 4) 36 กF F b cos C + c cos B ก F
31. F f = {(x , y) ∈ R×R | y = log(x 2) log(8 x)} 1) 3 2) 4
F f ก 3) 5 4) 6
1) F ก F 5 37. F 1
3 sin x + 6 cos x
ก F
 
2) 5 2
3 6
3) 6 1) 2 2) 2
4) กก F 6 3) 4 4) 8
F -3-

1 1 44. ก F 10 11111
log 3 log 36 log 4 9
38. F 81
5
+ 27 9
+3 7
ก F F 0ก 1 ก
1) 122 2) 124
1) F ก F 600
3) 126 4) 128
2) F F 700 ก 800
45. 4 4 F F
3) F F 800 ก 900
Fก ก 2 F ก
4) กก F 900
1) 4!4! 2) 2!4!4!
39. F u v ก F θ
3) (2!)4 4) 4!(2!)4
F uก v u+v =4 46. ก1 F 3 F 3
u − v = 2 13 F F (u ⋅ v ) u v cosθ Fก F F ก ก F ก
ก F 1) 72 2) 96
1) 9 2) 9 3) 18 4) 81 3) 120 4) 144
− 1  6 2x −1 x ≤1
40. F u =   v =   θ 47. F f(x) =  F F k∈R
 3 − 2  3x + k x >1

F uก v F F sin 2θ ก F Ff กF F x=1 F
24 24 7 7 1) 2 2) 2 3) 4 4) 4
1) − 2) 3) − 4) 48. กF x Fก
25 25 25 25
41. F ก F F n F ก ก Fก F 400 x F F ก F Fก
ln(log23) ln(log43) ln(log54) ln(logn(n 1))= (10)log2 ln25
1 F ก
1) n 2) n 1) 100 2) 150
3) n ก F F 4) F ก F 3) 200 4) 250
d
42. ก F ก F 49. F d (sin u) = cos u du F F (sin x cos x )
dx dx
F 60 ก ก F
20% F F Fก 4 F F 1) cos2 x 2) 2 cos2 x
F F ก F 2.5 F F F F 1
3) cos 2x 4) cos 2x
ก 4 ก F 2
1) 80 2) 85 50. F F F F y = x3 ก ก X
3) 90 4) 95 ก x= 1 x=2 ก F
43. F F F 1) 3.50 . F 2) 3.75 . F
F 50 ก x2 = 50y F 3) 4.00 . F 4) 4.25 . F
ก ก F
1) 1,150 2) 1,250
3) 1,350 4) 1,450 F F F ก F
F -4-


F F
12 ก ก 2551 F 16 ก 2551

( .4- .6)

ก
ก
F
45 12.52 11,362

- 38 12.41 2,379
- ก 35 12.03 4,483
- ก 40 13.68 1,188
- ก 36 12.53 696
- F 41 12.24 1,246
- ก 45 13.55 1,370

F http://www.toptestcenter.com ก


ก F F
ก F
612737 F ก 45 1 . F F ก
612723 F กF 44 2 . F F ก
612728 F 43 3 . F F ก

ก F F
ก F
612739 F ก Fก 42 1 ก . F F ก
610454 กF 41 1 F F .
609694 F 40 1 ก F .
600330 F 38 1 F ก . F
609127 F ก 36 1 ก .
601313 F 36 1 ก F F .
601427 35 1 .
ก

ก F F
ก F
610453 ก F 40 1 . F .
612734 39 1 ก . F F ก
612748 39 1 ก . F F ก
602067 ก F 37 1 . .
610001 F 36 1 . ก ก .
605409 F F 36 1 . .
603515 34 1 . F .
604013 34 1 . F .
603514 ก 34 1 . F .
601017 Fก 34 1 . F .
603496 ก F 34 1 . F .
600343 33 1 . F F ก . F
602036 F 32 1 . F .
609692 ก F 32 1 . F .
611517 ก F 31 1 . ก .
612660 F 30 1 . F .
( . )
609375 F 30 1 . .
609237 F ก 29 1 . ก .

ก F F ( F)
ก F
606614 F ก 29 1 . F F . F
602452 ก F 28 1 .ก F ก F F .ก F
601428 F F 27 1 . .
611474 F ก F 27 1 . .
609190 27 1 . .
612853 27 1 .ก .ก
612256 F ก 26 1 . .
606874 กF 25 1 . F ก " " . F
601316 24 1 . F F .
609744 F F 23 1 .F .F
605370 23 1 .F ก F .F
600681 F ก 23 1 . กF F . กF
602426 F 23 1 . ก ก . ก
606943 F 23 1 . F F .
602617 ก F 23 1 . F F . F
602550 F ก 23 1 . F F . F
602692 F 23 1 . F F . F
610427 ก F 23 1 . กF .
601072 F 22 1 . F ก 3 . F
600798 ก F ก F 22 1 . F . F
600726 F 22 1 . .
607870 F 22 1 . ก ก F .
603152 ก F 22 1 . F F . F
606812 22 1 . .
600793 F 22 1 . F . F
606409 F F 21 1 . .
610904 21 1 . .
610659 ก 21 1 . .
603773 ก F 21 1 . ก . ก
612361 ก 21 1 . .
610623 ก 21 1 . .
608676 Fก 21 1 . ก ก F ก F . ก
ก
610981 ก F F 21 1 . .
611265 ก ก F 19 1 . .
609398 ก F 19 1 . .

ก F F ( F)
ก F
612205 ก F ก 19 1 . ก ก . ก
600279 ก F 19 1 . F .
611524 F 19 1 . F F F . F
611406 ก 19 1 . .
607805 ก 18 1 . .
610497 18 1 . .
612786 F 18 1 .ก F .ก
602959 ก ก F 17 1 . .
601631 ก F 17 1 .ก F ก .ก
602472 กF 17 1 . ก F F .
608976 17 1 .F .F
609422 17 1 . F . F
602819 F F 17 1 . .
602852 17 1 . .
601772 17 1 . F . F
602949 17 1 . .
602848 F 17 1 . .
602836 กF F 17 1 . .
602478 ก 17 1 . ก F F .
609767 กF 16 1 . F .
609782 F ก 16 1 . F .
609225 ก F 15 1 . ก ก . ก
609223 F ก 15 1 . ก ก . ก
609224 ก F 15 1 . ก ก . ก
606703 F 14 1 .ก .ก
606702 14 1 .ก .ก

1. F 4) 3. F 2)
n(B ⊄ X ⊂ A) = n(X ⊂ A) n(B ⊂ X ⊂ A) ก Fก ก ก
= 29 24 = 512 16 = 496 ก ก ก F F
2. F 2) ก F
F (ก) ก ( A ∩ C ) ( B ∪ D) = ( ∩ ) ( ∪ ) 4. F 1)
= =
F () F A = {1 , 2} , C = {1 , 3 , 5 , } F
D = {2 , 4 , 6 , } F (C A) ∩ D = ∅ ( ก ) ก F
F (ก) ก F F F
F Fก

5. F 2) 13. F 4)
22 F F d=3 3 = 0 →
ก , 0.12345 , 1.69 , 3 − 27
7 3
1 F F r= =1 →
ก , 1.4142... 3
π 111
ก กก F ก 2 F ก , , ,...
333
6. F 4) ก F F d=0
Fe ก ก F * a*e = e*a = a 14. F 1)
a*e = a → a+e 5 = a →e=5∈R  5 16n 4 n 
5 + 16n − 4
n  n + − 
e*a = a → e+a 5 = a →e=5∈R lim  = lim  n n
3 n +2  2 
ก ก Fe 5 n→∞  n +  n→∞  n 3 n
+ + 
7. F 3) ก (3)5 = (3×3×3×3×3)  n n n 
3 ก 5  5 +4 − 1 
0 + 4 −0
= lim  n
4 n
8. F 3) = =4
 1
n →∞ 1 +
2  1+ 0 + 0
24x 2 = 36x 3 → (22)2x 1 = (33)2x 1  6 n+ n
 
1 15. F 3)
42x 1 = 92x 1
2x 1 = 0 → x = ∈ [0 , 1]
2 ก P(A ∪ B) = P(A) + P(B) P(A ∩ B)
9. F 2)
0.9 = 0.6 + 0.7 P(A ∩ B)
ก n( A ) = 2 n( A × A ) = 4
P(A ∩ B) = 0.6 + 0.7 0.9 = 0.4
F ก A×A A 24 × 2 = 256
P(A ∪ B′) = 0.2 + 0.4 + 0.1 = 0.7
10. F 3)
16. F 3)
4 3
ก tan A = sin A = tan A = cot A = cos A = n n n n
cos A 3 sin A 4 ก (x + y)n =  xn + xn−1y1 + xn−2y2+...+ yn
       
      
4 3 16 + 9 25 0  1  2  n
tan A + cot A = + = = F x=y=1 FF
3 4 12 12
25 n n n  n  n
F กก F 3 (1 + 1)n = 2n =   +   +   + ... +   +  
0 1 2  n −1  n 
12          
11. F 4) n n  n  n n n
 + +...+  = 2   −   = 2 2
n
ก cosec2 B cot2 B = 1 1   2  n −1    
   
    0 n
(cosec B + cot B)(cosec B cot B) = 1 17. F 4)
( 0.5)(cosec B cot B) = 0.5(cot B cosec B) = 1 n 9
1 H.M. = = 1 + 1 + 1 + 1 + ... + 1
n  1 
cot B cosec B = =2 2 6 12 20 90
0. 5 ∑  
12. F 3) i=1  x i 
ก กF f F Df = [ 3 , 3] , Rf = [0 , 3] 9
= 1 1 1 1 1
กF g F Dg = ( ∞ , 4] ∪ [4 , ∞) 1×2 + 2×3 + 3×4 + ... + 8×9 + 9×10
Rg = [0 , ∞) ก 9
= 1 1 1 1 1 1 1 1
F (ก) Rf ∩ Dg = ∅ gof F F F 1 − 2 + 2 − 3 + ... + 8 − 9 + 9 − 10
F ( ) Rg ∩ Df ≠ ∅ fog F F 9 9
= 1 1 = 10−1 = 10
F () ก F 1 − 10 10

F -1-

1 F ()
18. F 2) F Q1 (5 + 1) = 1.5
4 [(p ∨ q) ∧ ∼ q] → p
3 F
F Q3 (5 + 1) = 4.5
4 T T F
x +x x +x
Q1+Q3 = 1 2 + 4 5 = 5 +12 = 17 F T F
2 2 ก ก F
19. F 3)
ก F
10
F (ก) ก ∑ xi − a F F 2 F
i=1 23. F 4)
10 10
a = Med ∑ xi − 7 > ∑ xi − 6 4 4 − x2 ( x − 2 )( x + 2 )
2 ≥ 1 → 2 ≥0 → ≤0
i=1 i=1 x x x2
10
F () ก ก ∑ (x i − b)
2
F F (x 2)(x + 2) ≤ 0 x≠0
i=1 F x≠0
10 10
b= X ∑ ( x i − 7) 2 < ∑ ( x i − 4 ) 2
i=1 i=1 [ 2 , 0) ∪ (0 , 2]
F () ก F
20. F 2) 24. F 3)
a ก a = 20 12 = 8 F a = x2 x 2 b = x2 + 2x 3
b ก X = 150 = X ก ก F F a2 + b2 = ( a b)2
b = X = 150 a2 + b2 = a2 + 2ab + b2 → 2ab = 0
N S2 + N S2 F F ab = 0 → (x2 x 2)(x2 + 2x 3) = 0
2
c ก S = → (x 2)(x + 1)(x + 3)(x 1) = 0
N +N
x = 2, 1, 3 , 1
2 12(2 2 ) + 8(S2 ) 48 + 8S 2 ก (2)( 1)( 3)(1) = 6 ∈ (1 , 7)
3 = → 9=
12 + 8 20 25. F 2)
180 − 48
S2 = = 16.5 = c2 22 = 15(1) + 7 1 = 15(1) + 7( 2)
8 15 = 7(2) + 1 = 15(1) + [22(1) + 15( 1)]( 2)
a + b + c2 = 8 + 150 + 16.5 = 174.5
7 = 1(7) + 0 = 15(3) + 22( 2)
21. F 1)
(15 , 22) = 1 a=3,b= 2
∼ [p → (q ∨ r)] ≡ p ∧∼ (q ∨ r)
F 2 F 3 1 F
≡ p ∧∼ q ∧ ∼ r 2 = 3( 1) + 1
ab = 0 F a ≠ 0 b ≠ 0 26. F 3)
22. F 3) 1 + 2 + 3 2 + 5 − 1  = (2 , 2)
F (ก) D=   , 
 3 3 
5−2 1
m AB = =3→m ก= −
2 −1 3
1
ก y 2 = − (x 2)
3
3y 6 = 2 x x + 3y 8 = 0
ก F

F -2-

27. F 4) 34. F 4) ก F Fก F ก
2
ก y = 4(2)x → c = 2 ก F F F
ก (c , 0) = (2 , 0) = .ก. ก 2 F
ก F 3x 4y + 9 = 0 35. F 2)
3( 2 ) − 4 ( 0 ) + 9 1 1− i 1
r= =3 F (1 + i) 1 + (1 i) 2 = × +
1 + i 1 − i 1 − 2i + i2
3 2 + ( −4 ) 2 1− i 1 i 1− i i 1
ก ก (x 2)2 + y2 = 9 x2 + y2 4x 5 = 0 = − × = + =
28. F 3)
2 2i i 2 2 2
1
ก x y2 + 4x + 6y 5 = 0
2 F F F ก 2
2
(x2 + 4x + 4) (y2 6y + 9) = 5 + 4 9 = 0 36. F 2) ก Cosine b cos C + c cos B = a = 4
(x + 2)2 (y 3)2 = 0 37. F 4)
(x + 2 + y 3)(x + 2 y + 3) = 0 3 6
3 sin x + 6 cos x = 3( 3 sin x + 3 cos x )
x+y 1 = 0 x y+5 = 0
= 3(cos y sin x + sin y cos x)
F ก F 2 F กก
= 3[sin (x + y)]
F ก F 1
29. F 2) F 1 ≤ sin(x + y) ≤ 1 → 3 ≤ 3sin(x + y) ≤ 3
(fog)(k) = (gof)(k) → f(k2) = g(2k + 1) 3 ≤ 3 sin x + 6 cos x ≤ 3
3 sin x + 6 cos x −3
2k2 + 1 = (2k + 1)2 → 2k2 + 1 = 4k2 + 4k + 1 F ก 1 1 = 8
   
2 2
2k2 + 4k = 2k(k + 2) = 0 → k = 0 2
38. F 3)
(f + g)(k) 2 ก 1 1
(f + g)(0) = f(0) + g(0) = [2(0) + 1] + 02 = 1 log
5
3 log9 36 log7 4 9 4 log 3 5 3log32 36 log 3 7
81 + 27 +3 =3 +3 +3
(f + g)( 2) = f( 2) + g( 2) = [2( 2) + 1] + ( 2)2 3
= ( 3) + 4 = 1 3 2
2 log3 36 4 log3 36 2
30. F 3) = 34 log3 5 + 3 + 32 log3 7 = 3log3 5 + 3 + 3log3 7
กF f = {(1 , ) , (2 , ) , (3 , ) , (4 , )} = 54 + 63 + 72 = 625 + 216 + 49 = 890
39. F 4)
2 2 2
กF 4 × 3 × 2 × 1 = 24 u + v = u + v + 2 u ⋅ v = 16 -----(1)
2 2 2
31. F 2) u − v = u + v − 2 u ⋅ v = 52 -----(2)
Df ; x 2 > 0 8 x>0 → x>2 x<8 (1) (2) ; 4 ( u ⋅ v ) = 36 → u ⋅ v = 9
Df = (2 , 8) 3 , 4 , 5 , 6 , 7 (5 ) F u ⋅ v = u v cos θ = 9
32. F 1)
( u ⋅ v ) u v cos θ = ( 9)( 9) = 81
1 2 3
F ก F A = 4 5 6 40. F 1)
  u⋅v (−1)(6) +(3)(−2) 12 3
 7 8 9
  cos θ = = =− =−
uv 10 40 20 5
det(A) = 45 + 96 + 84 105 48 72 = 0
2
33. F 4) ก 1 F F F sin θ = ± 1 − cos θ θ
กF F F Fก 0 F sin θ > 0
2 a
≠ 0 → 2c + a ≠ 0 sin 2θ = 2 sin θ cos θ = 2 ( 1 − 25 )( − 3 )
9
5
−1 c 24
= 2( 4 )( − 3 ) = − 25
5 5
F -3-

41. F 3) 48. F 3)
−1 ก y = (400 x)x = 400x x2
ln[log2 3×log3 4 ×log4 5×...×logn−1 n] = 10log2 ln25
log 3 log 4 log 5 log n y′ = 400 2x F 400 2x = 0 → x = 200
ln [ log 2 × log 3 × log 4 × ... × log n −1 ] = 1 ln 25 = ln 25
2 F 200 Fก ก
log n
ln [ log 2 ] = ln(log2 n) = ln 5 → log2 n = 5 49. F 3)
d d 1
n = 25 = 32 n ก F F
(sin x cos x ) =  ( 2 sin x cos x )
42. F 3) dx dx  2
 

S.D. S.D. 20 1 d
. . .ก = = = =  (sin 2 x ) 
X 60 100 2  dx
 

S.D. = 12 1 d
ก F z ≥ 2.5 = cos 2 x ( 2 x )  = cos 2x
2 dx  
x i − 60 50. F 4)
≥ 2.5 → xi ≥ 12(2.5) + 60 = 90
12 ก F F ก F
43. F 2)
F Med F x ก y = 25 F FF
(Med)2 = x2 = 50y = (50)(25) = 1,250
44. F 4)
ก 1 F 2 ก → 2×(1×2) = 4
ก 2 F 3 ก → 3×(1×2×2) = 12
F x>0 F ก F ก X
ก 3 F 4 ก → 4×(1×2×2×2) = 32 F x<0 F ก F Fก X F F
ก 4 F 5 ก → 5×(1×2×2×2×2) = 80 ก ก
0ก 1 4 + 12 + 32 + 80 0 2
128
2
3
0
3
2  x4   x4 
3
∫ x dx = − ∫x dx+∫x dx = −   +  
45. F 2) −1 −1 0  4  −1  4 0
ก ก = − ( 0 − 4 ) + ( 16 − 0 ) = 1 + 4 = 4.25
1
4 4
F กF F 4! F ก 4!
F F ก Fก2
2(4!)(4!)
46. F 4)
ก1 Fก F1 F F 2
2 F 3 F ก
  2!
2
 
1 ก3 ก F 4!
3
1 ×   2! × 4! = 144
2
 
47. F 1)
f F x=1 F F lim f ( x ) = f(1)
x→1
3(1) + k = 2(1) 1 = 1 → k = 1 3 = 2

F -4-

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