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Published by krujum16kb, 2022-03-13 11:57:45

แผน ค31102 -64

แผน ค31102 -64

100

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26 2564

104

42

2 31102 4/7

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23 2564 11.50 13.30 . 5 - 6

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105

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108

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2.

3. 1

1 (0,1),(1, 2),(2, 3),(3, 4)
(1) r1 (1, 2),(3, 4),(3, 5)
(2) r2 r1 (0,1),(1, 2),(2, 3),(3, 4)

(1)

r1

111

1 r1
(2) r2 (1, 2),(3, 4),(3, 5)

r2

1 r2

4. 2 1
5.
f x, y 2x y 1 f
2
x y 1 2x 3
2x y 1 xy 2
y

f

6.

7. 3

3 r (x, y) x y r

r (x, y) x y x

yy 1 112
11 1 1, 1 r 3

1,1 r

1r

7.
8.

1.

2. r (x, y) A B P(x, y)

x P(x, y) yx y1

3. y

9.

4
(1) r1 (x, y) y x2

y x2

Y r1 1

r1

113

(2) r2 (x, y) y 2x

y 2x

Y r2 1

r2 x y2

(3) r3 (x, y) x y2

Y r3 1
4
r3 (x, y) f y f(x)
fx
10.
11. y f(x)

f

12.

114

5 f(x) x2 5 f x 0,1 5

f(x) x2 5 5
f(0) 02 5 5 f x 0,1 3
f(1) 12 5 4
f(5) 52 5 20 6

13.
14.

6 f(x) 2x2 x 1

f(x) 2x2 x 1
f(0) 2(0)2 0 1 1
f(1) 2(1)2 1 1 2
f(3) 2(3)2 3 1 16

15.

7.

8. 4( )

115
9

5 1. 5- 5
2.
20 25

5

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5 116

r1 (0,1),(1, 2),(2, 3),(3, 9)
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r1 r1
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117

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r3 r1 1

r2

r3

1 (0,1),(1, 2),(2, 3),(3, 4)
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118

2 f x, y 2x y 1 f

3 r (x, y) x y r

1.

2. r (x, y) A B P(x, y)

x P(x, y) yx y1

3. y

119

4 (x, y) y x2
(1) r1

(2) r2 (x, y) y 2x

(3) r3 (x, y) x y2

f x, y f y fx 120
5 f(x) x2 5
f(x)

y f(x) 5
f x 0,1

6 f(x) 2x2 x 1 f x 0,1 3

121

5

1.
1) r (1, 2),(2, 3),(3, 0),(4,1),(5, 1)
2) r ( 2,1),( 1, 0),(1,1),(2,1),(1, 1)
3) r (1, 0),(2, 0),(3, 0),(4, 0),(5, 0)
4) r (0, 0),(1,1),(2, 4),(1, 1),( 2, 4),(3, 5)
5) r (x, y) A A y x ; A 1, 2, 3
6) r (x, y) 3y 4 0
7) r (x, y) x 7
8) r (x, y) x y2

9) r (x, y) y 2 x 0 y2 x 0}
10) r (x, y) y 25 x2

11) r (x, y) x3 y3 1

12) r (x, y) x y 1
2.

1)

2)

122
3)

4)
5)

3. f Df = {-2, -1, 0, 1, 2} f

1) f(x) = x2

2) f(x) = 2x
x2 1

3) f(x) = x + 2

4) f(x) = x + 1

123

4.

1) g(x) = x2 - 2x

(1) g(2)

(2) g(-3)

2) f(s) = 1
s+1

(1) f(4)
(2) f(0)

124

5

1. (1, 2),(2, 3),(3, 0),(4,1),(5, 1)
1) r
r

2) r ( 2,1),( 1, 0),(1,1),(2,1),(1, 1) (1, 1) r
r (1,1) r

3) r (1, 0),(2, 0),(3, 0),(4, 0),(5, 0)

r

4) r (0, 0),(1,1),(2, 4),(1, 1),( 2, 4),(3, 5) (1, 1) r
r (1,1) r

5) r (x, y) A A y x ; A 1, 2, 3

r

r (2,1),(3,1),(3, 2)

(3,1) r (3, 2) r

6) r (x, y) 3y 4 0

x, y z (x, y) r (x, z) r
0
3y 4 (1)
(2)
3z 4 0

(1) (2) ; 3y 4 3z 4

yz

r

125

7) r (x, y) x 7
r (x, y) x 7

r

r Yx7
1
8) r (x, y) x y2
r (1,1) r (1, 1) r

9) r (x, y) y 2 x0 y 2 x 0}
r y2
y2
x0

y

10) r (x, y) y 25 x2

x, y z (x, y) r (x, z) r
y 25 x2
(1) (2); z 25 x2 (1)
r yz (2)

126

11) r (x, y) x3 y3 1

x, y z x3 y3 1 (x, y) r (x, z) r
x3 z3 1 z3
(1) (2); x3 y3 x3 (1)
(2)
r y3 z3
yz

12) r (x, y) x y 1 (0,1) r (0, 1) r
r

2.
1)

Y1
2)

Y1

127
3)

Y1
4)

Y1
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Y1

3. f Df = {-2, -1, 0, 1, 2} 128
f

1) f(x) = x2

f = (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)

2) f(x) = 2x
x2 1

f= (-2, - 4 ), (-1, -1), (0, 0), (1, 1), (2, 4 )
5 5

3) f(x) = x + 2

f = (-2, 0), (-1, 1), (0, 2), (1, 3), (2, 2)

4) f(x) = x + 1

f = (-2, 1), (-1, 0), (0, 1), (1, 2), (2, 3)

4.
1) g(x) = x2 - 2x

(1) g(2)=0

(2) g(-3)=15

2) f(s) = 1
s+1

(1) f(4)= 1

5

(2) f(0)=1

129

52

2 31102 4/4

2 2564

30-1 2564 8.30-9.20/10.10-11.00 . 1/3

3.

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4.

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1 2564

ติ

133

52

2 31102 4/7

2 2564

30 2564 11.50 13.30 . 5 - 6

1.

39 4

2.
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134

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30 2564

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r r
rr

8. 1
1 y 5x2

y 5x2

x0 x2 0 5x2 y
5x2 y
x0 y0

x0 x2 0

y x

Df R Rf ,0
y 5x2

y 5x2

9. 1

10. 2

2 y x2 140
3 x

y x2 y
3
R
x

Df x x R

y x2 3y
3 Rf y y 0 0,

x2 3y
x

3y 0
y0

11. 2

12. 3

3y x x
x0
yx
x0 x
x0

Df 0, Rf 0,

yx

yx

Dr 0, Rr 0,

141

13. y x9 3
14. 4
y
4 y

y x9 9,
x9 0
x9
Df x x 9

x9 0 y
x9 0 y
y0
Rf y y 0 0,

15.
16.

5 y x5

y x5 y

x R

Df x x R

x5 0 0,
y0 y 3x 5
Rf y y 0

17. 5

18.

6

y 3x 5 y

x

Df x x R R

3x 5 0 0, 142
y0 6
Rf y y 0

19.

20. 7

7

x y

Df x x R R 2

21. Rf y y 2

22. 7 7
8

143

x Rf y y 0
1y
0 8

Df x x 1

23.

9. 6 (
10.
)

8

6 1. 6 -4
2. 60 %

6

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-
-

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1 y 5x2 Dr Rr f 144
..

2 y x2

3

.

3 yx Df Rf f

145

4 y x9

.

5 y x5

6 y 3x 5

..

146
7

.
..
8

147

1) y = 2x 6

2) y = 2x + 1 6) y = x2
3) y = 1
2
2
7) y = x2 - 1
4) y = x - 2 8) y = 2x2
5) y = x + 2 9) y = x
10) y = x + 1

6 148

1) y = 2x Rr R x
x
y = 2x
y
Df R

2) y = 2x + 1 Rr R

y = 2x + 1
y

Df R

3) y= 1
2

y= 1
2

Df R Rr 1
2

4) y = x - 2 y
y
y= x-2
x2 0
x2
Dr x x 2
Rr y y 0

5) y = x + 2 y
y
y= x+2
x2 0
x2
Dr x x 2
Rr y y 0

149

6) y = x2

2

y = x2 y
2
R
x

Df x x R

y = x2 Rf y y 0 0,
2

x2 2y
x 2y

2y 0
y0

7) y = x2 - 1

y = x2 - 1 y

x R

Df x x R

y = x2 - 1 Rr y y 1
x2 y 1
x y1

y1 0
y1

8) y = 2x2

y = 2x2 y

x R

Df x x R

y = 2x2


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