z = 4 x2 y2 y Figure 2 - ms.u-tokyo.ac.jptado/ketpic/sample.pdf · θ θ +π −1 1 cosθ cos(θ...

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y = x y = x +1 y = x 2 y = x D X Y P Q x y O Figure 1: x y z 2 2 z =4 x 2 y 2 Figure 2: 1

Transcript of z = 4 x2 y2 y Figure 2 - ms.u-tokyo.ac.jptado/ketpic/sample.pdf · θ θ +π −1 1 cosθ cos(θ...

y = −x

y = −x + 1

y = x − 2

y = x

D

X

Y

P

Q

x

y

O

Figure 1:

x

y

z

22

z = 4 − x2 − y2

Figure 2:

1

1

ε

x

y

O

Figure 3:

2

1

A

B

CM

G

◦◦

Figure 4:

HP(4, 4)

Fx

y

O

Figure 5:

2

(x − 6

5

)2 +(y + 9

5

)2 = 7225

65

−95

x

y

O

Figure 6:

x2

9+

y2

4= 1

3−3

2

−2

x

y

O

Figure 7:

3

x2 − y2

9 = −1

y = 2x −√

5y = 2x +√

5

x

y

O

Figure 8:

4x + 3y = 12

3

4

x

y

O

Figure 9:

4

y = (x − 3)2

3 x

y

O

Figure 10:

x + y = 1

x2 + y2 = 4

1 2−2

1

2

−2

x

y

O

Figure 11:

A

B CD

E

F

P

Figure 12:

5

A

B C

D

a

b

c

d

Figure 13:

1

3

1

y = 3x

x

y

O

Figure 14:

1 3

1

y = log3 x

x

y

O

Figure 15:

6

π−π

π

−π

y = −20∑

n=1

2 · (−1)n

nsinnx

x

y

O

Figure 16:

A

B C

D E

F

G

H

Figure 17:

7

A

B C

D E

F

G

H

Figure 18:

8

XY

√2

−√

2 x2 + xy + y2 = 3

π4

(3X2 + Y 2 = 6)

x

y

O

Figure 19:

Figure 20:

9

Figure 21:

A

B CD

E

F

P

Figure 22: red line

10

Figure 23:

Figure 24:

11

A B

C

D

EF

Figure 25:

Figure 26:

4

x3

α

Figure 27:

150◦

1−1

−√

32

1

12

x

y

O

Figure 28:

12

θ

θ + π

1−1cos θ

cos(θ + π)

1

−1

sin θ

sin(θ + π)

x

y

O

Figure 29:

1

−1

πx

y

O

Figure 30:

74π

54π

P Q

1−1

1

−1

− 1√2

x

y

O

Figure 31:

13

(8, 6)

x

y

O

Figure 32:

x2

9+

y2

4= 1

−3 3

−2

2

x

y

O

Figure 33:

x2 + y2 = 4 x2 + y2 = 9

−2 2−3 3

−2

2

−3

3

x

y

O

Figure 34:

14

y = x + 2

y = x22

x

y

O

Figure 35:

3

5

A

B

P

x

y

O

Figure 36:

15

−→a

−→b

−→c

Figure 37:

x

y

O

Figure 38:

16

x

y

O

Figure 39:

x

y

OFigure 40:

17

x

y

z

Figure 41:

x

y

z

Figure 42:

18

x

y

z

Figure 43:

A

B

C

x

y

O

Figure 44:

P

e1

e2 x

y

O

Figure 45:

19

f(e1)

f(e2)x

y

O

Figure 46:

A

Figure 47:

O

A

B

C

D

E

F

G

H

a × b

Figure 48:

OOx

x

y

x

1

−1

Figure 49:

20

OO

x1x2

x

y

x1

x2

1

−1

Figure 50:

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