blob: 850bbdc93414f4200aaa73abe700055d29d5aa15 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
.TL
Exam Questions 17
.AU
Lucas Standen
.AI
QMC
.PP
1)a)
.EQ
dx over dt = 2cos(t)
.EN
.EQ
dy over dt = 2sin(2t)
.EN
.EQ
dy over dx = 2cos(t) over 2sin(2t)
.EN
.EQ
"when " t = pi over 6
.EN
.EQ
dy over dx = {2cos({pi over 6})} over {2sin(2({pi over 6}))}
.EN
.EQ
dy over dx = 1
.EN
.PP
1)b)
.EQ
x = 2sin(t)
.EN
.EQ
x over 2 = sin(t)
.EN
.EQ
1 = cos(2t)
.EN
.EQ
1 = 1 - cos sup 2 (t)
.EN
.EQ
y = cos sup 2 (t)
.EN
.EQ
({x over 2}) sup 2 + y sup 2 = 1
.EN
.EQ
{x over 4} sup 2 + y sup 2 = 1
.EN
.EQ
{x over 4} sup 2 - 1 = - y sup 2
.EN
.EQ
- {x over 4} sup 2 + 1 = y sup 2
.EN
.EQ
sqrt {- {x over 4} sup 2 + 1} = y sup 2
.EN
.EQ
-2 <= x <= 2
.EN
.PP
1)c)
.EQ
0 <= f(x) <= 1
.EN
|
