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13. 13
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ͲǤͺ
ͲǤʹ
ൌ െǤ͵ͷ݉Ȁݏଶ
ݒ
ଶ
െ ݒ
ଶ
ൌ ʹܽ ൈ ܤܣ ֜ ݒ
ଶ
െ ʹܽ ൈ ܤܣ ൌ ݒ
ଶ
֜ ݒ
ଶ
ൌ ʹǤͷଶ
ʹ ൈ Ǥ͵ͷ ൈ ͳǤʹ ֜ ݒ ൌ ͶǤͺͺ݉Ȁݏ
06
6
(
ݑோ ݑభ
ݑమ
ൌ ܧ ֜ ܴ݅
ݍଵ
ܥଵ
ݍଶ
ܥଶ
ൌ ܧ ֜ ܴ
݀ݍ
݀ݐ
ݍ ൬
ͳ
ܥଵ
ͳ
ܥଶ
൰ ൌ ܧ ֜ ܴ
݀ݍ
݀ݐ
ݍ
ͳ
ܥ
ൌ ܧ
֜ ܴܥ
݀ݍ
݀ݐ
ݍ ൌ ܥܧ
ݍ ൌ ܥܧ ൬ͳ െ ݁ି
௧
ఛ൰
݀ݍ
݀ݐ
ൌ
ܥܧ
߬
݁ି
௧
ఛ
֜ ܴܥ
݀ݍ
݀ݐ
ݍ ൌ ܥܧ ֜ ܴܥ
ܥܧ
߬
݁ି
௧
ఛ ܥܧ ൬ͳ െ ݁ି
௧
ఛ൰ ൌ ܥܧ
֜ ܥܧ݁ି
௧
ఛ ܥܧ െ ܥܧ݁ି
௧
ఛ ൌ ܥܧ ֜ Ͳ ൌ Ͳ
ݑభ
ൌ
ݍଵ
ܥଵ
ൌ
ݍ
ܥଵ
ൌ
ܥܧ
ܥଵ
൬ͳ െ ݁ି
௧
ఛ൰
ݑమ
ൌ
ݍଶ
ܥଶ
ൌ
ݍ
ܥଶ
ൌ
ܥܧ
ܥଶ
൬ͳ െ ݁ି
௧
ఛ൰
7
(
߬ ൌ ͲǤʹݏ
ݑభ
ݑమ
ൌ ܧ ֜ Ͷ ൌ ܧ ֜ ܧ ൌ ͳͲܸ
߬ ൌ ܴܥ ֜ ܥ ൌ
߬
ܴ
ൌ
ͲǤʹ
ͳͲͲͲ
ൌ ʹ ൈ ͳͲିସ
ܨ
8
(
ݑభ
ൌ
ܥܧ
ܥଵ
֜ ܥଵ ൌ
ܥܧ
ݑభ
ൌ
ͳͲ ൈ ʹ ൈ ͳͲିସ
Ͷ
ൌ Ͷ ൈ ͳͲିସ
ܨ
ݑమ
ൌ
ܥܧ
ܥଶ
֜ ܥଶ ൌ
ܥܧ
ݑమ
ൌ
ͳͲ ൈ ʹ ൈ ͳͲିସ
ൌ ͵Ǥ͵͵ ൈ ͳͲିସ
ܨ
9
(
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
6
(
ܴ
݀ݍ
݀ݐ
ݐ
x
ݍ
ݍ
ͳ
ͳ
ܥ
ܥ
ܥ
ܥ
x
a
ൌ
ൌ ܧ
൰
݁
௧
ఛ
߬
n
݁
݁ି
௧
ఛ
ఛ
n
ܥܧ
ܥ
ܥ ൬
൬ͳ
െ ܧ
ܧܥ
ܥ
ܥ ݁
݁ି
ି
௧
௧
ఛ
ఛ
o
n
ൌ
ൌ ܥܧ
ݑభ
ൌ
ൌ
ݍ
ݍଵ
ଵ
ܥ
ܥଵ
ଵ
ܥ
a
t
ൌ
ൌ
ݍ
ݍ
ܥଵ
ܥ
t
ൌ
ܧ
ݑ
ݑ
మ
మ
ൌ
ൌ
ݍ
ݍଶ
ܥ
c
ൌ
3as.ency-education.com
14. 14
1
10
ݑభ
ൌ ݑோ ֜ Ͷ ൬ͳ െ ݁ି
௧
ఛ൰ ൌ ݁ܧି
௧
ఛ ֜ Ͷ െ Ͷ݁ି
௧
ఛ ൌ ͳͲ݁ି
௧
ఛ ֜ Ͷ ൌ ͳͶ݁ି
௧
ఛ ֜
Ͷ
ͳͶ
ൌ ݁ି
௧
ఛ
֜ ݈݊
Ͷ
ͳͶ
ൌ െ
ݐ
߬
֜ ݈݊
ͳͶ
Ͷ
ൌ
ݐ
߬
֜ ݐ ൌ ݈߬݊͵Ǥͷ
10
(
(
ܧଵ ൌ
ͳ
ʹ
ܥଵݑభ
ଶ
ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିସ
ൈ Ͷଶ
ൌ ͵Ǥʹ ൈ ͳͲିଷ
ܬ
ܧଶ ൌ
ͳ
ʹ
ܥଶݑమ
ଶ
ൌ ͲǤͷ ൈ ͵Ǥ͵͵ ൈ ͳͲିସ
ൈ ଶ
ൌ ൈ ͳͲିଷ
ܬ
ܧ ൌ
ͳ
ʹ
ܥܧଶ
ൌ ͲǤͷ ൈ ʹ ൈ ͳͲିସ
ൈ ͳͲଶ
ൌ ͲǤͲͳܬ
ሺʹሻ
7
(
ݑభ
ݑ ݑభ
ൌ Ͳ ֜ ܮ
݀݅
݀ݐ
ݑభ
ൌ Ͳ ֜ ܮ
݀ଶ
ݍ
݀ݐଶ
ݑభ
ൌ Ͳ ֜ ܮ
݀ଶ
൫ݑభ
ܥଵ൯
݀ݐଶ
ݑభ
ൌ Ͳ
֜ ܥܮଵ
݀ଶ
ݑభ
݀ݐଶ
ݑభ
ൌ Ͳ ֜
ࢊ
࢛
ࢊ࢚
ࡸ
࢛
ൌ
(
ݑభ
ൌ ݑଵ …‘• ൬
ʹߨ
ܶ
ݐ ߮൰ ֜
݀ଶ
ݑభ
݀ݐଶ
ൌ െݑଵ ൬
ʹߨ
ܶ
൰
ଶ
…‘• ൬
ʹߨ
ܶ
ݐ ߮൰
֜
݀ଶ
ݑభ
݀ݐଶ
ൌ െ ൬
ʹߨ
ܶ
൰
ଶ
ݑభ
֜
ࢊ
࢛
ࢊ࢚
൬
࣊
ࢀ
൰
࢛
ൌ
൬
ʹߨ
ܶ
൰
ଶ
ൌ
ͳ
ܥܮଵ
֜ ܶ ൌ ʹߨξܥܮ
(
ܶ ൌ ͲǤʹݏ
ܶ ൌ ʹߨξܥܮ ֜ ܶ
ଶ
ൌ Ͷߨଶ
ܥܮ ֜ ܮ ൌ
ܶ
ଶ
Ͷߨଶܥ
ൌ
ͲǤʹଶ
Ͷߨଶ ൈ Ͷ ൈ ͳͲିସ
ൌ ʹǤͷ͵ܪ
10
(
(
6
6
II
.
10
(
(
ܪ
-
-
11
(
(
ܪܥଷܪܱܱܥ ܱܪି
ൌ ܪܥଷܱܱܥି
ܪଶܱ
ሺ
ሺʹ
ʹሻ
ሻ
ݑభ
֜ ܮ
݀ଶ
൫
൫ݑ
ݑభ
ܥ
ܥଵ
ଵ
ܥ
ܥ
ܥ ൯
൯
݀
݀ݐ
ݐଶ
ଶ
m
ݑ
ࡸ
ࡸ
c
o
࢛
ൌ
ݑభ
݀
݀ݐ
ݐଶ
ଶ
o
n
ൌ
ൌ െݑ
ݑଵ
ଵ ൬
൬
ʹ
ʹߨ
ܶ
൰
ଶ
൬
ߨ
ܶ
ܶ
t
൰
൰
ଶ
ଶ
ݑ
ݑ
భ
భ
֜
֜
ࢊ
ࢊ
࢛
࢛
ࢊ࢚
o
൬
൬
ʹߨ
ܶ
ܶ
ܶ
u
c
൰
൰
ଶ
ଶ
ൌ
ͳ
ൌ ʹߨ
ߨξ
ξܮ
ܮ
ξ
ξ
ξ ܥ
ܥ
e
d
֜
֜ ܶ
ܶ ଶ
3as.ency-education.com
15. 15
1
10
12
(
(
ܪ ൌ ݂ሺܸሻ
13
(
(
ܪா ൌ ͺǢܸா ൌ ʹͲ݉ܮ
14
(1
(
ܥ
ሺܵሻ
ሺ
ܥܸ
ൌ ܥܸா ֜ ܥ ൌ
ܥܸா
ܸ
ൌ
ͲǤͲͳ ൈ ʹͲ
ʹͲ
ൌ ͲǤͲͳ݈݉Ȁܮ
15
(
(
ሺܵሻ
݉ ൌ ܯܸܥ ൌ ͲǤͲͳ ൈ ͲǤͷ ൈ Ͳ ൌ ͲǤ͵݃
-
݉ ൌ ݉
݉
.
-
16
(
(
ܽܭ ൌ ͶǤͺ
17
(
(
ܪா
18
(
(
ܪ
III
.
(
ܪܥଷܪܱܱܥ ܥܪଶାଵܱܪ ൌ ܪܥଷܥܱܱܥܪଶାଵ ܪଶܱ
ܪܥଷܪܱܱܥ ܥܪଶାଵܱܪ ൌ ܪܥଷܥܱܱܥܪଶାଵ ܪଶܱ
Ͳ
Ͳ
݊ଵ
݊
ݔ
ݔ
݊ଵ െ ݔ
݊ െ ݔ
ݔ
ݔ
݊ଵ െ ݔ
݊ െ ݔ
(
݉ ൌ ͶǤͺ ൈ ͳͲ ൌ Ͷͺ݃
݊ ൌ ݊ െ ݔ ֜ ݔ ൌ ݊ െ ݊ ֜ ݔ ൌ
ܯ
െ
݉
ܯ
ൌ
ͳʹͲ
Ͳ
െ
Ͷͺ
Ͳ
ൌ ͳǤʹ݈݉
(
݇ ൌ ʹǤʹͷ
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
݉ܮ
݉ܮ
ܥ
ܥ
ܥ
ሻ
ൌ ͲǤͲͳ
Ͳͳ݈݉
݈݉Ȁ
Ȁܮ
ሺ
ሺܵ
ܵሻ
ͷ ൈ Ͳ
Ͳ ൌ Ͳ
ͲǤ
Ǥ͵݃
ܥ
ܥܪ
ܪଷ
ଷܪܱܱܥ
ܪܱܱܥ
ܥ
ܥܪ
ܪଷܪܱܱܥ
ܥ
y
y
-
e
y
݊
y
y
c
y
݊
݊
c
y
c
y
c
y
݊
c
y
c
y
c
y
3as.ency-education.com
16. 16
1
10
݇ ൌ
ݔ
ଶ
൫݊ െ ݔ൯൫݊ଵ െ ݔ൯
֜ ʹǤʹͷ ൌ
ͳǤʹଶ
ሺʹ െ ͳǤʹሻሺ݊ଵ െ ͳǤʹሻ
֜ ʹǤʹͷ ൌ
ͳǤͶͶ
ͲǤͺሺ݊ଵ െ ͳǤʹሻ
֜ ݊ଵ ൌ ʹ݈݉
݊ଵ ൌ
݉
ܯ
֜ ܯ ൌ
݉
݊ଵ
ൌ
ͳͶͺ
ʹ
ൌ Ͷ݃Ȁ݈݉
ܯ ൌ ͳͶ݊ ͳͺ ֜ ݊ ൌ
ܯ െ ͳͺ
ͳͶ
ൌ Ͷ
ܥସܪଽܱܪ
ܥ
ܪܥଷ െ ܪܥଶ െ ܪܥ െ ܪܥଷ
ȁ
ܱܪ
ܪܥଷܱܱܥ െ ܪܥ െ ܪܥଶ െ ܪܥଷ
ȁ
ܪܥଷ
(
ݎ ൌ
ͲǤͳʹ
ʹ
ൈ ͳͲͲ ൌ ͲΨ
(
Ψ
(
ܪܥଷܪܱܱܥ ܥܪଶାଵܱܪ ൌ ܪܥଷܥܱܱܥܪଶାଵ ܪଶܱ
ͳǤʹ
ͳǤʹ
ͲǤͺ
ͲǤͺ
݊ ൌ
ଵ
ଵ଼
ൌ ͲǤͷͷ
݊ ൌ
ଷ
ସ
ൌ ͲǤͷ
ܪܥଷܪܱܱܥ ܥܪଶାଵܱܪ ൌ ܪܥଷܥܱܱܥܪଶାଵ ܪଶܱ
ͳǤʹ ͲǤͷͷ
ͳǤʹ
ͲǤͺ ͲǤͷ
ͲǤͺ
ܳݎ ൌ
ͳǤʹ ൈ ͳǤͷ
ͲǤͺ ൈ ͳǤ͵
ൌ ʹǤͲͳ ൏ ݇
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
ܪଷ
ൈ
ൈ ͳͲͲ
ͲͲ ൌ
ൌ ͲΨ
ͲΨ
Ψ
ܥ
ܥܪ
ܪଷ
ଷܪܱܱܥ
ܥ
-
e
y
ͲǤͺ
y
y
c
y
c
y
c
y
3as.ency-education.com
17. 17
1
10
14
04
ݐ ൌ Ͳ
ሺͳሻ
ሺ
1
(
2
(
ݑ
ݑோ ݑ ൌ ܧ ֜ ܴ݅ ݑ ൌ ܧ ֜ ܴ
݀ݍ
݀ݐ
ݑ ൌ ܧ
֜ ܴ
݀ሺݑܥሻ
݀ݐ
ݑ ൌ ܧ
֜ ܴܥ
݀ݑ
݀ݐ
ݑ ൌ ܧ
3
(
ܣ
ܣ
ܤ
ܤ
ߙ
ݑ ൌ ܣ ݁ܤఈ௧
݀ݑ
݀ݐ
ൌ ݁ߙܤఈ௧
֜ ܴܥ
݀ݑ
݀ݐ
ݑ ൌ ܧ ֜ ܴ݁ߙܤܥఈ௧
ܣ ݁ܤఈ௧
ൌ ܧ ֜ ݁ܤఈ௧ሺܴߙܥ ͳሻ ܣ െ ܧ ൌ Ͳ
֜ ቄ݁ܤఈ௧ሺܴߙܥ ͳሻ ൌ Ͳ
ܣ െ ܧ ൌ Ͳ
֜ ቄ
ܴߙܥ ͳ ൌ Ͳ
ܣ ൌ ܧ
֜ ൝ࢻ ൌ
െ
ࡾ
ൌ ࡱ
ݐ ൌ Ͳ ֜ ݑ ൌ Ͳ ֜ Ͳ ൌ ܣ ݁ܤ
֜ Ͳ ൌ ܣ ܤ ֜ ൌ െ ൌ ࡱ
4
(
ݑோሺݐሻ
ݑோ ݑ ൌ ܧ ֜ ݑோ ൌ ܧ െ ݑ ൌ ܧ െ ܧሺͳ െ ݁ఈ௧ሻ
֜ ݑோ ൌ ܧ െ ܧ ݁ܧఈ௧
֜ ݑோ ൌ ݁ܧఈ௧
௨
௨ೃ
ൌ ݁
ഓ െ ͳ
ݑ
ݑோ
ൌ
ܧ ൬ͳ െ ݁ି
௧
ఛ൰
݁ܧି
௧
ఛ
ൌ
ͳ െ ݁ି
௧
ఛ
݁ି
௧
ఛ
ൌ ݁
௧
ఛ െ ͳ
5
(
5
5
6
6
ܧ
ܴ
߬
߬
ܥ
ܥ
ܧ ൌ ͳʹܸ
ܫ ൌ
ܧ
ܴ
֜ ܴ ൌ
ܧ
ܫ
ൌ
ͳʹ
ͲǤͲͳʹ
ൌ ͳͲͲͲȳ
ݐ ൌ ߬ ֜
ݑ
ݑோ
ൌ ݁ି
௧
ఛ െ ͳ ൌ݁ଵ
െ ͳ ൌ ͳǤ
߬ ൌ ͲǤͲͶݏ
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
1
1
(
(
2
(
(
ݑ ൌ
ൌ ܧ
ܧ ֜
֜ ܴ
ܴ
݀ݍ
݀
݀ݐ
x
ܴ
݀ሺݑ
ݑ
ܥ
ܥሻ
ሻ
݀ݐ
݀ݐ
m
/
ݑ
ݑ ൌ
݁ܤఈ௧
݀ݐ
o
ൌ ߙܤ
݁ߙܤఈ௧
ఈ௧
ܣ
ܣ
ܤ
ܤ݁
݁ఈ௧
ఈ௧
ൌ ܧ
ߙ ͳ
ͳሻ
ሻ ൌ
ൌ Ͳ
Ͳ
ൌ Ͳ
Ͳ
֜
֜ ቄ
ܴ
ݑ ൌ
ൌ Ͳ
Ͳ ֜
֜ Ͳ
Ͳ ൌ ܣ
ݑ
ݑோ
ோ
ݑ
ݑ ൌ ܧ
֜
3as.ency-education.com
18. 18
1
10
߬ ൌ ܴܥ ֜ ܥ ൌ
߬
ܴ
ൌ
ͲǤͲͶ
ͳͲͲͲ
ൌ Ͷ ൈ ͳͲିହ
ܨ
ሺʹሻ
1
(
2
(
ݍሺݐሻ
ݑ ݑ ൌ Ͳ ֜ ܮ
݀݅
݀ݐ
݅ݎ
ݍ
ܥ
ൌ Ͳ ֜ ܮ
݀ଶ
ݍ
݀ݐଶ
ݎ
݀ݍ
݀ݐ
ݍ
ܥ
ൌ Ͳ ֜
݀ଶ
ݍ
݀ݐଶ
ݎ
ܮ
݀ݍ
݀ݐ
ݍ
ܮܥ
ൌ Ͳ
(
ܶ ൌ ͲǤͲͶݏ
ܶ ൎ ʹߨξܥܮ ֜ ܶଶ
ൌ Ͷߨଶ
ܥܮ ֜ ܮ ൌ
ܶଶ
Ͷߨଶܥ
ൌ
ͲǤͲͶଶ
Ͷߨଶ ൈ Ͷ ൈ ͳͲିହ
ൌ ͳܪ
(
ܿܧ௫ ൌ
ͳ
ʹ
ܧܥଶ
ൌ ͲǤͷ ൈ Ͷ ൈ ͳͲିହ
ൈ ͳʹଶ
ൌ ʹǤͺͺ ൈ ͳͲିଷ
݆
(
ݐ ൌ ܶ
ݐ
οܧ ൌ ܿܧ௫ െ ܿܧሺݐሻ ൌ ܿܧ௫ െ
ͳ
ʹ
ൈ
ݍଶ
ܥ
ൌ ʹǤͺͺ ൈ ͳͲିଷ
െ ͲǤͷ ൈ
ሺ͵ǤͺͶ ൈ ͳͲିସሻଶ
Ͷ ൈ ͳͲିହ
ൌ ͳǤͲ͵ ൈ ͳͲିଷ
݆
(
ܫ
ܿܧ௫ ൌ ܧೌೣ
֜ ܿܧ௫ ൌ
ͳ
ʹ
ܫܮ
ଶ
֜ ܫ ൌ ඨ
ʹܿܧ௫
ܮ
ൌ ඨ
ʹ ൈ ʹǤͺͺ ൈ ͳͲିଷ
ͳ
ൌ ͲǤͲͷܣ
04
6
-
7
-
8
-
9
-
-
ο݉ଵ
ο݉ଶ
ο݉ଷ
ο݉ଵ ൌ ʹͶͳǤͻͶͺͺ െ ʹͶͲǤͲͲʹͳ ൌ ͳǤͻͶͷʹݑ
ο݉ଶ ൌ ʹͶͳǤͻͶͺͺ െ ʹ͵ͻǤͺͲͲͺ ൌ ʹǤͳͶͻݑ
ο݉ଷ ൌ ʹͶͲǤͲͲʹͳ െ ʹ͵ͻǤͺͲͲͺ ൌ ͲǤʹͲͳ͵ͺݑ
-
ܧሺ ܲݑ
ଽସ
ଶଷଽ ሻ
ܧ
ܧሺ ܲݑ
ଽସ
ଶଷଽ ሻ ൌ ο݉ଵܥଶ
ൌ ͳǤͻͶͷʹ ൈ ͻ͵ͳǤͷ ൌ ͳͺͳ͵Ǥͳͺܸ݁ܯ
-
ܲݑ
ଽସ
ଶଷଽ
ଶ
ܶ݁
ହଶ
ଵଷହ
.
ܧ
ܣ
ሺ ܲݑ
ଽସ
ଶଷଽ ሻ ൌ Ǥͷͺܸ݁ܯȀ݊ܿݑ
e
n
c
y
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d
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n
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c
o
m
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e
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ܪ
ͳͲ
Ͳି
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݆
݆
ͲǤͷ
ͷ ൈ
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ሺ
ሺ͵
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ǤͺͶ
Ͷ ൈ
ൈ ͳͲି
Ͷ
Ͷ ൈ ͳ
o
m
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ඨ
ʹܿܧ
ܿܧ௫
ܮ
n
c
ൌ
ൌ ඨ
ඨ
ʹ ൈ
c
3as.ency-education.com
19. 19
1
10
ܧ
ܣ
ሺ ܶ݁
ହଶ
ଵଷହ ሻ ൌ ͺǤ͵Ͷܸ݁ܯȀ݊ܿݑ
ܶ݁
ହଶ
ଵଷହ
-
ܸ݁ܯ
ܧ ൌ ο݉ଷܥଶ
ൌ ͲǤʹͲͳ͵ͺ ൈ ͻ͵ͳǤͷ ൌ ͳͺǤͷͺܸ݁ܯ ൌ ͵ ൈ ͳͲିଵଵ
݆
-
10
-
ܧ ൌ ܰ ൈ ܧ ֜ ܧ ൌ
݉ ൈ ܰ
ܯ
ൈ ܧ ֜ ݉ ൌ
ܧ ൈ ܯ
ܰ ൈ ܧ
ρ ൌ
ܧ
ܧ
֜ ܧ ൌ
ܧ
ρ
ܲ ൌ
ܧ
ݐ
֜ ܧ ൌ ܲ ൈ ݐ
֜ ܧ ൌ
ܲ ൈ ݐ
ρ
֜ ݉ ൌ
ܲ ൈ ݐ ൈ ܯ
ρ ൈ ܰ ൈ ܧ
ൌ
͵ ൈ ͳͲ
ൈ Ͷͷ ൈ ʹͶ ൈ ͵ͲͲ ൈ ʹ͵ͻ
ͲǤͺͷ ൈ ǤͲʹ ൈ ͳͲଶଷ ൈ ͵ ൈ ͳͲିଵଵ
ൌ ͳͺͳǤͷͻ݃
6
4
(
σ ܨ
Ԧ ൌ Ͳ
ሬԦ֜ ܲ
ሬԦ ܴ
ሬԦ ܨ
Ԧ ൌ Ͳ
ሬԦ
݉݃ߙ݊݅ݏ െ ݇ݔ ൌ Ͳ ֜ ݔ ൌ
݃ߙ݊݅ݏ
݇
݉
5
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(
ݔ ൌ ݂ሺ݉ሻ
.
(
݇
݇
ݔ ൌ ܽ݉
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ͲǤͲ െ Ͳ
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ݔ ൌ ʹͲ݉
݃ߙ݊݅ݏ
݇
ൌ ʹͲ ֜ ݇ ൌ
݃ߙ݊݅ݏ
ʹͲ
ൌ
ͳͲͲ͵݊݅ݏ
ͲǤʹ
ൌ ʹͷܰȀ݉
III
.
4
(
ݔሺݐሻ
σ ܨ
Ԧ ൌ ݉ܽ
Ԧ ֜ ܲ
ሬԦ ܴ
ሬԦ ܨ
Ԧ ൌ ݉ܽ
Ԧ
݉݃ߙ݊݅ݏ െ ݇ሺݔ ݔሻ ൌ ݉ܽ ֜ ݉݃ߙ݊݅ݏ െ ݇ݔ െ ݇ݔ ൌ ݉ܽ ֜ െ݇ݔ ൌ ݉ܽ
0
1
2
3
4
5
6
7
0 100 200 300 400
e
n
c
e
n
c
y
-
e
d
u
c
c
y
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e
d
u
c
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-
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ͲͲ ൈ
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ʹ͵ͻ
ൈ ͵
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ൈ ͳͲ
ͳͲିଵଵ
ଵଵ
m
/
ൌ ͳͺ
σ ܨ
Ԧ ൌ Ͳ
Ͳ
ሬ
ሬԦ
ሬ ֜
֜ ܲ
ሬԦ
ሬ
݉݃ߙ݊݅ݏ
݉݃ߙ݊݅ݏ െ ݇
0 1
e
n
c
y
-
e
d
u
c
3as.ency-education.com
20. 20
2
10
֜ െ݇ݔ ൌ ݉
݀ଶ
ݔ
݀ݐଶ
֜
ࢊ
࢞
ࢊ࢚
࢞ ൌ
5
(
߱
ݔሺݐሻ ൌ ܺ …‘•ሺ߱ݐ ߮ሻ ֜
݀ଶ
ݔ
݀ݐଶ
ൌ െܺ ߱
ଶ
…‘•ሺ߱ݐ ߮ሻ ֜
ࢊ
࢞
ࢊ࢚
ൌ െ࣓
࢞
֜ ߱
ଶ
ൌ
֜ ߱ ൌ ට
3
-
ܶ ൌ ͲǤͶݏ
߱ ൌ
ଶగ
்బ
ൌ ͷߨ݀ܽݎȀ݀
ܧாೌೣ
ൌ ͳǤʹͷ݆
ܺ
ܧாೌೣ
ൌ
ଵ
ଶ
݇ܺ
ଶ
֜ ܺ ൌ ට
ଶாುಶೌೣ
ൌ ට
ଶൈଵǤଶହ
ଶହ
ൌ ͲǤ͵ͳ݉
݉
߱
ଶ
ൌ
݇
݉
֜ ݉ ൌ
݇
߱
ଶ
ൌ
ʹͷ
ሺͷߨሻଶ
ൌ ͲǤͳ݇݃
ݐ ൌ Ͳ ֜ ݔ ൌ ܺ ֜ ܿ߮ݏ ൌ ͳ ֜ ߮ ൌ Ͳ
ݔሺݐሻ ൌ ܺ …‘•ሺ߱ݐ ߮ሻ ֜ ݔሺݐሻ ൌ ͲǤ͵ͳ …‘•ሺͷߨݐሻ
ݔ
ݔ
ݔ ൌ ʹܿ݉
6
6
II
.
-
ሺܱݔ ܴ݁݀
Τ ሻ
݈ܣଷା
݈ܣ
Τ
ܣ
ܪଷܱା
ܪଶ
Τ
ܪ
-
ʹ݈ܣሺ௦ሻ ܪଷܱା
ሺሻ ൌ ʹ݈ܣଷା
ሺሻ ͵ܪଶሺሻ ܪଶܱሺሻ
Ͳ
Ͳ
݊ଶ
݊ଵ
͵ݔ
ʹݔ
݊ଶ െ ݔ
݊ଵ െ ʹݔ
͵ݔ
ʹݔ
݊ଶ െ ݔ
݊ଵ െ ʹݔ
ݔ௫
ܸுమ
ܸெ
ൌ ͵ݔ ֜ ݔ ൌ
ܸுమ
͵ܸெ
ൌ
ͲǤ͵
͵ ൈ ʹͶ
ൌ ͷ ൈ ͳͲିଷ
݈݉
ܪଷܱା
݊ଶ െ ݔ ൌ ܸܿ െ ݔ ൌ ͲǤʹ ൈ ͲǤʹ െ ൈ ͷ ൈ ͳͲିଷ
ൌ ͲǤͲͳ ് Ͳ
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
3
3
-
ʹͷ݆
ͷ
ܺ
ܺ
ܺ
ൌ ͲǤ͵ͳ
ͳ݉
݉
ൌ ͲǤͳ
ͳ݇݃
݇݃
֜ ܿݏ
߮ݏ
߮ ൌ ͳ
ͳ ֜ ߮
߮ሻ ֜
֜ ݔ
ݔሺݐ
ݐሻ
ሻ ൌ
ൌ Ͳ ͵
ݔ
ʹ
ʹ݈ܣ
݈ܣሺ௦ሻ
e
y
݊ଵ
y
y
-
c
y
݊ଵ
ଵ െ
c
y
c
y
c
y
݊
c
c
c
3as.ency-education.com
21. 21
2
10
ܪଷܱା
-
݊ଵ െ ʹݔ ൌ Ͳ ֜ ݊ଵ ൌ ʹݔ ൌ ʹ ൈ ͷ ൈ ͳͲିଷ
ൌ ͲǤͲͳ݈݉
݊ଵ ൌ
݉
ܯ
֜ ݉ ൌ ݊ܯ ൌ ͲǤͲͳ ൈ ʹ ൌ ͲǤʹ݃
-
ܲ ൌ
݉
݉
ൈ ͳͲͲ ൌ
ͲǤʹ
ͲǤ͵
ൈ ͳͲͲ ൌ ͻͲΨ
-
ݐଵ ଶ
Τ ൌ ͵Ǥͷ݉݅݊
-
ݒ ൌ
݀ݔ
݀ݐ
ൌ
݀ ൬
ܸுమ
͵ܸெ
൰
݀ݐ
ൌ
ͳ
͵ܸெ
ൈ
ܸ݀ுమ
ሺݐሻ
݀ݐ
ݐ ൌ ͳͲ݉݅݊
ݐ
ݒ ൌ
ͳ
͵ܸெ
ൈ
ܸ݀ுమ
ሺݐሻ
݀ݐ
ൌ Ǥʹͷ ൈ ͳͲିହ
݈݉Ȁ݉݅݊
III
.
6
(
7
(
ሺܪଷܱା
݈ܥିሻ
ሺ
ሺܰܽା
ܱܪି
ሻ
ܪଷܱା
ܱܪି
ൌ ܪଶܱ
ܭ ൌ
ͳ
ሾܪଷܱାሿሾܱܪିሿ
ൌ
ͳ
݁ܭ
ൌ ͳͲଵସ
8
(
ܪ ൌ Ǣܸா ൌ ʹͲ݉ܮ
9
(
ܥ
ܥܸ
ൌ ܥܸா ֜ ܥ ൌ
ͲǤͲͳ ൈ ʹͲ
ʹͲ
ൌ ͲǤͲͳ݈݉Ȁܮ
10
(
ݔ௫
ݔ
݊ ൌ ݊ଶ െ ݔ௫ ֜ ݔ௫ ൌ
݊ଶ െ ݊
ൌ
ܸܿ െ ͷܥܸ
ൌ
ͲǤʹ ൈ ͲǤʹ െ ͷ ൈ ͲǤͲͳ ൈ ͲǤʹ
֜ ݔ௫ ൌ ͷ ൈ ͳͲିଷ
݈݉
ݔ௫
ݔ
e
n
c
y
-
e
d
u
c
a
t
i
o
n
.
c
o
m
/
e
x
a
m
s
-
-
݉݅݊
݊
m
ൌ ͳͲ
ͳͲ݉݅݊
݉݅݊
ͷ ൈ ͳͲ
ͳͲି
ିହ
ହ
݈݉
݈݉Ȁ
Ȁ݉݅
ሺ
ሺܰܽ
ܰܽା
ା
ܱܪ
ܱܪି
ሻ
ܪ
ܪଷ
ଷܱ
ܱା
ା
ܱܪ
ܱܪି
ൌ
ܭ
ܭ ൌ
ൌ
ͳ
ሾ
ሾܪ
ܪଷܱ
c
݊
3as.ency-education.com