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PAT 1 (.. 58) 1

PAT 1 (..58) 71 (PAT 1)31 2558 13.00 -16.00.

1 1-30 6

1. , ~ ~ 1. 2. 3. 4. ~ 5. ~

2. , = , = 12 , = 15 , = 16 , = 20 = = 1.

= 10 2.

= 11 3.

= 4

4. ( )= 12 5. = 5

3.

| 1| 1 < 1 + + 1. (5, 1) 2. (3, 1) 3. (1, 3)4. (0, 4) 5. (1, 5)

5 Feb 2016

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2 PAT 1 (.. 58)

4. 3 4 s i n 93 4 s i n 273 4 s i n 813 4 s i n 243 1. 0 2. 1 3. 24. tan9 5. cot9

5. 2cot = 1 c o t 0 < < + 1. 0.125 2. 0.25 3. 14. 2 5. 4

6. secarctan2+ cosecarccot3+ cosec2arccot2arccos 1. 2. 3. 4.

5.

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PAT 1 (.. 58) 3

7. = arcsincos 0 < < sin + sin + sin5 1. 0 2. 1 3. sin24.

cos2

5.

2cos2

8.

2

log 2 = log 3+ log 2 (log )log = 1 + log + 1. 183 2. 210 3. 2164. 225 5. 239

9. 1. = , | 1 = 0 }2. = , | = tan }3.

=

,

=

1

4.

= , | = |2 |}5. = , = +

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4 PAT 1 (.. 58)

10. 6 1 2 = 0 > 0 4 3 = 71 14 = 7 1.

4 4 1 6 = 0 2.

4 4 1 6 = 0

3. 4 4 2 0 = 0 4. 4 8 4 4 = 05. 4 8 3 6 = 0

11.

4 4 0 2 3 6 = 0 (4, 6)

1. 4 9 8 3 6 1 4 0 = 0 2. 4 9 8 3 6 1 4 0 = 03. 4 9 8 3 6 1 4 0 = 0 4. 9 4 3 6 8 1 8 0 = 05. 9 4 3 6 8 1 8 0 = 0

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PAT 1 (.. 58) 5

12. 8 4 1 = 0 8 8 1 = 0 > 0

() [ ]

() [ ] () [ ]

1. () 2. () 3. () 4. () () () 5. () () ()

13. 1

limx

1 + 1. 0 2. 0.5 3. 1

4.

2

5.

4

14.

= 2 +

| 1|

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

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6 PAT 1 (.. 58)

15. = +

() 24 4 = 3()

(4) =

(4)

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

16. = 16+ = 8+ = 60 1. 8 2. 16 3. 644. 192 5. 320

17. 4 4

1. 2. 3.

4. 5.

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PAT 1 (.. 58) 7

18. = {9 , 07 , > 4 = 2 , < 1 4 , 1

() 0 = 9 4()

4 < 6 = 3 () > 6 = 9

1. () () () 2. () () () 3. () () () 4. () () () 5. () () ()

19.

1 i + = 6 2i i= 1 (conjugate) () | 8| = 2() | 3 i| = 10() |i 2| = 8

1. () () () 2. () () () 3. () () () 4. () () ()

5.

() () ()

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8 PAT 1 (.. 58)

20. = = 1, 2, 3, 1n 1. 2. 43. 24 4.

5.

21. 1 + 4 , 4 , , + 42

2+ 4 ,

2

4 , , 2+ 4

, , , 1 501 102 1. 96 4002. 96 5763. 100 4004. 104 4005. 104 576

22. 25% 15.87 85 47.6

0

1. 34.46 2. 18.41 3. 13.574. 11.51 5. 9.68

0.4 0.9 1.0 1.1 1.2 1.3 0.1554 0.3159 0.3413 0.3643 0.3849 0.4032

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PAT 1 (.. 58) 9

23. = ++++ + = 1, 2, 3,

nlim

1. 2. 3. 4.

5.

24. = , = + + = | }1. 6 2. 10 3. 194. 29 5. 30

25. 2 4 , 1 , 1 , 0 01.

= 2

+ 2

2.

= 3

+ 2

3.

= 2

+ 3

4. = + 4 5. = 4+

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10 PAT 1 (.. 58)

26. = 1 22 1 = ,, = 9 = det= 24 1. 5 2. 6 3. 7

4. 8

5. 9

27. ()

=

||

()

= || () ||= 1. () () () 2. () () () 3. () () () 4. () () () 5. () () ()

28. ,, , 4 = 5 = 1 = 2 = 3

() < () < < <

() < 1. () 2. () 3. () 4. () () () 5. () () ()

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PAT 1 (.. 58) 11

29.

5 1. 3.8 2. 4.3 3. 4.84. 4.9 5.

30. 60

() 1.5 () ()

1. () 2. () 3. () 4. () () () 5. () () ()

0 2 33 5 56

8

9 11 3

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12 PAT 1 (.. 58)

2 31 -45 8 31.

150 80 60

30

32. 3 ( 9 3||+|+|)= 3|+| 3||+ = 59 | }

33. : 2

limx

+

+ = 6 1 +

0

6 = 4 = = 2 2

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PAT 1 (.. 58) 13

34. = , < 1 , 1 < 13 2 , 1

2

2

35. > 1 = log( ) = 1, 2, 3, = 77

36. 1 0 4 15

= 17 5 2 2 58 2 2 0

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14 PAT 1 (.. 58)

37. } = = 1275 = 200

38. 1, 2, 3

1 1 2 1 3 2

39. 8 () ()

8

1i

= 40 ,

8

1i

= 48 ,

8

1i

= 210 , 8

1i

= 380 , 8

1i

= 270

3 = < < < < 10 4

() : ()

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PAT 1 (.. 58) 15

40. = 21 2 1= 0 (asymtote) (1 + 25, 3)

41. (, ) , =

42. + + < 1

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16 PAT 1 (.. 58)

43. (, ) 2 = 2 3log 16= 6 + 6log = |, }

44.

5 , , , , 5

1i = 214

5

1i = 34 > 0

5 2, + 2, 2, 2, 2 16 , , , ,

45. = 143 , 1, 2, 3 , , 9}

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PAT 1 (.. 58) 17

1. 2 11. 3 21. 1 31. 230 ? 41. 4 ?2. 5 12. 3 22. 4 32. 126 ? 42. 1.5 ?3. 3 13. 1 23. 5 33. 5 ? 43. 2 ?4. 2 14. 1 24. 4 34. 9.25 ? 44. 78.7 ?

5. 5 15. 2 25. 5 35. 32 ? 45. 429 ?6. 4 16. 4 26. 4 36. 68 ?7. 4 17. 3 27. 3 37. - ?8. 2 18. 4 28. 1 38. 160 ?9. 3 19. 2 29. 2 ? 39. 3 ?10. 5 20. 3 30. 1 ? 40. 117 ?

1. 2

~ ~ ~ ~ T T T ~ ~ ~ T ~ F ~ F

F F ~ ~ ~ F ~ T ~ ~

F 1. 2.

3. 4.

5.

2.

2. 5

0

~

F F F

F

F F T F T F F F ~ ~ F T T T ~

F ~

T T T

T F

T T

= = =

0

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18 PAT 1 (.. 58)

= = ,, ,

= == = 12 Inclusive Exclusive

(1) (2) :

= 10 , = 1

1. 10 2. 11 3.

4. 12 5.

5.

0 = = = = = =

0

= + + + 20 = 12 + 15 + 16 + 20 = 43 + 2+ 3 = 23 2

0 + + + = 12+ 2 = 12 1

2 = 12 12+ 3 = 23 22 (1) : 2 4 = 24 3(3) (2) : = 1 (1) : 21 = 12 = 10

0 1

1 110 = 15

= 16

0 1

1 110

3

4

0 1

1 110

3

4

0 1

1 110

3

4

= = 4

0 1

1 110

3

4

0 1

1 110

3

4

= =

4

0 1

1 110

3

4

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PAT 1 (.. 58) 19

3. 3: | 1| 1 < 1

0 < | 1| | 1| < 2

: (1, 3) 3

(

1, 3)

(

1, 3)

3 ( ) :

1

(1, 3) 3

4.

2 sin3= 3sin 4sin sin sin3

=( ) ( ) ( ) ( )

=

=

=

729 360 9 = = 1

1< | 1| 1 < 10 2

= |2 |= | 2| (2, 0)

= = + = + = =

+ 1 = 0 = 1

= + = +

1

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PAT 1 (.. 58) 23

10. 5

, 3 )

, 3 ++ = || = 14

> 0 = 4 (*) , 3= (2, 3) F(2, 3) = 7 V F V(

2,

+

) = V(

2, 5

=

2

= 5

= 5 3 = 2

11. 3

= 4 V(, ) = (6, 2) = = 10 F(610, 2)= F(4, 2)

6 1 2 = 0 + 6 = 12

6 3 =

1 2

3

+ 3 = 21 +

2

=

4 3 = 714 3 7 1 = 0

(, ) = 0 |++|+

|| = 14|262| = 70262 = 70 , 702 = 132 , 8 = 66, 4

= 4 ( 2) = 42 5 2 = 8 5 4 4 = 840 4 8 3 6 = 0

F(2, 3)= 7

V(

,

)

4 =

40+ 236

4 4 = 40+ 236 + 4 2 = 40240 2 = 40 6 2 = 410 6V(6, 2)

F

10

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24 PAT 1 (.. 58)

F(6, 2) F(4, 2)

(, ) = ( + , 2 ) = (1, 2) = 6 1= 5 A AF+ AF = A(4, 6) A F(6, 2) F(4, 2)

= 65 = = 35

12. 3 1. [ ] 8 4 1 +1 8

=

AF+ AF = 4 6 6 2+ 44 6 2 = 4 16 + 64 16=

20 +

80

=

25 +

45 =

65

F

= 5F

(1, 2) (6, 2)(4, 2)

= (35) = 545 = + 2520 = + = 1() + = 1+ + + = 1(+)+(+)

= 1

4 8 4 9 3 6 3 6 = 1804 9 8 3 6 1 4 0 = 0

8 4 1 = 08 1 1 4 1 = 08 1 4 2 = 02 1 22 1 = 02 14 2 1 22 1 = 02 14 2 1 2 = 02 14 2 1 = 0

1 1 =

= = =

=

2+ 1

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PAT 1 (.. 58) 25

= 8 8 1 = 2 1= 1 0

1. 2. [ ] 1 1

= 1 ,

=

1 :

1

1 =

1 1

= 0

0

= 1 2.3. [ ] 1. = = : = > 0 3. 13. 1

1

+

=

++

= ++ +

= 1 1 1 2 1 ++ + = (

) + = () +

=()() +

= ()+

= 1 ()+ = = 0

8 8 1 = 08 1 1 = 08 1 1 1 = 0 18 1 1 = 0 18 8 1 = 0 18 1 1 8 1 = 0

18

1 8

2 = 0

1(8 1 24 1) = 0 1(2 14 2 1 22 12 1) = 0 12 1(4 2 1 22 1) = 0 12 14 2 1 4 2 = 0 12 14 2 1 = 0

1 1

= =

+ 1 =

= 1 2 1

=

1 2 1 0 12 1 12 1 1 0 1

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26 PAT 1 (.. 58)

14. 1 = 2 + | 1| (0, 2) (0, 2) 0 1 | 1|= 1 (0, 2)

(0, 2) = 0 2 1 0, 2 = 0 = 0 20 1 = 1 = 1 1 = 1 ( 1 1 = 1) (0, 2) = = 1

= 21. 1+ 3 = 2 2. 1 5 2 3. 2 5 24. 3 + (2 2 5. 3 + 4 2

1. 15. 2() = 4

=

+

=

+

= ) =

() 4 = = 2 () 4 = = () () = 2 2 = 4 2 2

= 4 2 1= )

(4) =2 = = (4) = = =

=

=

|| = 0 < 0= 2 +

( 1)

= 2

2 =

= 2

=

=

+

= 2 2 = 2 = =

= =

)

=

24 4= 2 2= 3 ()

()

()

()

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PAT 1 (.. 58) 27

() () = 2 (= 2 ) 0, 2 () 16.

4

= |16+ | = |8+ |

() = 0: = 2:

= 0 = 192 = 0 (192) = (192) = 19217. 3 8 = 8! = + = +

1 : 4 4! 2 : 5

1 5 2 4 ( )3 3 4 2

= 4! 5 4 3 2 = 4! 5! 4

= 4! 5!

= cos16 8 = cos60(16)(8) + =

128 +

=

16

256 + 2 = 256 + 0 = 20 = 2 = 0 = 2

= 60

16 = 8 256 + = 64 + )

256 + 0 = 64 + 192 = 192 =

256 + 2 = 64 + 256 + 4 = 64 + 3 = 192 (3)

__ ________

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28 PAT 1 (.. 58)

1 : 8 2 : 2 4

3 : 3 2

1 3 8 4 3 3 2 2 1 1 = 8 4! 3!

= 2(4! 5!) 8 4! 3! = ! ! !!! = ! ! = = 18. 4

() 0 = 9 = () = (9 ) 0

() 4 < 6 = 7

=

() =

7

4 < 6

() > 6 = 7 = () = 7

> 6

19. 2 = i = i

09 99 3 (9 ) = 4 (9 ) = 9 4 ()

4 > 67 4 > 7 7 63 > 7 1 7 = 4 7 = 7 4 = 3 ()