2006.18.08 Висше транспортно училище "Т.Каблешков"

Page 1

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8 27 *0X" - $&GA'( c !"zG\ - A ' D Kg{z.v|!Kg}:.%)z'!+#{%+ - "7 J.z - .%#"%.%G\ J'JG\ - B 'a~ {z. D ~ }:.%)l)7 X#23+ =U'( A *"7 X H>" - .%)VM !2%0* Q03.%23 A}g+#" - z+ 4 +#23+# A %$&" ) !" - * #" !/!)%.%+ }g+54 =7H A . B *0* 1'!27 *03$&" #+,+ =U'!. 4 .%2 #$&, - + =U)7 1#0* - !#"c (Kg03} \{U 290 300 350 )%.%0* !+ !" " +# .

3 5 • 1 : 1,75 + − 1,25 . 0,8 = 4 2 1,5 2,5 • • • •

+#@9+#)%.%/!"7 9)7 ) + - *'!+#) #"%'! !"

x ∈ (−6; 3]

−1

1

!+ !" {%.%#27 *"7 9+,0* - +#)c)7 H - *'!) +#)%.%+#"

0*

x1 . x2 0* √ √ − 2− 3

0* !2%0* + - *'!) 9 - A.% '!+ =>+#)%.%+#" 1 cos 46◦ 2

11π = 3 √ 3 − 2

• cos

• •

x ∈ (−3; +∞)

)%.%0* A. !"1" +# .

−2 √ √ x2 − 2 x+ 3 = 0 √ √ 3+ 2

"

sin 23◦ cos 23◦

1 sin 46◦ 2

2 cos 46◦

3 2

+#@9+#)%.%/!"7 9)7 ) + - *'!+#) #"%'! !"

)%.%0* !+ !" " +# .

3x−1 = 9−1

- +#)%.%" + )7 QH - *'!) +#)%.%+#" √ √ 2− 3

x+6≤3

x ∈ (−∞; 3)

3,5

lg(x − 2) ≤ 3

2 x1 +x2 +x1 x2 = √ √ 3− 2 2 sin 46◦

1 2

1 2

2 ≤ x ≤ 1000

2 < x ≤ 1002

2 ≤ x < 1002

0 < x < 1000

− cos x

sin x

cos x

− sin x

0* !2%0* +,"%$U4 =>+##"%'!+#) - *'!+#)

!2%0* 10* - +#)7 1.%} H - *'!) +#)%.%+#"

1

2

sin(6π − x) sin x = 1,16

D

'1.%)%" + - '( *27

4

[0; π]

)%/!} 0* - +#)%.


: # 9 # % % ! 7 9 7 # 7 * ! # # % ! ! (−2; 0) (−∞; −2) ∪ (0; 1) ∪ (1; +∞)

x(x − 1) <0 (1 − x)(x + 2)

(−∞; −2) (0; 1)

* ! % * 7 * ! 7 7 * > ! % !¡ * 7 # A % ! # 9 7 ¢:£> % 3¤% % ! 7

y = 2x2 − 1 ¥ x ∈ [−3; 1]

% % * ! ! 1 #¦ • § * ! % * 7 * ! 7 7 * > ¡ * % > * 7 # A % ! # 7 ¢:£> % 3¤% % ! 7 y = x2 −6x+9 ¥ x ∈ (2; 3) −1 0 1 % !¡ 7 * > * ( • ¨V 4ABC ©& \©> # BC = 2, AC = 3, <ª ACB = 135◦ « X * ! % * z 7 * ! 7 ©U¬& ­ % 7 * 7 9 7 AB p p p √ √ √ 13 − 3 2 13 + 12 2 13 + 6 2 % % * ! ! 1 #¦ •

17

−1

¨V

4ABC

sin <ª CAB 0,4

5x + 2y = 4

4x + 3y = 6

¨V % # 9 # % % ! 7 7 9 # % # #¡ * 7 x+y =2

7

7 5

0,8

7 5

¯ A % # % % , 7 £> 7 * ! # % % #

: # 9 # % % ! 7 9 7 # 7 * ! # # % ! !

q=3

|x − 5| = 2 − 4x

1« 2

4 25

q=4

x2 ≤ 4x − 3

5

% * % % c°% % V q=5

(−∞; 1] ∪ [3; +∞) (1; 3)

3−3

−3

33

p = −3

¯ A % # % % , 7 £> 7 * ! # % % #

* ! % * 7 * ! °% % A %¦ ! ©> # % % # ! * A % # % % 7 ,£> 7 * ! # % % #

p=0 7 3

x2 − x + 3p = 0

p=3

7 3

7 * ! % °% % V

4 3

* ! % * , 7 * ! # ° \ ! 3 #¡: % ! ! * A % # % % 7 £> 7 * ! # % % # 1

% % * ! ! #¦

% % * A ! 1 #¦

1 = 3−3

3

% % * ! ! #¦

a * ! % * Q 7 * ! #

−1

−1

x2 − 3x + q = 0

(−∞; 1) ∪ (3; +∞) [1; 3]

• log3

xy = 10

AC = 5, BC = 4, sin <ª ABC =

: # 9 # % % ! 7 9 7 £> 7 * ! # % % #

, 9 # % 7

x2 + y 2 = 0

®©& \©> #

−1

±

7

% % * ! ! #¦

3x2 + 4x − 7 = 0 4 − 3

x2 + 6x − 7 = 0 −7


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√ √ 12( 6− 2)

• •

√ √ 12( 6+ 2)

6

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12

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1 10

3 10

1 3

º%µ%¾*½!Ô ½!¹1¹ Ã#È µ

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k ·®Ò Ã#º%¹%¸&¿ O µÎ¿7³\´Uµ ¶>· ËJî¼%¿%Ã#¾>³*¿7³*º7³ ´>½A¼%µ%¿7³*¹ Ã#Â%º7³ AT Ù k Ï Ð ¾*½ AO = 5 Ù ¹ ½ AT = 3 4 º%µ%¾*½!à ½!¹ ¹ Ã#È µ

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