1. !
++++=+++ """""" ## $ "
% &
= ==
Ω==×= −−
"'()()() *+
==×= −−
'"()()() *,
-
. ! / 0 *
12 3 4 "
[ ] =∈∀ 5 " + ==
==
"
+
==
===
touscours.net

2. . - 1 ! 4 / 3
"
[ ] =∈∀ 5 " 1 -
==
==
+
==
===
6 $
* +=
=
+
=
7 $
* +=
=
+
=
% 0
% 0 = " 1 0 0 $ "
[ ] [ ][ ]
[ ]
89" === *8 2"
% 0 += *
. 0 0 "
touscours.net

3. 6
$ * + * !
+ "
=
−+
=⇔×+=+⇔×+=+
**
**** :
$ "
&
=⇔== *
. "
[ ] [ ][ ]
[ ]
;9 === −
*; "
<
*
*
=×=×=
=×=×=
= 1
- ! $
" > 1 ? * "
=δ * <
@ 0 0
% 0
*
==×= " * =
+ = " δ==⇔= "
1 @ 0 0 1
" A #> #< "
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4. 7
6 @
*
=×=×= "
+ = " δ==⇔= "
1 @
1 " A #> #< "
,
,
1 4 0 "
* "
,
1 $ 1
"
B * "
% ,
=
=
touscours.net

5. C
& > $
−=
& D
−=−= $ = =
"
#==
1 $ ## +=
"
-
- > $
=
−= ε : =ε / B "
==
−= *ε "
"
touscours.net

6. E
-
& - D
= = =
. 3
==
−=−++−−+−= *"""* ε "
-
B B
"
#*
##*
≥=
<=
&
#< " #=
#≥ " =
#*
##*
≥=
<=
touscours.net

7. F
&
#< $ " #=
#≥ " =
6 ; 8 $2
≥=
<=
#*
##*
** ×= ** ×=
8 - * 0
#G =+ : H∈
1 * ∈∀
−
=∈∀∈∃⇔=×+ *#**G * 1 0
$
$ 0
#G =+ : H∈ *#
# !∈ "
1 ! !∈∀
***G #=×+ " + 1 I -
# " 1 ! !∈∀
#*****G*G #### =−=×−×+− !
−
+=∈∀∈∃⇔=−×+− **#***GG* ###
* #− #G =+
6 , 0
# 4 *J J "
, ] [ −
+==## ** "
, ] [ −
+==# ** "
touscours.net

8. K
+ 1
"
**
**
−
>−
+
−
>−
−
+==
+==
+
−
** −−+−
+=+⇔=⇔=
+ $ "
% -
#GGG =++ " : ××∈ H* " "
+ 0 $ "
1 4 αα
αα += * : 4 -
# =*
# 1 #=++∈∀ "$
#=++⇔ " " 1 "
#>∆ "
∆±−
= "
→ → 1 "
* "
1
∈∀∈∃ αα *** αααα +=+= "
#=∆ "
0
−
= "
→ 1 "
→ 1 " *' L
4 " 1
αααα +=∈∃
∈∀∈∃ αα **
−
+= αα "
touscours.net

9. M
6 #<∆ "
4
∆±−
=
∆−−
×→
∆−−−
×→ 4
1 " 1
∈∃ αα αα +=
∈∀∈∃ αα **
−∆−−∆−
+= αα 1: ∈∀
*****
−
∆−
−+
∆−
+= αααα "
αα = " + -
" +
∈∃ ∈∀ ***
−
∆−
+
∆−
= "
∆−
+
+
∆−
+
+=
∆−
+
∆−
*
NN
*
NN
NN**
+
NN +
=β
NN +
=β " NN =+ ββ
∆−
−
∆−
+=
∆−
+
∆−
**NN** ϕϕ
$ [ [5# πϕ ∈ βϕ = βϕ −= "
*NN** ϕ+
∆−
+=
∆−
+
∆−
"
1
[ [πϕ 5#* ×∈∃ +
∈∀ ** ϕ+
∆−
=
−
"
$ 0
O/ 1 $
- # 1 J J
- # 1 - "
# 1 $ 0 ? ,
- # P, - * ## − "
touscours.net

10. #
!
1 -
#* =−−
+=* " $ 0 "
% & !
≥
<
=×=
#
##
** %
& H
−
∈×==+⇔=+
−
*"##
, ±∞=×≠
−
∞−
# 0 2 "
#= " #* =
& H
+
∈×+==+⇔+=
−
*"
. $ 0 0 "
−=⇔=+⇔= +−
##*#*
≥−
≤
= −
#
##
*
>
<
==
≥−
≤
=×=
−
−
#
##
#
##
touscours.net

11. =τ
=
+
=#
=τ 4 "
+ Q
#< #=
τ>> ≈
τ6# <<
τ= ×=−= RE6**τ
τ6= ×= RMC6* τ
τ "
& 0
=
≥
<
=−×=
##
#
** %
& H
−
∈×+==+⇔+=
−
*"
/ #= " =*
& H
+
∈×==+⇔=+
−
*"##
=⇔= +−
#*#*
≥
≤
=
−
#
#
*
Sτ
touscours.net

12. >−
<
==
≥
≤
=×=
−
−
#
##
#
#
S
S
τ
τ
#≥
τS
<
−
==
+∞== # <
*#*#*
#***
*
#*
#
S
#
+∞−=×−=
=−×−=
−
==
+∞
+∞
−
+∞
ττ
.1 @ ! #= 0 0 <
"
' ! 1
#≥
=
−=
−
−
τ
τ
S
S
& 0
( )−=
=
−
−
τ
τ
S
S
* τ>>& $ 4 "
touscours.net

13. 6
. 1 >
+ <<
#< 1 *# 1 "
<=×+=
==−
#0*&
.*#
#≥ 1 * " −= *
0 "
1 -
∈×=⇔
=×
+
+⇔
=+×+×
+
−
#
*
#
. 0 0 "
#*#*#* ++−
−=⇔= " −=
touscours.net

14. 7
!
*
*
*
=+
+=
=+×=+=
% & !
= ** %×=
, #<
∈×=×=⇔=+ −−
*# SS τ
/ #*# ==
. ! $ 1
B "
, #>
∈×+=⇔=+ −
* Sτ
#=+ −=
≥−=
≤=
−
#**
##*
Sτ
>
<
==
≥−
≤
==
−
−
#
##
#*
##
S
S
τ
τ
τ 4 2 - "
touscours.net

15. C
& 0
** ×=
#<
=
∈×+=⇔=+ −
*
* Sτ
τ
#>
ττ
τ
SS
*# −−
×=×=⇔=+
≥=
≤=
−
#*
#*
Sτ
>−
<
=
≥
≤
=
−
−
#
##
#
#
S
S
τ
τ
#> * #≠
−=⇔=+⇔=+⇔=+ ###
+
###
#*
=−=−=
+∞+∞+∞
.1 @ ! #= 0
1 < "
' ! 1
#≥
=
−=
−
−
τ
τ
S
S
*
& 0
−=
=
−
−
τ
τ
S
S
touscours.net

16. E
!
&
+ ## #*5#* ==
1 -
#
#
=++⇔
=++
+ =
1 $ #=++ #=++
+ - "
+
*
G*
# =
=
ω
λλ
.1 $
## =++ ωλ *#
λ
ω
=
##
#
=++ ω
ω
[ ] [ ] [ ]55 # === −−
ωλ
& 1
.1 1 ## =++ ωλ''
*777 ## ωλωλ −=−=∆
*# # <>>∆ ωλ
+ 4 ## <−±−=
∆±−
= ωλλ
λ
'
. 1 1
'' ** ##
*
ωλλωλλ −−−−+−
+=+=
+ "
touscours.net

17. F
4 #5# ## =≠
''
''* +==
$ 0 0 ##* # =+⇔=+
''
###* =+⇔=+
−
−
=
−
=
#
#
''
'
''
'
0
λ−≈''
. λS
-
*# # ===∆ ωλ
+ 0 #ωλ
λ
−=−=
−
='
.
×−
+= λ
** "
#5# ## =≠
×−×−×−
−+−=+−== λλλ
λλλ ***
## ==− λ ## == λ
×−
+= λ
λ** # " ×−
×−= λ
λ#*
. : #>∆ "
. $ λS * 0 "
6-
*# # ><<∆ ωλ
#*777 ## <−=−=∆ ωλωλ " + B*# λωω −=
7ω−=∆ " ' ×±−= ωλ
, *
* $"*
""*
** ''
+=+=
+=
+=+=
×−
×−
×−××−
ϕω
ωω
βαβα
λ
λ
ωωλ
touscours.net

18. K
+
( )*"*"
""*""**
ωλωωλω
ωωωωωωλ
λ
λλ
−−×++−×=
+−++−=
×−
×−×−
+ "
#5# ## =≠
=
=
=
=+−
ω
λ
ωλ
#
#
#
#
+
=−
+
=
+
+
=
+=
×−
×−
*
#
#
:"*
""**
λω
λ
ϕ
λω
ω
ϕ
ϕω
ω
λω
ω
ω
λ
ω
λ
λ
#
#
"**
*
# ωω
ω
λλ
+−= ×−
&
λS
[ ] ∈+
−
=⇔=+⇔=+⇔= #
&
#""***
ω
π
ω
ϕ
πϕωϕω
λS
&&
&&
&&
&&
×−+−
×−+−
=++×+−=+
=++×+=+
λλ
λλ
ϕωω
ω
λ
ϕω
ω
λ
*****
****
*
#
*
#
touscours.net

19. M
+ &×= λδ *
4S
==×=
λ
λδ
&
&
0G
!G
⇔
⇔δ
G
!G
⇔
⇔δ
& 1
+ >> ###
#
" ωλωωω
ω
λ ≈−=<<=
#
#
#
<<=×===×= &
π
ω
πω
ω
π
λ
ω
π
λλδ
+ 1 0 "
% & !
*
*
*
# =++
=++⇔
++=++=
ωλ
& H
− #* =
#*#*## ===++ ωλ *
& H
+ =*
=++ #ωλ
JJ*
,T8,*
#ωλ+=
+=
touscours.net

20. #
""** "
ωωλ
++= −
$ # λωω −=
* * ##* =+
ω
λ
ω
λ −
==−==+ # * $
+−= −
""** "
ω
ω
λ
ωλ
=
+∞→
*
λS
λSU λS>>
++=*
++=× *
, % 0< ++=
0 #* =
#
#
<−=+⇔
=++
=
* $ # $ λS
1 1
**
**
"
"
&
&
&
&
λ
λ
−
−
=+
=+
( ) ( ) &&
&& "
*
*
** λ−
=
+
++×=+
touscours.net

21. $ 1 1
&&
( "
*
** λ−
−=
+−
=
0 * >>
<<=
π
δ
$ $ =
+≈
&&
""
λλ
−≈−
" &(
π
λ" =≈
( 1 $ "
>> 0
≈ * (
π
≈ 1 $
1 $ 0 >>
touscours.net