O'zbekiston respublikasi oliy va o'rta maxsus talim vazirligi samarqand davlat universiteti haydarov Akram matematik fizika va analizning zamonaviy usullari va nokorrekt masalalari

c. n

1. 
   sin(3n
   
2. 
   sinnfl
   
3. 
   
   _eq+i
   96.To'g'ri munosabatni keltiring
   e^qsinf3
   
   sinn(3
   

e
e^2q-e^qcosl3+1 e^q
cosfi sinfi
2q

. e^qsin(3
d. Sinnf] -^r
97.To'g'ri munosabatni keltiring

,2 ^e
(e4-i)3
2
₂ e+1)
^a' ⁷¹ (e

_eq+l


С. П d. 71
Ь. n'
e^-i 2 _ ^
98.To'g'ri munosabatni keltiring
717Г
a. cos— -^г^ ~ л
4 e²<7-2e<7cos-+l

-l
4

= X(-D 19
|| 1| ~ ^ 31
\l, 0<(р<7Г 68
0, 123
1, 123
2,—<в<2п A 123

99.To'g'ri munosabatni keltiring
e^qsin-
птт
, . птт
b. sin —
4 e^q+1

. птт
e^q-l

С. sin—

_eq+1
4

птт

. COS—
4
Umumlashgan funksiya nima?

1. 
   uzluksiz funksiyalar fazosida berilgan chiziqli funksional
   
2. 
   chugaralangan funksiyalar fazosida berilgan chiziqli funksional
   
3. 
   uzluksiz funksiyalarning limiti
   
4. 
   integrallanuvchi funksiyalar limiti Dirakning S - funksiyasiga ta'rif bering
   

a. Agar 8(x — x₀) funksiya




агар x Ф x_Q агар x = x₀







xe[a, b] х₀е[а, b]

2. 
   bu funksiyani Dirak S - funksiyasi deymiz
   
3. 
   S(x — x₀) funksiya uzluksiz funksiyalar ketma - ketligi limiti
   
4. 
   S(x — x₀) - differensiallanuvchi ketma - ketliklar limiti
   
5. 
   integrallanuvchi ketma - ketliklar limiti To'g'ri tenglikni ko'rsating
   
   1. 
      
      _eq-1
      S(x — x₀)sinxdx = sinx₀
      
   2. 
      f™ S(x — x₀)cosxdx = cos2x₀
      

00
c. S(x — x₀)£^xdx = £²x₀

d. f™ S(x — x₀)x²dx = x₀
S - shaklli funksiyani ko'rsating

d. 5_£(x,x₀) = 1
S - shaklli funksiyani ko'rsating

00

О S ч 2 y,_n . птт . птт
a. O_n\X, Xq) —~2-ili=± SLTL — XSin — Xq

d. 5_n(x,x₀) =
(x,x₀)ⁿ

105. 
     To'g'ri tenglikni ko'rsating
     
     1. 
        S(x — 0 )sinxdx = 0
        
     2. 
        S (x — ^ sinx = 1
        
     3. 
        S (x — ^ cosxdx = 1
        
     4. 
        f^ S (x — ^j sinxdx = 0
        

rl x > 0

105. 
     Xevisayd funksiyasi 0(x) — |q' _{x <} q
     
     1. 
        0'(x) = 5(x)
        
     2. 
        6>'0) = O)
        
     3. 
        0'(x)=x²
        
     4. 
        6>'(x) =-
        

X

105. 
     ning umumlashgan hosilasini toping
     
     1. 
        = 25(x)
        
     2. 
        m" = i*i
        
     3. 
        = 0(x)
        
     4. 
        = 26(x)
        
106. 
     To'g'ri tenglikni ko'rsating
     
     1. 
        (£ + Л(0(х)е-^я*)) = 5(х)
        
     2. 
        (£ + Л(0(х>Г^я*)) = 0(х)
        
     3. 
        (± + л(в(х)е~**))=±в(х)
        
     4. 
        ^ + Я(0(х)е-^Ах)) = 26>(x)
        
107. 
     To'g'ri tenglikni ko'rsating
     

а. ₊ =
/ d \ d}¹

105. 
     A ( —) = Yuk=o^ak~^n 0 bo'lsa, qaysi tenglamaning echimi A operatoming fundamental echimi deyiladi
     
106. 
     А = operatorning fundamental echimini toping
     
     1. 
        £(x) = в(x) — Xevisayd funksiyasi
        
     2. 
        q(x) = S(x)
        
     3. 
        £(x) = 2S(x)
        
     4. 
        £(x)=^5(x)
        

d²

105. 
     /I = — operatorning fundamental echimini toping
     
     1. 
        e(x)=i|x|
        
     2. 
        s(x) = |x|
        
     3. 
        e(x) = 0(x)
        
     4. 
        e(x) = - |x|
        
106. 
     A = + A operatorning fundamental echimini toping
     
     1. 
        e(x) = 0(х)е^_Ях
        
     2. 
        e(x) = e
        
     3. 
        £(х)=^е^_Ях
        
     4. 
        £(х)=-е^_Ях
        

^{v y} 4
d² ₉

105. 
     Л = — + or operator uchun e(x) ni toping
     

CO
sina>x

со
sincox

1. 
   £ (x) = 0(x)
   
2. 
   £(x) =
   

3. 
   £ (x) = e(x)sina)x
   
4. 
   £ (x) = -6(x)sin(L>x
   

115. Л (J^j и = 3u"(x) - u'(x) = 5(x) bo'lsa, A operatorlik fundamental echimini toping

1. 
   £(x) = 6(x) • (e"¹)
   
2. 
   £(x) = ез
   
3. 
   £(x) = 6>(x) ■ (e^x/³ - 2)
   
4. 
   d. ф) = е^х/3 - 3
   
   116. 
        А и = и" + и' = /(х) xeC(R)f(x) = 0, agar |х| > cost
        

tenglama fundamental echimini toping.

1. 
   s(x) = в(х)(1 — cosx)
   
2. 
   s(x) = 1 — cosx
   
3. 
   s(x) = в(х)
   
4. 
   e(x) =-6(x)sinx
   
116.