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

S²+C0² S + Ct)


S² + C0²
6V./(t) = со scot funksiya tasvirini toping
s

1. 
   

S² + C0²

68. 
    /(t) F(s) bulsa, to'g'ri munosabatni ko'rsating
    
    1. 
       f(t - a) e~^asF(s)
       
    2. 
       fit - a) e^asF(s)
       

d. f(t - a) <- e^F (§)

68. 
    fit) = e~^at sincot originalning tasvirini toping
    

CO
(s+a)²+co²
b ¹
(s+a)²+co²
a
(s+a)²+co² ^ a+co
(s+a)²+co²

68. 
    x^ + —I- a_nx = fix) ko'phadning xarakteristik ko'phadini toping
    
    1. 
       Lis) = sⁿ + a₁sⁿ~¹ + -- + a_n
       
    2. 
       Lis) = s^n_1 H 1-1
       
    3. 
       Lis) = sⁿ + 1
       
    4. 
       Lis) = sⁿ- 1
       
69. 
    x" + 2x' + x = e^_t, x(0) = 0, x'(0) = 0 masalaning xarakteristik ko'phadini toping
    

a. s² + 2s + 1

2. 
   s² — 2s + 1
   
3. 
   s² + 2s
   
4. 
   s² + l
   
   72. 
       x" + 2x' + x = e~^z, x(0) = 0, x"(0) = 0 Koshi masalasi echimini toping
       
       1. 
          x(t) = ^t²e^_t
          
       2. 
          x{t)=\t²
          
       3. 
          x(t) =
          
       4. 
          x(t) = it²-e^_t
          
   73. 
       x" + 2x' + x = e~^z, x(0) = 1, x'(0) = 0 masala tasvirlar sohasida qanday ko'rinishga keladi
       
       1. 
          (s + l)²X(s) = -^+2 + s
          
       2. 
          (5 + 1)²ВД = ^
          
       3. 
          (s + 1)²ВД = 2 + s
          
       4. 
          (s + l)X(s) =7^7+2
          

fx' + у = 0 [x + у' = 0

fx + у = 0
⁷⁵ {x + у' = о ^{= = _1 б}У^лса' tasvirni toping
qanday ko'rinishga ega bo'ladi? Г sX(s) + Y(s) = 1 ^a" U(s) + sY(s) = -1 Г ВД + 7(s) = 1 U(s)-sY(s) = -l ( sX(s) - Y(s) = 1 ^C" U(s) + sY(s) = -1 Г s*(s) - 7(s) = 1 U(s) - sY(s) = -1 r_x' + у = 0
l

1. 
   —
   

s-1

2. 
   -2-
   

d.
S + 1
s²+l 1
fx' + у = 0
76.) x(0) = 1, y(0) = — 1 булса, 7(s) tasvirni toping
"T" у — U
a.

s+1

fx' + у = 0
74.) , x(0) = 1, y(0) = —1 Koshi masalasi tasvirlar sohasida
(x + у = 0 ^

s-1

s+1
d. -2-
s—1
fx' + y = 0
[x + у' = 0

77.
x(0) = 1, y(0) = —1 bo'lsa, x(t) originalni toping

a.	e^c
b.	e^-t
	i
c.	et
	i
d.	e~

fx' +y = 0 [x + у' = 0

1. 
   e^_t
   
2. 
   e^t
   
3. 
   1 - e^f
   
4. 
   l + e^t fx' +y = 0 [x +y' = 0
   

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

80.res

3i

z²+ 9
ni toping

a.
6e³

b. -i-
6e³ i
C. -
6

ni toping

ni toping
d. -4
cos2z
81.res
(z-l)3 '

1. 
   —Icosl
   

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

3
ez2
82.res
a. 3

b. 2

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

ni hisoblang

83 .res

z — 0
2

tasvirning originalini toping
s² + 2S+5

1. 
   —e^sinlt
   

2

2. 
   — ~e^tsin2t
   

2

3. 
   -e^tsin2t
   

2

4. 
   -esint 2
   
   85. 
       F(s) = j- funksiya originalini toping
       
       1. 
          - (s/it — sint)
          
       2. 
          - (cht — sint)
          
       3. 
          - (s/it — cost)
          
       4. 
          - (cht + sint)
          
   86. 
       F(s) = funksiya originalini toping
       

tⁿ

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

1. 
   e^tsin^t
   
2. 
   -e^tsinpt
   
85. 
    
    84.F(s) =
    F(s) = tasvirning originalini toping
    

a.
,at ^ ■
cos(3t

2. 
   e^atsin(3t
   
3. 
   e^atch(3t
   
4. 
   e^atsh(3t
   
   89. 
       /(t) = sin^3t tasvirning originalini toping
       

6
^a' (s² + l)(s²+9)
b ¹
' (s² + l)(s²+9)
1
Q
(s² + 1)(s²+4)
d ¹
(s²-1)(s²-4)

89. 
    Laplas diskret almashtirishining chiziqlilik xossasini keltiring
    
    1. 
       Z?=i cj fj(n) <- Tj₌₁^ci
       
    2. 
       57₌₁c_;/_y(n) <- z?₌₁c_;f;Q)
       

C. /» <- J%₌₁Cj F/iq + 1)
d. I?₌₁ Cj fj(n) <- n₌₁Cj F/(2q)

89. 
    Tasvirni differensiallash xossasini keltiring
    

к
a. n^k/(n) <-(-i)*f-F*(
dq
к

dq d

к

с. n^k/(n) ^F*(q + 1)

к
d. n^fc/(n) +

f(n) n
f(n) r oo
92.Tasvirni integrallash formulasini keltiring
^a- ^ ^ L^ar(s)-/(0)]ds (n>l)
71 4.
S,[F*(s)-f(0)]ds
Tl
^c- ^ ^ ГГС^ + ЯО)]^
^d-^ ^ JoV(s)-/(0)№
93.Siljish xossasini keltiring

1. 
   e^anf(ri) <- F*(q-a)
   
2. 
   e^an/(n) F*(q + a)
   
3. 
   e^an/(ri) <- F*(<7/a)
   
4. 
   e^an/00 <- F*(q-a)f(n) <- F*(™?) 94.Diskret originalga ko'ra diskret tasvirni toping
   

оЧ

e^q

2. 
   а" <- ^
   

_eq-1
ГУ ^с

2. 
   а^а <г- ——
   

_еа _eq+1

2. 
   CL^a ^ —
   

95.To'g'ri munosabatni keltiring
e^q

_eq+1
e^q e^q
a • и <-
b. n