Ixtiyoriy natural son bo’lsa, unda mavhum birlik



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Agar n-ixtiyoriy natural son bo’lsa, unda mavhum birlik i uchun qaysi tenglik o’rinli ?

i2n=(−1)n .

i2n=i .

i2n=−1 .

i2n=−i .

i2n=1 .



Ta’rifni to’ldiring: z=x+iy ko’rinishdagi ifoda kompleks son deb ataladi. Bunda i−mavhum birlik (i2=−1 ) va x,y − ∙∙∙ sonlarni ifodalaydi.

haqiqiy .

irratsional .

ratsional .

natural .

butun .



z =x+iy kompleks son uchun Rez qanday aniqlanadi?

Rez=x .

Rez=x+y .

Rez=

Rez=y .

to’g’ri javob keltirilmagan .



z =−3+4i kompleks son uchun Imz nimaga teng?


4

1

5

-4

3



kompleks sonning moduli qanday aniqlanadi?

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z =3−4i kompleks sonning moduli z nimaga teng?

5

25

7

1

-1



O’zaro qo’shma kompleks sonlar uchun quyidagi tengliklardan qaysi biri o’rinli emas ?





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z1=2a−4i va z2=6+b2i kompleks sonlar a va b parametrlarning qaysi qiymatida teng bo’ladi?

to’g’ri javob keltirilmagan .

keltirilgan barcha hollarda .

a =3, b=2 .

a =3, b=−2 .

a =3, b=±2



z1=x1+iy1 va z2=x2+iy2 kompleks sonlarni qo’shish amalining ta’rifi qayerda to’g’ri ifodalangan?

z1+z2=(x1+x1)+i(y1+y2) .

z1+z2=(y1+y2)+i(x1+x2) .

z1+z2=(x2+y1)+i(x1+y2) .

z1+z2=(x1+y2)+i(x2+y1) .

z1+z2=(x1+y1)+i(x2+y2) .



z1=5+3i va z2=−1+2i kompleks sonlarning z1+z2 yig’indisini toping.

4+5i .

8+i .

7+2i .

2+7i .

5+4i .



Kompleks sonlarni qo’shish amali uchun quyidagi tengliklardan qaysi biri o’rinli bo’lmaydi ?

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z+0=z .

z1+z2= z2+z1 .

z1+(z2 +z3)=( z1+z2 )+z3 .

z+z=2z .



z1=x1+iy1 va z2=x2+iy2 kompleks sonlarni ayirish amalining ta’rifi qayerda to’g’ri ifodalangan?

z1z2=(x1x1)+i(y1y2) .

z1z2=(y1y2)+i(x1x2) .

z1z2=(x2y1)+i(x1y2) .

z1z2=(x1y1)+i(x2y2) .

z1z2=(x1y2)+i(x2y1) .



z1=5+3i va z2=−1+2i kompleks sonlarning z1z2 ko’paytmasini toping.

−11+7i .

8+5i.

15−2i .

10−3i .

−5+6i .



z1=3(cos450+isin450) , z2=4(cos300+isin300) kompleks sonlarning z=z1z2 ko’paytmasini toping.

z=12(cos750+isin750) .

z=5(cos150+isin150) .

z=5(cos750+isin750) .

z=12(cos150+isin150) .

z=7(cos750+isin150) .



z0=2(cos150+isin150) kompleks son bo’yicha z=(z0)5 kompleks sonni toping.

z=32(cos750+isin750)

z=10(cos750+isin750)

z=10(cos200+isin200)

z=7(cos750+isin750)

z=32(cos200+isin200) .




Muavr formulasining davomini ko’rsating: (cosφ+isinφ)n= ....... .

cosnφ+isinnφ .

cos(φ+n)+isin(φ+n) .

cosnφisinnφ .

cosnφ+isinnφ .

cosnφisinnφ .



z4=−1 ikki hadli tenglama nechta ildizga ega ?

ildizga ega emas .

4

3

2

1



w=f(z) (z=x+iy) funksiya uchun Ref(z)=x2y2 , Imf(z)=−2xy bo’lsa, w=f(z) funksiyani toping .

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w=z2 .

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Kompleks funksiyalarni differensiallash qoidasi qayerda noto’g’ri ifodalangan ?

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[Cf(z)]'=Cf '(z) (C – const.) .

[f(z)g(z)]'=f '(z)g(z)+ f (z)g'(z) .

[f(z)−g(z)]'=f '(z) −g'(z) .

[f(z)+g(z)]'=f '(z)+g'(z) .



Quyidagi shartlardan qaysi biri f(t) original uchun talab etilmaydi?

f(t) monoton funksiya .

t<0 bo’lganda f(t)≡0 .

ixtiyoriy [a,b] chekli kesmada f(t) funksiya bo’lakli-uzluksiz .

biror musbat M va s o’zgarmas sonlar uchun |f(t)|<Mest .

keltirilgan barcha shartlar talab etiladi .



f(t) originalning tasviri F(p) (p=x+iy) qaysi formula bilan aniqlanadi?

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Agar original |f(t)|<Mest shartni qanoatlantirsa, uning tasviri F(p) o’zgaruvchining qanday qiymatlarida aniqlangan bo’ladi?

Rep>s .

Rep<s .

Imp>s .

Imp<s .

|p|>s .



Agar L{f}=L{g} bo’lsa, quyidagi tasdiqlardn qaysi biri noto’g’ri ?

keltirilgan barcha tasdiqlar to’g’ri .

|f(t)|≡ |g(t)| .

Imf(t)≡Img(t) .

Ref(t)≡Reg(t) .

f(t)≡g(t) .



σ0(t) Hevisayd funksiyasining tasviri nimaga teng?

1/p .

1/(p2+1) .

1/(p2−1) .

1/(p+1) .

1/(p−1) .




f(t)=sint (t≥0) trigonometrik funksiyaning tasviri nimaga teng?

1/(p2+1) .

1/p .

1/(p2−1) .

1/(p+1) .

1/(p−1) .



f(t)=cost (t≥0) trigonometrik funksiyaning tasviri nimaga teng?

p/(p2+1) .

1/p .

p/(p2−1) .

p/(p+1) .

p/(p−1) .




f(t)=e−t (t≥0) ko’rsatgichli funksiyaning tasviri nimaga teng?

1/(p+1) .

1/(p−1) .

1/(p2−1) .

1/(p2+1) .

1/p .



f(t)=eαt (t≥0) ko’rsatgichli funksiyaning tasviri nimaga teng?

1/(p−α) .

1/(p+α) .

1/(p2−α2) .

1/(p22) .

α/p .



Quyidagi tengliklarning qaysi biri Laplas almashtirishining chiziqlilik xossasini ifodalaydi ?

L{f±g}=L{f}±L{g} .

L{1/f}=1/L{f} .

L{fg}=L{f}∙L{g} .

L{f2}= L2{f} .

L{f/g}=L{f}/ L{g} .




f(t)=2et+3e−t (t≥0) funksiyaning tasvirini toping

(5p−1)/(p2−1) .

5/(p+1) .

5/(p−1) .

5/(p+1)2 .

(5p+1)/(p2+1) .



Laplas almashtirishi uchun o’xshashlik xossasini ko’rsating

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Agar f(t) originalning tasviri F(p)=4p/(p+1) bo’lsa, f(2t) original tasviri nimaga teng bo’ladi?

2p/(p+2) .

p/(2p+1) .

8p/(p+2) .

8p/(p+1) .

2p/(p+1) .




Laplas almashtirishi uchun siljish xossasini ko’rsating

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Agar f(t) originalning tasviri F(p)=p/(p+1) bo’lsa, etf(t) original tasviri nimaga teng bo’ladi?

(p−1)/p .

p/(p−1) .

p/(p+1) .

(p+1)/(p−1) .

(p−1)/(p+1) .


Agar f(t) originalning tasviri F(p)=p/(p+1) bo’lsa, f(t+2) original tasviri nimaga teng bo’ladi?

e2pp/(p+1) .

e2−pp/(p−1) .

e−2pp/(p+1) .

ep−2 p/(p+1) .

e2+pp/(p+1) .



Originalni differensiallash xossasi qayerda to’g’ri ko’rsatilgan ?

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Agar f(t) originalning tasviri F(p) va f(0)=a bo’lsa, f ′(t) hosilaning tasviri G(p) qanday topiladi?

G(p)=pF(p)+a .

G(p)=apF(p) .

G(p)=pF(p)−a .

G(p)=F(p)−ap .

G(p)=F(p)+ap .



Agar f(t) originalning tasviri F(p)=(p2−1)/(p3+p) va f(0)=−1 bo’lsa, f ′(t) hosilaning tasviri G(p) nimaga teng?

G(p)= −2/(p2+1) .

G(p)= −2+1/(p2+1) .

G(p)=(p −2)/(p2+1) .

G(p)= −2+p/(p2+1) .

G(p)=−2p/(p2+1) .

Agar f(t) originalning tasviri F(p)=cos2p bo’lsa, tf(t) originalning tasviri nimaga teng bo’ladi?

2sin2p .

(sin2p)/2.

cos2p2 .

(cos2p)/p .

pcos2p .



Agar f(t)=(t−1)/(t2+1) originalning tasviri F(p) bo’lsa, F(p) tasvirga mos keladigan g(t) originalni toping

g(t)=(tt2)/(t2+1) .

g(t)=(t−1)/(t3+t)

g(t)=(t2t)/(t2+1) .

g(t)=(t2+t)/(t2+1) .

to’g’ri javob keltirilmagan .



Tasvirlar jadvalidan olingan quyidagi tengliklardan qaysi biri noto’g’ri ifodalangan ?

L{tsinαt}=2p2 α2/(p2+a2) .

L{tcosαt}=(p2α2)/(p2+α2) .

L{tn}=n!/pn+1 .

L{tne−at}=n!/(p+a)n+1 .

keltirilgan barcha tengliklar to’g’ri ifodalangan .



f(t)=cos2t originalning tasvirini toping

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Agar L{f(t)}=p3/ (1+p)2 va f(0)=0 bo’lsa, L{f '(t)} nimaga teng bo’ladi?

p4/ (1+p)2 .

p2/ (1+p)2 .

p3/ (1+p)3 .

p4/ (1+p)3 .

to’g’ri javob keltirilmagan .



Differensial tenglama ta’rifini ko‘rsating

noma’lum funksiyaning hosilalari qatnashgan tenglama

noma’lum funksiyaning turli qiymatlari qatnashgan tenglama

noma’lum funksiya qatnashgan tenglama .

noma’lum funksiya va uning hosilalarining x0 nuqtadagi qiymatlari qatnashgan tenglama

noma’lum funksiya va uning integrallari qatnashgan tenglama



Quyidagilardan qaysi biri differensial tenglama bo‘ladi ?

y–2xy′+5=0 .

y2+5y–3cosx=0 .

3x2+4xy–1=0 .

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y(x)+2 y′(x0)–x=0 .



2−1)y′′+αy′+5xy+7=0 tenglama α parametrning qanday qiymatlarida differensial tenglama bo’ladi?

α(−∞, ∞) .

α≠±1 .

α≠−1 .

α≠1 .

α≠0 .

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