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Ixtiyoriy natural son bo’lsa, unda mavhum birlik
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| səhifə | 1/11 | | tarix | 04.02.2020 | | ölçüsü | 342,17 Kb. | | #30384 |
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Agar n-ixtiyoriy natural son bo’lsa, unda mavhum birlik i uchun qaysi tenglik o’rinli ?
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i2n=(−1)n .
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i2n=i .
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i2n=−1 .
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i2n=−i .
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i2n=1 .
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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.
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haqiqiy .
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irratsional .
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ratsional .
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natural .
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butun .
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z =x+iy kompleks son uchun Rez qanday aniqlanadi?
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Rez=x .
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Rez=x+y .
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Rez=
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Rez=y .
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to’g’ri javob keltirilmagan .
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z =−3+4i kompleks son uchun Imz nimaga teng?
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4
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1
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5
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-4
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3
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 kompleks sonning moduli qanday aniqlanadi?
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z =3−4i kompleks sonning moduli z nimaga teng?
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5
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25
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7
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1
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-1
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O’zaro qo’shma kompleks sonlar uchun quyidagi tengliklardan qaysi biri o’rinli emas ?
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 .
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z1=2a−4i va z2=6+b2i kompleks sonlar a va b parametrlarning qaysi qiymatida teng bo’ladi?
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to’g’ri javob keltirilmagan .
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keltirilgan barcha hollarda .
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a =3, b=2 .
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a =3, b=−2 .
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a =3, b=±2
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z1=x1+iy1 va z2=x2+iy2 kompleks sonlarni qo’shish amalining ta’rifi qayerda to’g’ri ifodalangan?
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z1+z2=(x1+x1)+i(y1+y2) .
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z1+z2=(y1+y2)+i(x1+x2) .
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z1+z2=(x2+y1)+i(x1+y2) .
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z1+z2=(x1+y2)+i(x2+y1) .
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z1+z2=(x1+y1)+i(x2+y2) .
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z1=5+3i va z2=−1+2i kompleks sonlarning z1+z2 yig’indisini toping.
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4+5i .
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8+i .
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7+2i .
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2+7i .
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5+4i .
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Kompleks sonlarni qo’shish amali uchun quyidagi tengliklardan qaysi biri o’rinli bo’lmaydi ?
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 .
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z+0=z .
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z1+z2= z2+z1 .
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z1+(z2 +z3)=( z1+z2 )+z3 .
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z+z=2z .
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z1=x1+iy1 va z2=x2+iy2 kompleks sonlarni ayirish amalining ta’rifi qayerda to’g’ri ifodalangan?
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z1−z2=(x1−x1)+i(y1−y2) .
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z1−z2=(y1−y2)+i(x1−x2) .
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z1−z2=(x2−y1)+i(x1−y2) .
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z1−z2=(x1−y1)+i(x2−y2) .
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z1−z2=(x1−y2)+i(x2−y1) .
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z1=5+3i va z2=−1+2i kompleks sonlarning z1∙z2 ko’paytmasini toping.
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−11+7i .
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8+5i.
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15−2i .
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10−3i .
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−5+6i .
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z1=3(cos450+isin450) , z2=4(cos300+isin300) kompleks sonlarning z=z1∙z2 ko’paytmasini toping.
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z=12(cos750+isin750) .
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z=5(cos150+isin150) .
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z=5(cos750+isin750) .
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z=12(cos150+isin150) .
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z=7(cos750+isin150) .
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z0=2(cos150+isin150) kompleks son bo’yicha z=(z0)5 kompleks sonni toping.
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z=32(cos750+isin750)
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z=10(cos750+isin750)
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z=10(cos200+isin200)
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z=7(cos750+isin750)
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z=32(cos200+isin200) .
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Muavr formulasining davomini ko’rsating: (cosφ+isinφ)n= ....... .
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cosnφ+isinnφ .
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cos(φ+n)+isin(φ+n) .
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cosnφ−isinnφ .
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cosnφ+isinnφ .
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cosnφ−isinnφ .
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z4=−1 ikki hadli tenglama nechta ildizga ega ?
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ildizga ega emas .
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4
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3
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2
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1
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w=f(z) (z=x+iy) funksiya uchun Ref(z)=x2−y2 , 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.) .
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[f(z)g(z)]'=f '(z)g(z)+ f (z)g'(z) .
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[f(z)−g(z)]'=f '(z) −g'(z) .
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[f(z)+g(z)]'=f '(z)+g'(z) .
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Quyidagi shartlardan qaysi biri f(t) original uchun talab etilmaydi?
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f(t) monoton funksiya .
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t<0 bo’lganda f(t)≡0 .
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ixtiyoriy [a,b] chekli kesmada f(t) funksiya bo’lakli-uzluksiz .
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biror musbat M va s o’zgarmas sonlar uchun |f(t)|<Mest .
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keltirilgan barcha shartlar talab etiladi .
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Agar original |f(t)|<Mest shartni qanoatlantirsa, uning tasviri F(p) o’zgaruvchining qanday qiymatlarida aniqlangan bo’ladi?
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Rep>s .
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Rep<s .
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Imp>s .
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Imp<s .
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|p|>s .
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Agar L{f}=L{g} bo’lsa, quyidagi tasdiqlardn qaysi biri noto’g’ri ?
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keltirilgan barcha tasdiqlar to’g’ri .
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|f(t)|≡ |g(t)| .
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Imf(t)≡Img(t) .
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Ref(t)≡Reg(t) .
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f(t)≡g(t) .
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σ0(t) Hevisayd funksiyasining tasviri nimaga teng?
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1/p .
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1/(p2+1) .
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1/(p2−1) .
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1/(p+1) .
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1/(p−1) .
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f(t)=sint (t≥0) trigonometrik funksiyaning tasviri nimaga teng?
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1/(p2+1) .
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1/p .
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1/(p2−1) .
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1/(p+1) .
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1/(p−1) .
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f(t)=cost (t≥0) trigonometrik funksiyaning tasviri nimaga teng?
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p/(p2+1) .
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1/p .
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p/(p2−1) .
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p/(p+1) .
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p/(p−1) .
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f(t)=e−t (t≥0) ko’rsatgichli funksiyaning tasviri nimaga teng?
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1/(p+1) .
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1/(p−1) .
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1/(p2−1) .
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1/(p2+1) .
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1/p .
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f(t)=eαt (t≥0) ko’rsatgichli funksiyaning tasviri nimaga teng?
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1/(p−α) .
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1/(p+α) .
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1/(p2−α2) .
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1/(p2+α2) .
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α/p .
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Quyidagi tengliklarning qaysi biri Laplas almashtirishining chiziqlilik xossasini ifodalaydi ?
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L{f±g}=L{f}±L{g} .
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L{1/f}=1/L{f} .
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L{f∙g}=L{f}∙L{g} .
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L{f2}= L2{f} .
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L{f/g}=L{f}/ L{g} .
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f(t)=2et+3e−t (t≥0) funksiyaning tasvirini toping
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(5p−1)/(p2−1) .
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5/(p+1) .
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5/(p−1) .
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5/(p+1)2 .
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(5p+1)/(p2+1) .
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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?
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2p/(p+2) .
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p/(2p+1) .
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8p/(p+2) .
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8p/(p+1) .
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2p/(p+1) .
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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?
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(p−1)/p .
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p/(p−1) .
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p/(p+1) .
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(p+1)/(p−1) .
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(p−1)/(p+1) .
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Agar f(t) originalning tasviri F(p)=p/(p+1) bo’lsa, f(t+2) original tasviri nimaga teng bo’ladi?
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e2pp/(p+1) .
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e2−pp/(p−1) .
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e−2pp/(p+1) .
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ep−2 p/(p+1) .
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e2+pp/(p+1) .
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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?
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G(p)=pF(p)+a .
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G(p)=apF(p) .
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G(p)=pF(p)−a .
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G(p)=F(p)−ap .
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G(p)=F(p)+ap .
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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?
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G(p)= −2/(p2+1) .
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G(p)= −2+1/(p2+1) .
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G(p)=(p −2)/(p2+1) .
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G(p)= −2+p/(p2+1) .
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G(p)=−2p/(p2+1) .
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Agar f(t) originalning tasviri F(p)=cos2p bo’lsa, tf(t) originalning tasviri nimaga teng bo’ladi?
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2sin2p .
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(sin2p)/2.
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cos2p2 .
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(cos2p)/p .
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pcos2p .
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Agar f(t)=(t−1)/(t2+1) originalning tasviri F(p) bo’lsa, F′(p) tasvirga mos keladigan g(t) originalni toping
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g(t)=(t−t2)/(t2+1) .
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g(t)=(t−1)/(t3+t)
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g(t)=(t2−t)/(t2+1) .
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g(t)=(t2+t)/(t2+1) .
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to’g’ri javob keltirilmagan .
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Tasvirlar jadvalidan olingan quyidagi tengliklardan qaysi biri noto’g’ri ifodalangan ?
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L{tsinαt}=2p2 α2/(p2+a2) .
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L{tcosαt}=(p2−α2)/(p2+α2) .
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L{tn}=n!/pn+1 .
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L{tne−at}=n!/(p+a)n+1 .
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keltirilgan barcha tengliklar to’g’ri ifodalangan .
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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?
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p4/ (1+p)2 .
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p2/ (1+p)2 .
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p3/ (1+p)3 .
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p4/ (1+p)3 .
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to’g’ri javob keltirilmagan .
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Differensial tenglama ta’rifini ko‘rsating
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noma’lum funksiyaning hosilalari qatnashgan tenglama
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noma’lum funksiyaning turli qiymatlari qatnashgan tenglama
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noma’lum funksiya qatnashgan tenglama .
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noma’lum funksiya va uning hosilalarining x0 nuqtadagi qiymatlari qatnashgan tenglama
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noma’lum funksiya va uning integrallari qatnashgan tenglama
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Quyidagilardan qaysi biri differensial tenglama bo‘ladi ?
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y–2xy′+5=0 .
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y2+5y–3cosx=0 .
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3x2+4xy–1=0 .
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y(x)+2 y′(x0)–x=0 .
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(α2−1)y′′+αy′+5xy+7=0 tenglama α parametrning qanday qiymatlarida differensial tenglama bo’ladi?
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α(−∞, ∞) .
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α≠±1 .
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α≠−1 .
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α≠1 .
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α≠0 .
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Dostları ilə paylaş: |
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