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5 маъруза хосмас интеграллар Чегаралари чексиз хосмас интегралл, DOC-20181023-WA0022, худойберганов, 01, aniq integ..., 1212, Algebra va analiz asoslarini faoliyatli yondashuv asosida oqitishda oquv masalaridan foydalanish metodikasi, Algebra va sonlar nazariyasi узб 200та (1курс), 6-mavzu. FUNKSIYANING HOSILASI VA DIFFERENSIALI, Mavzu, 33-8 3210 xat vazirlik, 1-semestr geom, @ilmuziyo2010 QMII, @ilmuziyo2010 Irrigatsiya Qarshi filial

KO‘FN dan testlar

##1# f(z) – golomorf funksiya bo‘lsin. U holda = ? ni hisoblang.##


A) Imf(z)
B) Ref '(z)
+C) f '(z)
D) - Ref '(z)
E) Imf '(z)
##2## f(z) – golomorf funksiya bo‘lsin. U holda =? ni hisoblang.##
A) Imf '(z)
B) i·Ref '(z)
+C) - ·f '(z)
D) Ref '(z)
E) –i·Imf '(z)

##3# Ref(z) = x3 +6x2y – 3xy2 – 2y3, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


A) 2iz3
+B) (1 –2i)z3
C) 3(z –1)3
D) 2z3 – 3
E) z3 + 2z2

##4# Ref(z) = ex(x·cosy – y·siny), f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


A) e z ·sinz
+B) z·e z
C) z ·cosz· e z
D) z + e z
E) e z(z –1)

##5# Ref(z) = x·cosx·chy + y·sinx·shy, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


+A) z·cosz
B) z·sinz
C) z·chz
D) z·shz
E) chz·cosz

##6# Imf(z) = y·cosy·chx + x·siny·shx, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


A) i·z·shz
B) i·z·cosz
C) sinz·chz
D) cosz·shz
+E) z·chz

##7# z = (1+i )8·(1 - i ) – 6 uchun |z| va arg z mos ravishda…….. va …… ga teng.##


A)
B)
C)
+D)
E)

##8# Parallelogrammning uchta uchlari berilgan: z1 = 1+i, z2 = 2 +1,5·i, z3 = 3+3·i. z2 uchiga qarama-qarshi yotuvchi to‘rtinchi z4 uchini toping.##


+A) z4=2+2,5·i
B) z4=1,5+2·i
C) z4=1,5+2,5·i
D) z4=2+2·i
E) z4=2,5+ i

##9# cos(2+i ) sonining haqiqiy qismini toping.##


A) cos2· sin1,
+B) ch1·cos2,
C) sin2·sin1
D) sh1·cos2
E) sh1·sin2.
##10# ctg( - i·ln2) sonining mavhum qismini toping.##
A) 5/7
B) 0
C) –1
D) 12/15
+E)15/17
##11# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f( i ) = 0, arg f '( i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##
A) i /2
+B) 1/3
C) i /4
D) 1/5
E) i /6

##12# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(2i ) = 0, arg f '( 2i ) = 0 shartlari bilan konform akslantirsin. U holda f( 3i )=? ni toping.##


+A) i /5


B) – i /4
C) 1 /3
D) – 2/3
E) 3i /4
##13# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(1+ i ) = 0, arg f '( 1+i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##
A) (i+1)/3
B) (i-1)/(3+i)
C) i/(5-i)
D) –i/(5+i)
+E) (i-1)/(3i-1)

##14# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w-1| < 1 doiraga f( i ) = 1, arg f '( i ) = 0 shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##


A) (i-3)/3
B) (3-i) /3
+C) (i+3)/3
D) –(i+3)/3
E) 3/2
##15# w = f(z) funksiya |z| < 2 doiraga Rew > 0 o‘ng yarim tekislikni f( 0 ) = 1, arg f '( 0 ) = shartlari bilan konform akslantirsin. U holda f(i )=? ni toping.##
+A) 1/3
B) 1/4
C) 1/5
D) 1/6
E) 1/2
##16# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) = 0 shartlari bilan konform akslantirsin. U holda f(0)=?
A) 1/2
B) i /2
C) –i /2
+D) –1/2
E) 1/3

##17# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) =/2 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##


A) –1/2
+B) 1/2
C) i /2
D) 1/4
E) –1/4.
##18# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 0 ) = 0, arg f ' (0) =-/2 shartlari bilan konform akslantirsin. U holda f (1/2)=? ni toping.##
+A) –i /2
B) i /2
C) 1/2
D) -1/3
E) i /3

##19# w = f(z) funksiya |z| < 1 doirani | w-1| < 1 birlik doiraga f(0) = 1/2, f (1 ) = 0 shartlari bilan konform akslantirsin. U holda f( 1/2 )=? ni toping.##


A) 1/3
B) 1/4
+C) 1/5
D) 1/6
E) 1/7

##20# w = f(z) funksiya |z-2| < 1 doirani |w-2i| < 2 birlik doiraga f( 2 ) = i , arg f ' (2 ) = 0 shartlari bilan konform akslantirsin. U holda f( 3/2) =? ni toping.##


A) i
B) (5i+1)/2
C) (-13+16 i )/15
+D) (-12+14 i )/17
E) 3i

##21# 1/(1-z)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1/2
B) –1/2
+C) 3
D) –3
E) 1/6

##22# 2/(1+z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


+A) 12
B) 6
C) 3
D) 1/3
E) 1/12

##23# z(z+2)/(2-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 2
B) –2
C) –1/2
+D) 1/2
E) 1/3

##24# 1/(z2 +9) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1/9
B) –1/25
C) 1/49
+D) -1/81
E) 1/121

##25# 1/(1+z2)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1
+B) –2
C) 3
D) –4
E) 5

##26# (z2+4z4+z6)/(1-z2)4 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 5
B) –4
C) 3
D) –2
+E) 1

##27# z/(1-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 0
B) 1/2
C) 1/3
+D) 3
E) 2

##28# 1/(z+1)(z-2) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## +A) –3/8


B) 3/4
C) 3/2
D) –3/2
E) 3/8

##29# (2z-5)/(z2-5z+6) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 25/127
B) 12/35
+C) –35/216
D) –13/41
E) 3/7

##30# 1/(z2-1)2(z2+4) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 6/17
+B) 7/16
C) 5/18
D) 9/14
E) 8/15

##31# 1/sinz funksiyaning z = 2 nuqtadagi qoldig‘ini toping.##


A) 
+B) 1/
C) 2
D) 1/2
E) -
##32# ctgz funksiyaning z = 3 nuqtadagi qoldig‘ini toping.##
+A) 1/
B) 
C) 3
D) 1/3
E) -

##33# thz funksiyaning z = i/2 nuqtadagi qoldig‘ini toping.##


A) 
B) -
C) 3
D) 2
+E) 1
##34# cth2z funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##
A) 
B) -
+C) 0
D) –1
E) 1

##35# cosz/(z-1)2 funksiyaning z = 1 nuqtadagi qoldig‘ini toping.##


A) cos1
B) –cos1
C) sin1
+D) –sin1
E) 0

##36# 1/(e z +1) funksiyaning z = i nuqtadagi qoldig‘ini toping.##


A) -
B) 
C) 0
D) 1
+E) –1

##37# sinz/(z-1)3 funksiyaning z =1 nuqtadagi qoldig‘ini toping.##


A) 2
B) 1
+C) 0
D) –1
E) -2

##38# 1/sinz2 funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##


+A) 0
B) 1/2
C) 1
D) –1
E) 1/3

##39# cos[(z+2)/2z] funksiyaning z =  nuqtadagi qoldig‘ini toping.##


+A) ,
B) -,
C) 0,
D) 1/,
E) –1/.

##40# z cos2(/z) funksiyaning z = nuqtadagi qoldig‘ini toping.##


A) 3
+B) 2
C) 
D) 1
E) 0

##41# Integralni hisoblang: .##


A) –2
B) –1
+C) 0
D) 1
E) 2
##42# Integralni hisoblang: .##
A) i
+B) 2i
C) 3i
D) -i
E) 0
##43# Integralni hisoblang: .##
A) i
B) -i/2
C)i/3
+D)-2i/3
E) 0
##44# Integralni hisoblang: .##
A) 2i cos1
B) 4i sin1
C) 2i(sin1+cos1)
D) 4i (sin1-cos1)
+E) 4i (cos1-sin1)
##45# Integralni hisoblang: .##
A) 2i sin1
+B) i (cos1+2sin1)
C) 4i (sin1 +2cos1)
D) 4i cos1
E) i (2sin1-cos1)
##46# Integralni hisoblang: .##
+A) -2i /9
B) 0
C) i /3
D) 1
E) i
##47# Integralni hisoblang: .##
A) i /3
B) -i /81
+C) -i /121
D) 0
E) 2i / 169
##48# Integralni hisoblang: .##
A) 0
B) i
C) –i
+D) i
E) -i
##49# Integralni hisoblang: .##
+A) 0
B) –i
C) 
D)-
E) 1
##50# Integralni hisoblang: .##
A) 2i
B) -2i
C)1
D)-1
+E) 0

##51# (z) – golomorf funksiya bo‘lsin. U holda =? ni toping.##


A) Imf(z)
B) Ref '(z)
+C) f '(z)
D) - Ref '(z)
E) Imf '(z).
##52# – golomorf funksiya bo‘lsin. U holda =? ni toping.##
A) Imf '(z)
B) i·Ref '(z)
+C) - ·f '(z)
D) Ref '(z)
E) –i·Imf '(z)
##53# Ref(z) = x3 +6x2y – 3xy2 – 2y3, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##
A) 2iz3
+B) (1 –2i)z3
C) 3(z –1)3
D) 2z3 – 3
E) z3 + 2z2

##54# f(z) = ex(x·cosy – y·siny), f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


A) e z ·sinz
+B) z·e z
C) z ·cosz· e z
D) z + e z
E) e z(z –1)

##55# Ref(z) = x·cosx·chy + y·sinx·shy, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


+A) z·cosz
B) z·sinz
C) z·chz
D) z·shz
E) chz·cosz

##56# Imf(z) = y·cosy·chx + x·siny·shx, f(0) = 0 bo‘lsin. U holda f(z) golomorf funksiyani toping.##


A) i·z·shz,
B) i·z·cosz,
C) sinz·chz
D) cosz·shz,
+E) z·chz.

##57# z = (1+i )8·(1 - i ) – 6 uchun |z| va arg z mos ravishda.##


A)
B)
C)
+D)
E)

##58# Parallelogrammning uchta uchlari berilgan: z1 = 1+i, z2 = 2 +1,5·i, z3 = 3+3·i. z2 uchiga qarama-qarshi yotuvchi to‘rtinchi z4 uchini toping.##


+A) z4=2+2,5·i
B) z4=1,5+2·i
C) z4=1,5+2,5·i
D) z4=2+2·i
E) z4=2,5+ i
##59# cos(2+i ) sonining haqiqiy qismini toping.##
A) cos2· sin1
+B) ch1·cos2
C) sin2·sin1
D) sh1·cos2
E) sh1·sin2
##60# ctg( - i·ln2) sonining mavhum qismini toping.##
A) 5/7
B) 0
C) –1
D) 12/15
+E)15/17
##61# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f( i ) = 0, arg f '( i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##
A) i /2
+B) 1/3
C) i /4
D) 1/5
E) i /6

##62# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(2i ) = 0, arg f '( 2i ) = 0 shartlari bilan konform akslantirsin. U holda f( 3i )=? ni toping.##


+A) i /5
B) – i /4
C) 1 /3
D) – 2/3
E) 3i /4
##63# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w| < 1 birlik doiraga f(1+ i ) = 0, arg f '( 1+i ) = - shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##
A) (i+1)/3
B) (i-1)/(3+i)
C) i/(5-i)
D) –i/(5+i)
+E) (i-1)/(3i-1)

##64# w = f(z) funksiya Imz > 0 yuqori yarim tekislikni |w-1| < 1 doiraga f( i ) = 1, arg f '( i ) = 0 shartlari bilan konform akslantirsin. U holda f( 2i )=? ni toping.##


A) (i-3)/3
B) (3-i) /3
+C) (i+3)/3
D) –(i+3)/3
E) 3/2

##65# w = f(z) funksiya |z| < 2 doiraga Rew > 0 o‘ng yarim tekislikni f( 0 ) = 1, arg f '( 0 ) = shartlari bilan konform akslantirsin. U holda f(i )=? ni toping.##


+A) 1/3
B) 1/4
C) 1/5
D) 1/6
E) 1/2

##66# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) = 0 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##


A) 1/2
B) i /2
C) –i /2
+D) –1/2
E) 1/3
##67# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 1/2 ) = 0, arg f ' (1/2 ) =/2 shartlari bilan konform akslantirsin. U holda f(0)=? ni toping.##
A) –1/2
+B) 1/2
C) i /2
D) 1/4
E) –1/4

##68# w = f(z) funksiya |z| < 1 doirani |w| < 1 birlik doiraga f( 0 ) = 0, arg f ' (0) =-/2 shartlari bilan konform akslantirsin. U holda f (1/2)=? ni toping.##


+A) –i /2
B) i /2
C) 1/2
D) -1/3
E) i /3

##69# w = f(z) funksiya |z| < 1 doirani | w-1| < 1 birlik doiraga f(0) = 1/2, f (1 ) = 0 shartlari bilan konform akslantirsin. U holda f( 1/2 )=? ni toping.##


A) 1/3
B) 1/4
+C) 1/5
D) 1/6
E) 1/7
##70# w = f(z) funksiya |z-2| < 1 doirani |w-2i| < 2 birlik doiraga f( 2 ) = i , arg f ' (2 ) = 0 shartlari bilan konform akslantirsin. U holda f( 3/2) =? ni toping.##
A) i
B) (5i+1)/2
C) (-13+16 i )/15
+D) (-12+14 i )/17
E) 3i

##71# 1/(1-z)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1/2
B) –1/2
+C) 3
D) –3
E) 1/6

##72# 2/(1+z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


+A) 12
B) 6
C) 3
D) 1/3
E) 1/12

##73# z(z+2)/(2-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## A) 2


B) –2
C) –1/2
+D) 1/2
E) 1/3

##74# 1/(z2 +9) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1/9
B) –1/25
C) 1/49
+D) -1/81
E) 1/121

##75# 1/(1+z2)2 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 1
+B) –2
C) 3
D) –4
E) 5
##76# (z2+4z4+z6)/(1-z2)4 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##
A) 5
B) –4
C) 3
D) –2
+E) 1

##77# z/(1-z)3 funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 0
B) 1/2
C) 1/3
+D) 3
E) 2

##78# 1/(z+1)(z-2) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.## +A) –3/8


B) 3/4
C) 3/2
D) –3/2
E) 3/8

##79# (2z-5)/(z2-5z+6) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 25/127
B) 12/35
+C) –35/216
D) –13/41
E) 3/7

##80# 1/(z2-1)2(z2+4) funksiyasining z = 0 nuqta atrofida Teylor qatoriga yoyilmasidagi с2 koeffitsiyentni toping.##


A) 6/17
+B) 7/16
C) 5/18
D) 9/14
E) 8/15

##81# 1/sinz funksiyaning z = 2 nuqtadagi qoldig‘ini toping.##


A) 
+B) 1/
C) 2
D) 1/2
E) -

##82# ctgz funksiyaning z = 3 nuqtadagi qoldig‘ini toping.##


+A) 1/
B) 
C) 3
D) 1/3
E) -

##83# thz funksiyaning z = i/2 nuqtadagi qoldig‘ini toping.##


A) 
B) -
C) 3
D) 2
+E) 1

##84# th2z funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##


A) 
B) -
+C) 0
D) –1
E) 1

##85# cosz/(z-1)2 funksiyaning z = 1 nuqtadagi qoldig‘ini toping.##


A) cos1
B) –cos1
C) sin1
+D) –sin1
E) 0

##86# 1/(e z +1) funksiyaning z = i nuqtadagi qoldig‘ini toping.##


A) -
B) 
C) 0
D) 1
+E) –1

##87# sinz/(z-1)3 funksiyaning z =1 nuqtadagi qoldig‘ini toping.##


A) 2
B) 1
+C) 0
D) –1
E) -2

##88# 1/sinz2 funksiyaning z = 0 nuqtadagi qoldig‘ini toping.##


+A) 0
B) 1/2
C) 1
D) –1
E) 1/3

##89# cos[(z+2)/2z] funksiyaning z =  nuqtadagi qoldig‘ini toping.##


+A) 
B) -
C) 0
D) 1/
E) –1/

##90# z cos2(/z) funksiyaning z = nuqtadagi qoldig‘ini toping.##


A) 3,
+B) 2,
C) ,
D) 1,
E) 0

##91# Integralni hisoblang: .##


A) –2
B) –1
+C) 0
D) 1
E) 2
##92# Integralni hisoblang: .##
A) i
+B) 2i
C) 3i
D) -i
E) 0
##93# Integralni hisoblang: .##
A) i
B) -i/2
C)i/3
+D)-2i/3
E) 0
##94# Integralni hisoblang: .##
A) 2i cos1
B) 4i sin1
C) 2i(sin1+cos1)
D) 4i (sin1-cos1)
+E) 4i (cos1-sin1)
##95# Integralni hisoblang: .##
A) 2i sin1
+B) i (cos1+2sin1)
C) 4i (sin1 +2cos1)
D) 4i cos1
E) i (2sin1-cos1)
##96# Integralni hisoblang: .##
+A) -2i /9
B) 0
C) i /3
D) 1
E) i
##97# Integralni hisoblang: .##
A) i /3
B) -i /81
+C) -i /121
D) 0
E) 2i / 169
##98# Integralni hisoblang: .##
A) 0
B) i
C) –i
+D) i
E) -i
##99# Integralni hisoblang: .##
+A) 0
B) –i
C) 
D)-
E) 1
##100# Integralni hisoblang: .##
A) 2i
B) -2i
C)1
D)-1
+E) 0

1 - C

21 - C

41 - C

61 - B

81 - B

2 - C

22 - A

42 - B

62 - A

82 - A

3 - B

23 - D

43 - D

63 - E

83 - E

4 - B

24 - D

44 - E

64 - C

84 - C

5 - A

25 - B

45 - B

65 - A

85 - D

6 - E

26 - E

46 - A

66 - D

86 - E

7 - D

27 - D

47 - C

67 - B

87 - C

8 - A

28 - A

48 - D

68 - A

88 - A

9 - B

29 - C

49 - A

69 - C

89 - A

10 - E

30 - B

50 - E

70 - D

90 - B

11 - B

31 - B

51 - C

71 - C

91 - C

12 - A

32 - A

52 - C

72 - A

92 - B

13 - E

33 - E

53 - B

73 - D

93 - D

14 - C

34 - C

54 - B

74 - D

94 - E

15 - A

35 - D

55 - A

75 - B

95 - B

16 - D

36 - E

56 - E

76 - E

96 - A

17 - B

37 - C

57 - D

77 - D

97 - C

18 - A

38 - A

58 - A

78 - A

98 - D

19 - C

39 - A

59 - B

79 - C

99 - A

20 - D

40 - B

60 - E

80 - B

100 - E

8
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