Matanalyzdan masalalar

[nodiriy]

O'rtoqlar, manga quyidagi masalalarni yechishga yordamlashib yuboringlar iltimos. Faqat yechimni izohlash kerak: qaysi teoremalar ishlatildi va h.k. Glavniysi tushunarliroq qilib, ya ne geniy. :)

Ho'p boshladik:

1. Quyidagi funkcional qator (0,2) intervalda tekis yaqinlashuvchanligini aniqlang (tekis yaqinlashuvchanmi yoki yo'qmi?):

Summa(n=2..Beskonechno) (-1)^n * (1+nx)/(n^2-x^2)

2. Quyidagi darajali qatorning yig'indisi nimaga teng (bunisini ushbu darajali qatorni integrallab yoki differenciallab hisoblash kerak):

Summa(n=1..Beskonechno) (-1)^(n-1) * x^(2n)/(n(2n-1))

3. f(x)=sign(cos(x)), xE(0,Pi], funkciyani (-cheksiz,+cheksizda) SINUSli Furie qatoriga yozing. (-cheksiz,+cheksiz)da potochechno yaqinlashadimi, agar yaqinlashsa, yig'indisini toping.


Yana bir savolim bor 1.masalaga: agar bu qatorni potochechno yaqinlashuvchi ekanligini isbotlasam, quyidagini hisoblab

lim(n->cheksiz) (-1)^n * (1+nx)/(n^2 - x^2),

unda avtomaticheskiy bu qator tekis yaqinlashuvchi boladimi yoki yo'qmi?

[Pythagor]

Erte kechgacha javobini olasiz, xudo xolasa...:D

[nodiriy]

Erte kechgacha javobini olasiz, xudo xolasa...:D

Shunchalik uzoq kutaman deb o'ylamagandim biroq. :) Hammasini yechish shart emas. Yechilganlarini post qilib yuboraveringlar. :)

[Pythagor]

Shunchalik uzoq kutaman deb o'ylamagandim biroq. :) Hammasini yechish shart emas. Yechilganlarini post qilib yuboraveringlar. :)Man xozi Univerdaman, ishlarim bor bir oz, erte tush vaqtlariga vaqtim bo'ladi, shunda qarab ko'raman,...:D

[Mahmud]

O'rtoqlar, manga quyidagi masalalarni yechishga yordamlashib yuboringlar iltimos. Faqat yechimni izohlash kerak: qaysi teoremalar ishlatildi va h.k. Glavniysi tushunarliroq qilib, ya ne geniy. :)

Ho'p boshladik:

2. Quyidagi darajali qatorning yig'indisi nimaga teng (bunisini ushbu darajali qatorni integrallab yoki differenciallab hisoblash kerak):

Summa(n=1..Beskonechno) (-1)^(n-1) * x^(2n)/(n(2n-1))


Berilgan qatorni ikki marta differenciallab quyidagi tenglikka ega bo'lamiz:

S''=2*(1-x^2+x^4-x^6+....)

Hosil bo'lgan qator yig'indisi:

S''=2/(1+x^2) , q=-x^2, xE(0;1)

Endi ikki marta integrallab qator yig'indisini topamiz:

S(0)=0 => S(x)=2*x*arctgx-ln(1+x^2).

ps: Differenciallash va integlash hisoblariga tuhtalmadim, buni uddalay olasiz albatta.

:)

[Pythagor]

1. Quyidagi funkcional qator (0,2) intervalda tekis yaqinlashuvchanligini aniqlang (tekis yaqinlashuvchanmi yoki yo'qmi?):
Summa(n=2..Beskonechno) (-1)^n * (1+nx)/(n^2-x^2) Bu misol tekis yaqinlashadi, man yordamchi funksiya kiritb tekshirib ko'rdim.
2. Quyidagi darajali qatorning yig'indisi nimaga teng (bunisini ushbu darajali qatorni integrallab yoki differenciallab hisoblash kerak):
Summa(n=1..Beskonechno) (-1)^(n-1) * x^(2n)/(n(2n-1))
Bu misolni Platon yechib qo'ygan shaklli, vaqt ajratmadim, bir oz izoh beraman: S' va S" funksiyalar, Leybnis alomatiga ko'ra tekis yaqinlashadi, o'shani uchun biza qo'rmasdan qatorning har bir hadidan xosila oldik.
3. f(x)=sign(cos(x)), xE(0,Pi], funkciyani (-cheksiz,+cheksizda) SINUSli Furie qatoriga yozing. (-cheksiz,+cheksiz)da potochechno yaqinlashadimi, agar yaqinlashsa, yig'indisini toping. A bunga tayyor formula borku, qo'ysez chiqadiyu.
potochechno yaqinlashadi, yig'indisini bilmadim, xisoblamadim.
Yana bir savolim bor 1.masalaga: agar bu qatorni potochechno yaqinlashuvchi ekanligini isbotlasam, quyidagini hisoblab
lim(n->cheksiz) (-1)^n * (1+nx)/(n^2 - x^2),
unda avtomaticheskiy bu qator tekis yaqinlashuvchi boladimi yoki yo'qmi?Qatorning potochechno yaqinlashuvchi bo'lishidan uning tekis yaqinlashuvchiligi har doim kelib chiqavermidi!
Bu limitni xisoblaganiz, faqat qatorni yaqinlashishi uchun zaruriy shartni tekshirib ko'rish demakdir.

omad

[nodiriy]

Berilgan qatorni ikki marta differenciallab quyidagi tenglikka ega bo'lamiz:

S''=2*(1-x^2+x^4-x^6+....)

Hosil bo'lgan qator yig'indisi:

S''=2/(1+x^2) , q=-x^2, xE(0;1)

Endi ikki marta integrallab qator yig'indisini topamiz:

S(0)=0 => S(x)=2*x*arctgx-ln(1+x^2).

ps: Differenciallash va integlash hisoblariga tuhtalmadim, buni uddalay olasiz albatta.

:)

Hammasi tushunarli, rahmat. Lekin bitta narsani tushunmadim, nimaga 2marta differenciallagandan so'ng xE(0;1) cheklanib qoldik?
Manimcha javobni ham bilaman - "chunki shu intervalda qator yaqinlashuvchi", lekin utochnit qilmoqchidim. :D

[nodiriy]

Bu misol tekis yaqinlashadi, man yordamchi funksiya kiritb tekshirib ko'rdim.

Usha tekshirishingizni bu yerga ham post qilib yuboring, iltimos.


Bu misolni Platon yechib qo'ygan shaklli, vaqt ajratmadim, bir oz izoh beraman: S' va S" funksiyalar, Leybnis alomatiga ko'ra tekis yaqinlashadi, o'shani uchun biza qo'rmasdan qatorning har bir hadidan xosila oldik.

Funkcional qatorlar uchun Leibnitz alomati ham bormi? Leibnitz alomati faqat sonli qatorlar uchun shekilli? Lekin Siz aytgandekka:
Sum(n=1..Infinity) a[n]*x^n qatorlarni yig'indisini hisoblash uchun Sum(n=1..Infinity) a[n] sonli qatorni yaqinlashuvchi ekanligini ko'rsatish kerakligini bilaman.

A bunga tayyor formula borku, qo'ysez chiqadiyu.
potochechno yaqinlashadi, yig'indisini bilmadim, xisoblamadim.

Usha tayyor formuladan chiqargunchaham o'zi bo'ladiganim bo'ldi. :) Potochechno yaqinlashishini qayerdan bildingiz?

Qatorning potochechno yaqinlashuvchi bo'lishidan uning tekis yaqinlashuvchiligi har doim kelib chiqavermidi!
Bu limitni xisoblaganiz, faqat qatorni yaqinlashishi uchun zaruriy shartni tekshirib ko'rish demakdir.

omad

Bunisini uje kitobni o'qib anglab yetdim. Kattakon rahmat. O'zi boshidan shu yerga murojaat qilish kerak ekan. :)

[MasxaraboZ]

bu yerdagi postlarni kurib bu akademiklar qayerdan paydo bulib qoldi deb uylanib qoldim :lool:


akademik bup ketlaring e :lool:

misollarga javoblar shunday yozilgan shunday yozilgan hatto akademiklar ham tushunmasa keragov :lool:

[Mahmud]

Hammasi tushunarli, rahmat. Lekin bitta narsani tushunmadim, nimaga 2marta differenciallagandan so'ng xE(0;1) cheklanib qoldik?
Manimcha javobni ham bilaman - "chunki shu intervalda qator yaqinlashuvchi", lekin utochnit qilmoqchidim. :D

q=-x^2 ga chalg'ibman shekilli, xE(-1;1) :D

ps: Hamma javobni bilib misollarni beryabsizmi? :D
Yana bo'lsa tashavering ;)
Qo'ldan kelgancha o'rinib ko'ramiz :)

[Mahmud]

Usha tayyor formuladan chiqargunchaham o'zi bo'ladiganim bo'ldi. :) Potochechno yaqinlashishini qayerdan bildingiz?


Chiqargan Sinusli Furie qatorini keltiring, ho'p? :)

[nodiriy]

q=-x^2 ga chalg'ibman shekilli, xE(-1;1) :D

ps: Hamma javobni bilib misollarni beryabsizmi? :D
Yana bo'lsa tashavering ;)
Qo'ldan kelgancha o'rinib ko'ramiz :)

Intervalni o'zgartirishga o'zgartiribsiz, lekin nega baribir xE(-1;1) ga chegaralandingiz? Faqat shu intervalda tekis yaqinlashuvchi bo'lgani uchunmi?

P.S. Hamma javobni bilib berayotganim yo'q, bularni o'zim yecha olmaganim uchun berayotgandim, tushuntirib beringlar deb iltimos qilib.
Imtihondan olgan natijalarga ko'ra yana misollar bo'ladiganga o'xshaydi :?

P.P.S. Aytgandek, esimdan chiqayozibdi, tekis yaqinlashuvchanlik bn potochechnno yaqinlashuvchanlikning farqi nimada? O'zimiznigicha tushuntirib beringlar, iltimos, definitionni bilaman, lekin baribir ko'z oldimga keltira olmayotibman farqini, hozircha.

[Pythagor]

Intervalni o'zgartirishga o'zgartiribsiz, lekin nega baribir xE(-1;1) ga chegaralandingiz? Faqat shu intervalda tekis yaqinlashuvchi bo'lgani uchunmi?
.Ha, faqat shu oraliqda tekis yaqinlashgani uchun, agar tekis yaqinlashmaganda edi, qatorning har bir hadidan hosila olishga haqqimiz yo'q edi.
P.P.S. Aytgandek, esimdan chiqayozibdi, tekis yaqinlashuvchanlik bn potochechnno yaqinlashuvchanlikning farqi nimada? O'zimiznigicha tushuntirib beringlar, iltimos, definitionni bilaman, lekin baribir ko'z oldimga keltira olmayotibman farqini, hozircha
Pototechno yaqinlashish: f_n(x), funksional ketma ketlik f funksiyaga R to'plamda pototechno(nuqtali) yaqinlashuvchi deyiladi, agarda fiksirlangan(tayinlangan) har bir x_0 nuqtada f_n(x_0) sonli ketma ketlik yaqinlashsa, ya'ni
"ixtiyoriy" E>0 son uchun "shunday" bir N=N(E, x_0) nomer(qadam) topilsaki, "barcha" n>N nomerlar(qadamlar) uchun !f_n(x)-f(x)!<E tengsizlik bajarilsa.
Tekis yaqinlashish: f_n(x), funksional ketma ketlik f funksiyaga R to'plamda tekis yaqinlashuvchi deyiladi, agarda "ixtiyoriy" E>0 son uchun "shunday" bir N=N(E) nomer(qadam) topilsaki, "barcha" n>N nomerlar(qadamlar) va "barcha" xER uchun !f_n(x)-f(x)!<E tengsizlik bajarilsa.

E'tibor bergan bo'lsez, nuqtali(pototechno) yaqinlashishda, N nomerimiz x_0 nuqtaga bog'liq bo'layapti(bu digani, har bir x_0 nuqtaga mos keladigan N nomer digani, bunaqangi N lar juda ko'p bo'lishi mumkin), tekis yaqinlashishda esa bog'liq bo'lmayapti(bu digani hamma x lar uchun bitta umumiy N nomer, boshqa bo'lishi mumkinamas).
Xulosa, nuqtali yaqinlashuvchi funksional ketma ketliklar top'lamini ichida tekis yaqinlashuvchi ketma ketliklar to'plami yotadi, ya'ni tekis yaqinlashgani har doim nuqtali yaqinlashadi, biroq aksinchasi har doim o'rinlimas. ehh charchab kettim...:D

ha etgancha, sizga qator uchun keragidi a? f_n(x) dip, anu S_n(x)ni olasiz, hammasi hal bo'ladi...
Qatorlar uchun yozganimda har bir qator uchun n=1 dan cheksizgacha dip yozurish kerekan, o'shani uchun ketma ketlik uchun yozib qo'yaqoldim, :D

p.s. kallada bori shu.

[nodiriy]

Ha, faqat shu oraliqda tekis yaqinlashgani uchun, agar tekis yaqinlashmaganda edi, qatorning har bir hadidan hosila olishga haqqimiz yo'q edi.

Pototechno yaqinlashish: f_n(x), funksional ketma ketlik f funksiyaga R to'plamda pototechno(nuqtali) yaqinlashuvchi deyiladi, agarda fiksirlangan(tayinlangan) har bir x_0 nuqtada f_n(x_0) sonli ketma ketlik yaqinlashsa, ya'ni
"ixtiyoriy" E>0 son uchun "shunday" bir N=N(E, x_0) nomer(qadam) topilsaki, "barcha" n>N nomerlar(qadamlar) uchun !f_n(x)-f(x)!<E tengsizlik bajarilsa.
Tekis yaqinlashish: f_n(x), funksional ketma ketlik f funksiyaga R to'plamda tekis yaqinlashuvchi deyiladi, agarda "ixtiyoriy" E>0 son uchun "shunday" bir N=N(E) nomer(qadam) topilsaki, "barcha" n>N nomerlar(qadamlar) va "barcha" xER uchun !f_n(x)-f(x)!<E tengsizlik bajarilsa.

E'tibor bergan bo'lsez, nuqtali(pototechno) yaqinlashishda, N nomerimiz x_0 nuqtaga bog'liq bo'layapti(bu digani, har bir x_0 nuqtaga mos keladigan N nomer digani, bunaqangi N lar juda ko'p bo'lishi mumkin), tekis yaqinlashishda esa bog'liq bo'lmayapti(bu digani hamma x lar uchun bitta umumiy N nomer, boshqa bo'lishi mumkinamas).
Xulosa, nuqtali yaqinlashuvchi funksional ketma ketliklar top'lamini ichida tekis yaqinlashuvchi ketma ketliklar to'plami yotadi, ya'ni tekis yaqinlashgani har doim nuqtali yaqinlashadi, biroq aksinchasi har doim o'rinlimas. ehh charchab kettim...:D

ha etgancha, sizga qator uchun keragidi a? f_n(x) dip, anu S_n(x)ni olasiz, hammasi hal bo'ladi...
Qatorlar uchun yozganimda har bir qator uchun n=1 dan cheksizgacha dip yozurish kerekan, o'shani uchun ketma ketlik uchun yozib qo'yaqoldim, :D

p.s. kallada bori shu.

Anchadan beri javob... eeee... savol deganim, bermaganimga uzr so'rayman. :) Ta'rifini tushunishga sal-pal tushundim shekilli, lekin usha nuqtali va tekis yaqinlashuvchi ketma-ketliklarni grafikida qanday farq bo'ladi, shuni ko'z oldimga keltirolmiyopman. Yaqinlashuvchi sonli ketma-ketliklarni predstavit' qilsa bo'ladi, funkcional ketma-ketliklarnichi?

[Aus]

anaka uzr temaga sal taluklimas
no mashu pastagi narsani manga misolda kursatib beromisilami

Метод множителей Лагранжа

hecham chunmayabman
oldindan rahmat

[Mahmud]

anaka uzr temaga sal taluklimas
no mashu pastagi narsani manga misolda kursatib beromisilami

Метод множителей Лагранжа

hecham chunmayabman
oldindan rahmat

javob bu erda (http://www.exponenta.ru/educat/class/courses/ma/theme32/theory.asp#2)bo'lsa ajabmas :)

Ikki o'zgaruvchili funksiyaga misol keltirib tushuntirish ozgina muskulroq, tushunish ham albatta...
Yuqorida link yordam beradi degan umiddaman!

Omadlar!

[Mahmud]

Anchadan beri javob... eeee... savol deganim, bermaganimga uzr so'rayman. :) Ta'rifini tushunishga sal-pal tushundim shekilli, lekin usha nuqtali va tekis yaqinlashuvchi ketma-ketliklarni grafikida qanday farq bo'ladi, shuni ko'z oldimga keltirolmiyopman. Yaqinlashuvchi sonli ketma-ketliklarni predstavit' qilsa bo'ladi, funkcional ketma-ketliklarnichi?

Nuqtali va tekis yaqinlashuvchi ketma-ketlik olib o'zingiz chizib ko'rishga harakat qiling, imtihonda yaxshi bo'ladi! :)
Funkcional ketma-ketlikda x ning ma'lum qiymatlarida tasavvur qilishingiz kerak bo'ladi, xolos.

Omadlar!

[Martingale]

Salom Matematiklar!

Quyidagi funksiyani integralini tiopish kerak, eng kamida nima uchun integral olinmasiligini kursatish kerak. Don't prove just show some hints.
Matlabmi yoki mathcadmi hohlaganizni ishlatib javobini bersez buldi:) . Uzim u prog larda ishlomiman.

Hullas F(t)=e^(-t^2)

Rahmat oldindan.

[Mahmud]

Salom Matematiklar!

Quyidagi funksiyani integralini tiopish kerak, eng kamida nima uchun integral olinmasiligini kursatish kerak. Don't prove just show some hints.
Matlabmi yoki mathcadmi hohlaganizni ishlatib javobini bersez buldi:) . Uzim u prog larda ishlomiman.

Hullas F(t)=e^(-t^2)

Rahmat oldindan.

Integralni qaysi oraliqda hisoblamoqchisiz?
Qanday aniqlikda?

ps: bu holat Matlabda hisoblashga imkon beradi :)

[Martingale]

Integralni qaysi oraliqda hisoblamoqchisiz?
Qanday aniqlikda?

ps: bu holat Matlabda hisoblashga imkon beradi :)



Oraliqni farqi yuq. 0 dan X gacha, Xni 1 deb ham olishiz mumkin.

[Mahmud]

Oraliqni farqi yuq. 0 dan X gacha, Xni 1 deb ham olishiz mumkin.

javob quyidagicha:

>> f = inline('exp(-(x.^2))');

>> format short
>> g = quadl(f, 0,1)
g =
0.7468

>> format long
>> g = quadl(f, 0,1)
g =
0.74682413398845

>> g = quadl(f, 0,1)
g =
7.468241339884472e-001

[Martingale]

javob quyidagicha:

>> f = inline('exp(-(x.^2))');

>> format short
>> g = quadl(f, 0,1)
g =
0.7468

>> format long
>> g = quadl(f, 0,1)
g =
0.74682413398845

>> g = quadl(f, 0,1)
g =
7.468241339884472e-001




Demak, bu oraliqda integral mavjud demoqchimisiz? Matlabga kiritilgan suzlarizni tushunmadim, siz F(x)-boshlangich funksiya qanaqa kurinishda bulishini yozing. Uzi bu graph integralnikimi yoki f=e(-x^2) nikimi?:)
manimcha bu funksiyadan integral olib bumasa kerak. Qulda harakat qilib kurin.:D

[Mahmud]

Demak, bu oraliqda integral mavjud demoqchimisiz? Matlabga kiritilgan suzlarizni tushunmadim, siz F(x)-boshlangich funksiya qanaqa kurinishda bulishini yozing. Uzi bu graph integralnikimi yoki f=e(-x^2) nikimi?:)
manimcha bu funksiyadan integral olib bumasa kerak. Qulda harakat qilib kurin.:D

funksiya shu oraliqda uzluksiz bo'lgani uchun integral mavjud.


Matlabmi yoki mathcadmi hohlaganizni ishlatib javobini bersez buldi:) . Uzim u prog larda ishlomiman.

yuqorida Matlabda javobi turibdi :) :D

savolda boshlang'ich ko'rinishini haqida oldinroq yozmaysizmi? Matlabni ustanovka qilmasdan yozib quya qolardim.....

[Mahmud]

e^x finksiyani Teylor qatori:

e^x=1+x/1!+x^2/2!+...+x^n/n!+Rn(x)


Rn(x)=x^(n+1)e^(kx)/(n+1)!, 0<k<1, Rn(x) - qoldiq hadi

x ni -x^2 bilan almashtirib, ko'phadni (0,1) yoki (0,x) oraliqda integralini topasiz...

Qolganini hisoblash qo'lingizdan keladi degan umiddaman:)

Omadlar!;)

[Martingale]

funksiya shu oraliqda uzluksiz bo'lgani uchun integral mavjud.


Gapiz tugri, bu oraliqda uzluksiz. funksiya ham chegaralngan. Demak integral mavjud, lekin boshlangich funksiyani kurinishi kerak.

yuqorida Matlabda javobi turibdi :) :D

savolda boshlang'ich ko'rinishini haqida oldinroq yozmaysizmi? Matlabni ustanovka qilmasdan yozib quya qolardim.....
Taqsir, aytdimku boshida matlabga tushunmiman deb. :D
Siz boshlangich funksiyani odam tushunadigan tilda yozib qoldirin. Rahmat oldindan.

tepadagi yuozgan narsezni tushunishim uchun ancha vaqt kerak buladi. :))
Ungacha uziz F(x) funksiyani kurinishini yozib qoldirsezam bulaveradi.

[SALAR]

e^x finksiyani Teylor qatori:

e^x=1+x/1!+x^2/2!+...+x^n/n!+Rn(x)


Rn(x)=x^(n+1)e^(kx)/(n+1)!, 0<k<1, Rn(x) - qoldiq hadi

x ni -x^2 bilan almashtirib, ko'phadni (0,1) yoki (0,x) oraliqda integralini topasiz...

Qolganini hisoblash qo'lingizdan keladi degan umiddaman:)

Omadlar!;)








As far as I get Mahmud he means expanding the function in the neighbourhood of 0 using Taylor Series http://mathworld.wolfram.com/TaylorSeries.html (in this particular case Maclauren Series) approximation. This must work as far as the function is continious in given interval. The point is to find the closed form to that approximation's integral. Mahmudjon r u going to give us the closed form???

Also e^(kx) in the last term of the expansion does not seem to be reasonable as it will =1 EYEROLLES

[SALAR]

Here is what I have after integrating that awful expression:

1+1/5-1/(9*(3!))+1/(17*(4!))-.......+1/((n(n+1)+1)*(n+1)!)

Anybody got the same???

[Martingale]

Here is what I have after integrating that awful expression:

1+1/5-1/(9*(3!))+1/(17*(4!))-.......+1/((n(n+1)+1)*(n+1)!)

Anybody got the same???
Hi Salar,

yes, it's just pain in ass, if you wanna figure out the antiderivative that way. The prof Im taking the class with has told me today that no one has been able to find the exact form of F(x) function yet. But it's possible to find the antiderivative in a range (0 to infinity) using polar coordinates - that's what he said - and it's equal to square root of Pi divided by 2 (sqrt(P)/2)*. I will post the way he solved it after I understand it myself.:lol:
by the way, are you math major? Im taking this hardcore calculus after 3 years break.

* edited: Actually p/4 is the answer for the quadratic function. You take the root of p/4.

[Pythagor]

Salom Matematiklar!

Quyidagi funksiyani integralini tiopish kerak, eng kamida nima uchun integral olinmasiligini kursatish kerak. Don't prove just show some hints.
Matlabmi yoki mathcadmi hohlaganizni ishlatib javobini bersez buldi:) . Uzim u prog larda ishlomiman.

Hullas F(t)=e^(-t^2)

Rahmat oldindan.Bu funksiya -cheksizdan +cheksiz oraliqda integrallanuvchi funksiya bo'lib, uning integrali Fresnel integrali deb ataladi.

int[0, x, F(t)]=x-(x^3)/3*1!+x^5/5*2!-x^7/7*3!+ ...

erf(x)=2/sqrt(pi)*int[0, x, F(t)]

Yuqoridagi integral, cheksiz qatorlani integrallash haqidagi teoremani qo'llash natijasida xosil qilamiz.
xususiy xolda:

int[0,"cheksiz", F(t)]=sqrt(pi)/2

bu integral bir oz boshqacharo usuldan foydalanilib hisoblansa tezda chiqadi ya'ni ikkinchi o'zgaruvchi kiritish kerak va qutb koordinatalar sistemasiga o'tib hisoblash kerak.

[Mahmud]

javob quyidagicha:

http://img71.imageshack.us/img71/231/11fs1.jpg (http://imageshack.us/?x=my6&myref=http://imageshack.us/index.php)


;)

[Martingale]

Mahmud, Pifagor, rahmat javobiylar uchun.
Aka Mahmud, bularkanu odam tushunadigan tilda yozsa.:D

[SALAR]

Hi Salar,

yes, it's just pain in ass, if you wanna figure out the antiderivative that way. The prof Im taking the class with has told me today that no one has been able to find the exact form of F(x) function yet. But it's possible to find the antiderivative in a range (0 to infinity) using polar coordinates - that's what he said - and it's equal to square root of Pi divided by 2 (sqrt(P)/2)*. I will post the way he solved it after I understand it myself.:lol:
by the way, are you math major?

Hi no I am not a math major and you? I hope you will have fun with CALCULUS :D I havenot enjoyed this stuff for 1 year already anyway good luck.

Im taking this hardcore calculus after 3 years break.

* edited: Actually p/4 is the answer for the quadratic function. You take the root of p/4.

Nice to see some people doing real stuff (i mean real math)
after this posting i remembered my prof.'s words "Do it yourself at home Try to programm it in Mathlab" ;)

[SALAR]

Hi Salar,

yes, it's just pain in ass, if you wanna figure out the antiderivative that way. The prof Im taking the class with has told me today that no one has been able to find the exact form of F(x) function yet. But it's possible to find the antiderivative in a range (0 to infinity) using polar coordinates - that's what he said - and it's equal to square root of Pi divided by 2 (sqrt(P)/2)*. I will post the way he solved it after I understand it myself.:lol:
by the way, are you math major?

Hi no I am not a math major and you? I hope you will have fun with CALCULUS :D I havenot enjoyed this stuff for 1 year already anyway good luck.

Im taking this hardcore calculus after 3 years break.

* edited: Actually p/4 is the answer for the quadratic function. You take the root of p/4.

Nice to see some people doing real stuff (i mean real math)
after this posting i remembered my prof.'s words "Do it yourself at home Try to programm it in Mathlab" ;)

[Martingale]

Nice to see some people doing real stuff (i mean real math)
after this posting i remembered my prof.'s words "Do it yourself at home Try to programm it in Mathlab" ;)
Hi,
Im not math major either. Just taking up some math classes this semester.
So what are you majoring in then? Computer science?

p.s. I liked your signature very much. :)

[SALAR]

Hi,
Im not math major either. Just taking up some math classes this semester.
So what are you majoring in then? Computer science?

p.s. I liked your signature very much. :)

I major in Business Administration

what is your major?


Thank you for p.s. :)