Download OU B.Sc 2018 Dec 2nd Year 3072 Real Analysis Question Paper

Download OU (Osmania University) BSc (Bachelor of Science - Maths, Electronics, Statistics, Computer Science, Biochemistry, Chemistry & Biotechnology) 2nd Year 1st Semester (Third Semester) (2-1) 3072 Real Analysis Previous Question Paper

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FACULTY OF SCIENCE
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PART- A {5 1: I I 33 Maria}
{short Answar Type}
Nate : Anamr any FIVE 131? than following quw?mF
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rF-?H i:-
1 Wins!? Iimitnfmasequanc?a?wmm 3.. =33:1 +__..??1-'.n * -
2 Leth=1andl =%?f3rnz'l.F1nd?-talimtn
3 lfn_=sin{%]?mn?ndlim smanandliminfan. -
4 mmal E _ unmargas if'a'ndhnly ifp}1.~
11:2 n??gn}?
I4: ? 2{_n? Ill. _ .1 .. ?
5 Furn=3.1.2. 3 .let 3. _[?5?J . Flndllm sup {3.3" lim4nf{a_.} .
i+2c435? m:
. .+J?..
E Lamu?
.PTW: that {fn} converges :.Ir1i!f::.~rr'?la.ur tn 0 an R-

2 Code No. 303%!
10 (a) [i] If the aaquanna (an) cunuarges. than prove that every subsaquence con verges
to the same limit.
{ii} State and prove BulzanunWaiarstraa-s theorem.
OR
(b) If {5?} mnvargas to a positive real number s and {tn} is any sequence then
preva that ?rm sup 5.1 tn = 3 lim sup tn.
1% gga?iILaftfa) be a sequence of functions de?ned and uniformly Cauchy on a set 3 5. R
' Then puma thait there exists a function f an S such that fn "-1 f uniformly an 3.
0R
[5} Derive an explicit formula for Engx? for J x | f- | and henae-eyahaate
n=f . '
33 ?5?:
11:! 3?
12113) Letf'be a bounded function an [a. b]. If F' and ?are partitions of [3. DJ and
'P 5; Fl. thigh prnuamat
L?. F) siL {f, a} g UH, u} 3 um f3)?.-
- :??R""*t ' . . .
{biz-Fta??h'thm-a bounded function fnn'wn Riemann integrable on La, 5] ?=- 11 is
mama: magnum. inmhich aasa th Ines of the integrais agree.
1-?: $45!?
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