Real Analysis BS 6 Semester/Term PU — University of the Punjab 2025
Discussion
Ask a question about this paper, or help someone else with theirs. Answers are emailed to whoever asked.
No questions yet — be the first to ask.
Need a paper or stuck on a question? Ask here — students reply and you get an email.
Ask about a paper-
BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
0 replies Reply → -
Literary criticism
1 reply Reply → -
this paper consists of 60 marks but now we have 35 marks paper.
1 reply Reply → -
Can you please tell me more past papers please because my exams are starting from next week
1 reply Reply → -
Did you provide the past papers of the science of society uos?
1 reply Reply →
More Real Analysis papers
See all
Paper text
UNIVERSITY OF THE PUNJAB
B.S. 4 Years Program / Sixth Semester - Spring 2025
Paper: Real Analysin Il
Course Code: MATH-307
Roll No. 7.
.....
Time: 3 Hrs. Marks: 60
THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDED
Q.1. Solve the following.
(6x5~30)
1. Show that = is integrable on any interval (0, k]
2. Show that the sum of two functions of bounded variation is of bounded variation.
3. Test the sequence (Ja) for uniform convergence, where
4. Examine the convergence of
5. If f and fa are two bounded and integrable functions on [a, b], then their product.
fi/½ is also bounded and integrable on (2. 5].
6. For the valucs of m and n for which the following integral converges?
Q.2.
Solve the following.
(3x10=30)
1. Show that the variation function of a function f of bounded variation is continuous
if and only if f is a continuous function.
2. A bounded function / is integrable on la, 5] iff for every e > 0, there exists a
partition P of a, 6] such that
U(P,f) - L(P,J) < c.
3. Check that whether fo 2m-1(1 -2)"-dr exists if and only if m, n are both positive.
