
Re: MTH621 Assignment 1 Solution and Discussion
Assignment # 01 MTH621 (Spring 2020)Maximum Marks: 20 Due Date: 10 062020
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Also remember that you are supposed to submit your assignment in Word format any other like scan images, etc. will not be accepted and we will give zero marks correspond to these assignments.Q1. Let S and T be nonempty sets of real numbers and define
ST={st│s∈S,t∈T}.
Show that if S and T are bounded, then
sup(ST)=supSinfT
and
inf(ST)=infSsupT
Q2. For what integer n is
1/n!>8^n/(2n)!?
Prove your answer by induction. 
Assignment 2 MTH621: Real Analysis 1
Lectures: 28 TO 32
Due Date: 26012020
Instructions:
• Attempt all questions.
• Submit assignment within time, no assignment will be accepted through email.Question 1 For the functions f(x)=√x," " g(x)=(9x^2)/(x+1). Check the continuity of f°g.
Question 2 Let f be a real uniformly continuous function on the bounded set E in R. Prove that f is bounded on E.
Question 3 Is continuity implies differentiability? Justify your argument with an example.

Assignment 1 MTH621: Real Analysis 1
Lectures: 07 to 12
Due Date: 09122019
Instructions:
• Attempt all questions.
• Submit assignment within time, no assignment will be accepted through email.Question 1
Find the open cover for the setQuestion 2
Give TWO examples of a sequences that does not converge but its subsequence does converge.
MTH621 Assignment 2 Solution and Discussion

Assignment 2 MTH621: Real Analysis 1
Lectures: 28 TO 32
Due Date: 26012020
Instructions:
• Attempt all questions.
• Submit assignment within time, no assignment will be accepted through email.Question 1 For the functions f(x)=√x," " g(x)=(9x^2)/(x+1). Check the continuity of f°g.
Question 2 Let f be a real uniformly continuous function on the bounded set E in R. Prove that f is bounded on E.
Question 3 Is continuity implies differentiability? Justify your argument with an example.

Q. 1 Solution:
Q.2 Solution:
Q.3 Solution: