Re: MTH621 Assignment 1 Solution and Discussion
Assignment # 01 MTH621 (Spring 2020)
Maximum Marks: 20 Due Date: 10 -06-2020
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Q1. Let S and T be nonempty sets of real numbers and define
S-T={s-t│s∈S,t∈T}.
Show that if S and T are bounded, then
sup(S-T)=supS-infT
and
inf(S-T)=infS-supT
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: 26-01-2020
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)=(9-x^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: 09-12-2019
Instructions:
• Attempt all questions.
• Submit assignment within time, no assignment will be accepted through email.
Question 1
Find the open cover for the set
Question 2
Give TWO examples of a sequences that does not converge but its subsequence does converge.
MTH621 Assignment 2 Solution and Discussion
MTH621 - Real Analysis I
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Assignment 2 MTH621: Real Analysis 1
Lectures: 28 TO 32
Due Date: 26-01-2020
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)=(9-x^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.
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Q. 1 Solution:
Q.2 Solution:
Q.3 Solution:
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