MTH621 - Real Analysis I

Re: MTH621 Assignment 2 Solution and Discussion

Re: MTH621 Assignment 1 Solution and Discussion Assignment # 01 MTH621 (Spring 2020) Maximum Marks: 20 Due Date: 10 -06-2020 DON’T MISS THESE: Important instructions before attempting the solution of this assignment: • To solve this assignment, you should have good command over 1 - 10 lectures. Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 1 to 10 lectures. • Upload assignments properly through LMS, No assignment will be accepted through email. • Write your ID on the top of your solution file. Don’t use colorful back grounds in your solution files. Use Math Type or Equation Editor Etc. for mathematical symbols. You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students. Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks. 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 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.