[Solved] MTH631 Assignment 2 Solution & Discussion Fall 2019

MTH631 Real Analysis II Assignment 2 Solution & Discussion Fall 2019

Assignment # 02                         MTH631 (Fall 2019)
 

Maximum Marks:  20                 Due Date: 20 -01-2020

DON’T MISS THESE: Important instructions before attempting the solution of this assignment:

 •      To solve this assignment, you should have good command over 23 - 26 lectures.

Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the 23 to 26 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 format like scan images, etc. will not be accepted and we will grade zero marks correspond to these assignments.
 

Q1. Use Bolzano-Weierstrass theorem to show that if is an infinite sequence of nonempty compact sets and then is nonempty. Show that the conclusion does not follow if the sets are assumed to be closed rather than compact.

Q2. Let when (x,y)≠(0,0) and f(x,y)=0 when (x,y)=(0,0). Determine f(x,y)Is function continuous at the origin?