IGNOU MTE 9 2026 - Verify Bozano-Weierstrass Theorem for the following sets:i) &nb

Question

Verify Bozano-Weierstrass Theorem for the following sets:
i)      Set of non-negative integers.
ii)     Interval $[-1, \infty]$
d)      Check whether the limit $\lim_{x \to 0} (x \operatorname{cosec} x)^x$ exists or not?

24 Mar 2026

Answer :

Word Count : 241

i) Consider the set of non-negative integers ( \mathbb{Z}_{\ge 0} = {0, 1, 2, 3, \dots } ). The Bolzano-Weierstrass Theorem states that every bounded sequence in ( \mathbb{R} ) has a convergent subsequence. Take any sequence ( a_n = n ) in this set. Clearly, ( a_n \to \infty ) as ( n \to \infty ), so it is unbounded. Since the

______ __________ _____ ____ ______ ___ __________ ___ ____ ____ ______.
___ __________ _________ ________ __________ ____ ________ ________ ____ ____ __________ ____.
____ ________ ___ ___ _____ _________ ______ _________ _________ _____ __________.
___ _________ ____ ________ _______ ____ __________ _____ _________ ___ ________ __________.
__________ _____ ________ __________ __________ ________ ____ _________ ___.
_________ _____ _______ ________ ____.
_______ _________ ______ _________ ________ ____ _______ __________.
________ _____ ___ ___ ____ ____ ___ ___ _______ ________ ______ ___.
_______ ___ __________ _________ ________ _________ ____ ________ _______ ______.
__________ _________ _________ ___ _________ __________ ________ ___.
___ ___ _________ ______ ________ _________ _________ ____ ____ _________ ____.
__________ ______ __________ __________ _________ ____ __________ ___ _____ _____ ___ ________.
__________ ____ _______ _______ __________.
_______ _____ _______ ____ ________ ________ ______ __________ _____ __________.
____ ___ ______ _____ ___ ___ ___ _____ __________ _________ _____ ___.
_______ __________ _________ ________ _________ _________ _________ ___ __________ __________.
_____ ________ ______ ___ _________.
______ _______ __________ ____ _____ ________ _____ ____ ________ __________ _____.
_________ ________ ________ ________.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers