Module 2 : Limits and Continuity of  Functions
Lecture 5 : Continuity  [ Section 5.2 : Continuity ]
     takes the value 0. Show that

(4) Let satisfy for all If is continuous at 0, show that is      continuous at every

(5)  Let , and be such that for every
      Show that is continuous.

(6)  Construct a function such that is one-one, onto but not continuous.

(7)  Let satisfy the following:
(i)  for some M, for all
(ii) for every  with .
     Show that is continuous.
  Optional Exercises:
 

Show that the function in Problem 4 satisfies the following relation:
      ,

(a) for all
(b) for all
(c) for all
(d) for all
Deduce that and for some

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