Suppose that a function f(x) is defined for all x in [-1,1]. Can anything be said about the existence of lim x-0 f(x)? Give reasons for your answer.

Question

Suppose that a function f(x) is defined for all x in [-1,1]. Can anything be said about the existence of lim x->0 f(x)? Give reasons for your answer.

zarkon · Answer

no

anonymous · Answer

how come?

zarkon · Answer

the limit may or may not exist

anonymous · Answer

so in other words, lim x->0- might not equal lim x->0+ ?

zarkon · Answer

that is one thing that could happen...it is possible the the right and left hand limits don't exist either

anonymous · Answer

alright

zarkon · Answer

consider the function f(x)

that takes the value 1 if x is rational and 
the value 0 if x is irrational

anonymous · Answer

limit  valuedepends up on the particular function f(x) under consideration.