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.

Answer 1

no

Answer 2

how come?

Answer 3

the limit may or may not exist

Answer 4

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

Answer 5

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

Answer 6

alright

Answer 7

consider the function f(x)

that takes the value 1 if x is rational and
the value 0 if x is irrational

Answer 8

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