Question

How do I solve this? Help please! "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.

Answer 1

For a limit to exist, it has to approach the same value from values slightly lower than the number (zero in this case) and slightly higher. Does this statement, that the function exists, guarantee that just above zero and just below zero are equal? consider the Heaviside function (look it up).

Answer 2

Based upon this then its correct right? Because it sustains the limit requirements slightly below and slightly above zero?

Answer 3

There may be a jump at zero.

Answer 4

Mathematically how do I note this?

Answer 5

graphically?

Answer 6

yes

Answer 7

limit isn;t the same value from left and right, but exists everywhere in domain [-1,1]

Answer 8

thanks