Question

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning

Answer 1

`lim_(x -> 2)` = 4

`lim_(x -> 2^-) f(x) = lim_(x -> 2^+) f(x)` = 4

When x approaches 2 from the left or from the right f(x) approaches 4.

Given that `lim_(x -> 2^-) (x) = lim_(x -> 2^+)f(x)` = 4

The existence or non-existence at x = 2 has no leaving on the existence of the limit of f(x) as x approaches to 2.

∴ We cannot conclude the value of f(2).