Definition

We now define the limit, c and L are real numbers.

In symbols,

lim_x→c f(x) = L

if whenever x ≈ c but x ≠ c, f(x) ≈ L. When there is no number L satisfying the above definition, we say that the limit of f(x) as x approaches c does not exist. Notice that the limit

lim_x→c f(x)

depends only on the values of f(x) for x infinitely close but not equal to c. The value f(c) itself has no influence at all on the limit. In fact, it very often happens that

lim_x→c f(x)

exists but f(c) is undefined.