# When is 0 any

Be a > 0, and let e®F.(e) a function that for -a a, but is not defined at the point e = 0. What is the limit value lime ® 0F.(e)?

This limit value intuitively exists if F.(e) against a number K strives whenevere gradually tends towards 0.

The formulation whenever refers to the way how e gradually approaches 0, any should be. That means we
• any sequence of numbers

e1, e2, e3, e4, e5,...

from the domain of F. can choose for the limn ® ¥en = 0 applies,

• and for each of these consequences

limn ® ¥F.(en)  =  K

receive. In other words: the associated sequence of function values

F.(e1), F.(e2), F.(e3), F.(e4), F.(e5),...

always strives towards the same number K.
If that is the case, we write

lime ® 0F.(e) = K

and denote K as the limit of the function F. for e ® 0. In this way, the Limit value of a function from the concept of Limit of a sequence of numbers (which corresponds to the intuitive idea of ​​a "step-by-step" approach).

If limn ® ¥F.(en) from the chosen sequence e1, e2, e3, e4, e5, ... depends or does not exist (for even one such sequence), we say that the limit lime ® 0F.(e) does not exist.