Question

what is the exact definition of limit?

Answer 1

a limit is the value that a function or sequence "approaches" as the input or index approaches some value

Answer 2

delta epsilon defination of limit?

Answer 3

Did that link help you out? Are you still stuck?

Answer 4

Definition: \[\lim_{x \rightarrow a}f(x) = L\]means:
for every epsilon > 0
there is a delta > 0 so that:
if 0 < |x - a| < delta
then |f(x) - L| < epsilon

You have to learn this by heart!
After that it takes some time and practice to understand what it means...

It says in precise mathematical language: the nearer you choose your x-value to a, the nearer f(x) will be to L.