what are limits and continuity in mathematics?

Question

what is its intuitive approiach?

Answer 1

Limits describe the behavior of a function as it approaches some point or value of one (or more) of its variables. For example
1+ 1/2 + 1/4 + ..... 1/2^n approaches 2 as a limit as n approaches infinity.
Continuity is a bit more subtle. We say a function is 'continuous' for some value of its variable if the limit of the function exists and is defined at that value of the variable. For example the value of x+2 is defined for all x and so x+2 is continuous. But something such as
(x² - 4)/(x-2) is continuous everywhere -except- at x=2 (since the denominator at x=2 is 0 and division by 0 is undefined).

HTH

Doug