A function f is continous at x=c if: f(c) is defined
lim x ->c f(x) exists
lim x->c f(x) = f(c)
A function is continuous at an interval if the function is continuous at eachpoint on the interval.
Limit: Given a function (f), the limit of the function f(x) as it's input value (x) approaches an inputted value (c) which is a real number (R) if the output value of f(x) can be made arbitrarily close to (R) but not equal to the inputted value (c).