1. What is a limit?
The limit of a function f(x) as x approaches a number is the value the function gets nearer to, as x gets nearer to the number. Simple, eh?
2. Why do we need to study limits?
The gradient function, one of the important functions in calculus, involves taking limits.
Without limits you would not be able to differentiate!
3. How can you tell if a function is continuous at a certain point?
The simple test is to trace over a graph with a pencil. The function will be continuous for all values of x if you do not have to remove the pencil from the paper.
Points of discontinuity include asymptotes and "holes".