A limit of a function is the value it approaches as the input approaches a certain value. The limit may be real, infinite, or undefined. The limit of f(x) as x approaches a number n may not necessarily reach f(n), it will get closer and closer to it, but not exactly reach it. Limits are useful for calculating the estimated value of a point that may not exist. Limits are also useful for calculating derivatives, which in turn are used to calculate rates of change.