Lesson 3: The limit of a function

The document defines the limit of a function as x approaches a value a. Specifically: 1) The limit of f(x) as x approaches a, written as lim f(x) = L, means that the values of f(x) can be made arbitrarily close to L by making x sufficiently close to a, without x being equal to a. 2) For the limit to exist, the left and right hand limits must be equal. The function must also be bounded near a and cannot oscillate with increasingly high frequency. 3) Formally, the limit is L if for any positive epsilon, there corresponds a positive delta such that if the absolute value of x - a is less than