By the end of the unit the student will learn that...
Given a function f, the limit of f(x) as x approaches c is a real number R if f(x) can be made arbitrarily close to R by taking x sufficiently close to c (but not equal to c). If the limit exists and is a real number, then the common notation is lim f(x) = R
The concept of a limit can be extended to include one-sided limits, limits at infinity, and infinite limits.
A limit might not exist for some functions at particular values of x. Some ways that the limit might not exist are if the function is unbounded, if the function is oscillating near this value, or if the limit from the left does not equal the limit from the right.
Numerical and graphical information can be used to estimate limits.
Limits of sums, differences, products, quotients, and composite functions can be found using the basic theorems of limits and algebraic rules.
The limit of a function may be found by using algebraic manipulation, alternate forms of trigonometric functions, or the squeeze theorem.