Learning Objective 1.1A

Learning Objective 1.1A(a) Students will be able to express limits symbolically using correct notation and (b) Interpret limits expressed symbolically.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In math, we tend to use symbols because words just take too long to write. No one wants to write "twenty-seven minus nine" when they could write "27 - 9". Limits are no exception. But you need to know what all these fancy new symbols really mean if you want to write expressions that make sense.

EK1.1A1 Shows you the basics which will let you write most limits

EK1.1A2 Shows you special cases involving one-sided limits and infinity

EK1.1A3 Shows you more about limits that don't exist

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Essential Knowledge 1.1A1 Students will know 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

.

Essential Knowledge 1.1A2 Students will know that the concept of a limit can be extended to include one-sided limits, limits at infinity, and infinite limits.

Essential Knowledge 1.1A3 Students will know that 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.