Section 2.2 The Limit of a Function “… that is what learning is. You suddenly understand something you’ve understood all your life, but in a new way.” - Doris Lessing

Definition: We Write: And say “the limit of , as x approaches a, equals L” If we can make the values of arbitrarily close to L (as close to L as we like) by taking x to be sufficiently close to a (on either side of a) but not equal to a.

Heaviside Function:

One-Sided Limits Definition We write And say the left-hand limit of as x approaches a [or the limit of as x approaches a from the left] is equal to L if we can make the values of arbitrarily close to L by taking x to be sufficiently close to a and x less than a. (Similar for right-hand limits)

If and only if And

Infinite Limits Find if it exists.

Definition: Let f be a function defined on both sides of a, except possibly at a itself. Then Means that the values of can be made arbitrarily large (as large as we please) by taking x sufficiently close to a, but not equal to a.

Definition: Let f be a function defined on both sides of a, except possibly at a itself. Then Means that the values of can be made arbitrarily large negative by taking x sufficiently close to a, but not equal to a.

Vertical Asymptotes

Find and

Find the vertical asymptotes of