Pre-Calculus

� (Video) http://www.calculus-help.com/tutorials

� What is a limit? � A limit is the intended height of a function

� Is it possible for limits NOT to exist? � yes � Are there different ways to find a limit? � Yes

� Let’s discuss some of the notation that comes up with limits, the proper way to write, and verbally pronounce.

� (a) The limit of the function �

�as x approaches 0.

� (b) The limit of the function �

�as x approaches 0

from the left side.

� (c) The limit of the function �� � 1 as xapproaches 2 from the right side.

� A function f (x) has a limit as x approaches c if and only if the right-hand and left hand limits at c exist and are equal.

� Symbolically,

� Examples: Using a graphing calculator, complete the following:

� As you can see, from the table and graph, the intended height is: 2

� As you can see, from the table and graph, the intended height is: 1

� As you can see, from the table, the intended height is: infinity (and at this time we will say since you cannot give a definitive number, infinity will be does not exist (DNE)).

� If c is any number in the domain of the given trigonometric function, then :

� What do all three of these graphs have in common?

� Find the limit as x approaches 1 for each.

� A function f ( x ) has a limit as x approaches c if and only if the right-hand and left hand limits at c exist and are equal.

� You need to show that: