February+Notes

__**Indeterminate Forms**__
 * __Monday, February 22, 2010__ **

// If its meaningless, it's indeterminate. // Be sure to remember that Infinity is a concept and not an actual number, meaning some calculations using Infinity cannot have a proper result. Also, 1/ (+/-) Infinity is equal to 0.
 * Indeterminate Forms: ** The value of a limit that can be 0 0, 0/0, 1 Infinity , Infinity - Infinity, Infinity/Infinity, 0 * Infinity or Infinity 0

A) __Proving 5/0 as undefined:__ //5/0 = k 5 = k * 0 5 = 0// But as well all know, 5 does not equal 0. Therefore, there is no value of k that can make this true. Thus, this is an undefined value.
 * Proving the Indeterminate to be false:**

B) __Proving 0/0 as an indeterminate:__ //0/0 = k 0 = k * 0 0 = 0// This means that k can be literally any value. Because there is an infinite amount of possibilities for the value of k, this must therefore be indeterminate as well.

Scenario A) //A situation in which there are an infinite amount of possibilities for an equivalent value (k)// Scenario B//) A situation in which there are no possible values that are equivalent (k)//
 * From these two examples, we can see two scenarios from which an indeterminate can arise:**

For more information, see the following sites:
 * [|http://www.sosmath.com/calculus/indforms/intro/intro.h]
 * []

· For defining Continuity (A lack of breaks in the graph line)/ (you can draw the graph without taking your hand off the paper) · For defining Derivatives · For Integration To simplify it into something we all know: As x --> blah (Where blah is a specific value or function) from the Right and Left, you need to ask yourself "What happens?". If a vertical asymptote, or "hole" is involved, then the graph is discontinuous and would require a limit.
 * __Uses of Limits:__**
 * The uses of limits are as follows: **

For more information, see the following sites: · __[]__ · __[|http://en.wikipedia.org/wiki/Limit_%28mathematics%29]__

__**Tuesday, February 23rd. 2010**__

**__Piecewise Functions:__** Functions where limits are put on the domain in order to apply different functions. When considering if it is continuous or discontinuous, one must consider it as a whole.
 * In this function, as x approaches zero from the positive side, y approaches 1 (fixed value). As x approaches zero from the negative side, y approaches negative infinity. Since y does not approach the same thing from either side, it is said to be discontinuous. **

This is how you would write it...
 * __Limit Notation:__**

For the previous example in "Piecewise Functions", we can also write the limit using limit notation.

In a second example, we can observe that although there is a value for x=2, it does not necessarily make the graph continuous.

In the graphs that were listed, the only difference between the two was the coefficient of x by 1. However, this caused g(x) to be factorable, and when simplified, it is a linear equation with a whole at x=-3. (observe my sketch)
 * __Graphs:__**

__**Geometric Series:**__



**__Wednesday, February 24th, 2010__** Conjugation, asymptotes and limits, and limit notation: 

__** Friday, February 26th, 2010 **__