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	<title>The Science That Draws Necessary Conclusions</title>
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	<description>To Learn Math</description>
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		<title>The Science That Draws Necessary Conclusions</title>
		<link>http://necessaryconclusions.wordpress.com</link>
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		<item>
		<title>Taking a Look at Wolfram&#124;Alpha</title>
		<link>http://necessaryconclusions.wordpress.com/2009/08/24/taking-a-look-at-wolframalpha/</link>
		<comments>http://necessaryconclusions.wordpress.com/2009/08/24/taking-a-look-at-wolframalpha/#comments</comments>
		<pubDate>Mon, 24 Aug 2009 13:26:01 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[not math]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=145</guid>
		<description><![CDATA[Lets take a small break from learning and look at a somewhat new tool. Wolfram&#124;Alpha is a &#8220;computational knowledge engine that draws on multiple sources to answer user queries directly.&#8221; While this tool has numerous applications, I will take a look at how it can be used for math. Simply by entering a number, you [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=145&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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			<media:title type="html">46 - Wolfram&#124;Alpha</media:title>
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			<media:title type="html">x^2 - Wolfram&#124;Alpha</media:title>
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		<item>
		<title>Shortcuts for Finding Derivatives</title>
		<link>http://necessaryconclusions.wordpress.com/2009/08/13/shortcuts-for-finding-derivatives/</link>
		<comments>http://necessaryconclusions.wordpress.com/2009/08/13/shortcuts-for-finding-derivatives/#comments</comments>
		<pubDate>Thu, 13 Aug 2009 14:35:49 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Calculus]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=117</guid>
		<description><![CDATA[Using the derivative formula to find the derivative of a function is a hassle. There are many shortcuts to finding the derivative. The first one is the Power Rule. It can be used with functions which are equal to a polynomial like . Each term&#8217;s coefficient is multiplied by the exponent and the exponent decreases [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=117&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>2</slash:comments>
	
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		<item>
		<title>Intro to Derivatives</title>
		<link>http://necessaryconclusions.wordpress.com/2009/02/16/intro-to-derivatives/</link>
		<comments>http://necessaryconclusions.wordpress.com/2009/02/16/intro-to-derivatives/#comments</comments>
		<pubDate>Mon, 16 Feb 2009 16:20:37 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Calculus]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=83</guid>
		<description><![CDATA[The derivative of f(x) at point a is the slope of the tangent line at point a or . Allow me to explain. As seen in the picture above, a secant line is a line that passes through two points of a function and a tangent line touches only one. The function to find the [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=83&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">Derivative Formula GIF</media:title>
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			<media:title type="html">deriv_alg_1</media:title>
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		<item>
		<title>Algebraically Finding a Limit</title>
		<link>http://necessaryconclusions.wordpress.com/2008/12/05/algebraically-finding-a-limit/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/12/05/algebraically-finding-a-limit/#comments</comments>
		<pubDate>Fri, 05 Dec 2008 14:36:16 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Calculus]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=66</guid>
		<description><![CDATA[Finding a limit may be as simple as plugging a number into a function, or it may require manipulating the function if it is undefined at that point. is a linear function continuous at all points. The limit as x approaches any point a is f(a), . To find the limit as x approaches 2 [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=66&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<item>
		<title>Continuity and Discontinuity</title>
		<link>http://necessaryconclusions.wordpress.com/2008/10/02/continuity-and-discontinuity/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/10/02/continuity-and-discontinuity/#comments</comments>
		<pubDate>Fri, 03 Oct 2008 01:49:06 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Calculus]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=51</guid>
		<description><![CDATA[A function is said to be continuous at a if . A continuous function&#8217;s points are all connected. Below are examples of functions that are not continuous. The graph above is an example of jump discontinuity. There is jump continuity at each integer. The limit from the positive and negative direction of each is a [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=51&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/09/jump.jpg?w=300" medium="image">
			<media:title type="html">Jump Discontinuity</media:title>
		</media:content>

		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/09/infinite.jpg?w=300" medium="image">
			<media:title type="html">Infinite Discontinuity</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/09/removable.jpg?w=300" medium="image">
			<media:title type="html">Removable Discontinuity</media:title>
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		<item>
		<title>Intro to Limits</title>
		<link>http://necessaryconclusions.wordpress.com/2008/09/26/intro-to-limits/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/09/26/intro-to-limits/#comments</comments>
		<pubDate>Fri, 26 Sep 2008 19:30:47 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Calculus]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=30</guid>
		<description><![CDATA[A limit is what f(x) approaches as x approaches a value from both directions. The limit of a function f(x) as x approaches 0 is written as . f(x) is pictured above. It is evident that . As x gets closer to the value 3, f(x) gets closer to 5. f(x) never needs to equal [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=30&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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			<media:title type="html">easy_limit</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/09/removed_point_limit.jpg" medium="image">
			<media:title type="html">removed_point_limit</media:title>
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			<media:title type="html">1_over_x_limit</media:title>
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		<item>
		<title>Quadratic Function and the Quadratic Formula</title>
		<link>http://necessaryconclusions.wordpress.com/2008/06/20/quadratic-function-and-the-quadratic-formula/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/06/20/quadratic-function-and-the-quadratic-formula/#comments</comments>
		<pubDate>Fri, 20 Jun 2008 14:37:20 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Functions]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=28</guid>
		<description><![CDATA[Quadratic equations are equations that have the variable raised to the second power. They are in the form of . The graph of a quadratic equation looks like a cross between a U and a V. There are two roots (where the funtion returns 0 also called a zero); they can be imaginary and both [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=28&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
		<wfw:commentRss>http://necessaryconclusions.wordpress.com/2008/06/20/quadratic-function-and-the-quadratic-formula/feed/</wfw:commentRss>
		<slash:comments>2</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/06/function_x2.png" medium="image" />
	</item>
		<item>
		<title>Linear Functions</title>
		<link>http://necessaryconclusions.wordpress.com/2008/04/23/linear-functions/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/04/23/linear-functions/#comments</comments>
		<pubDate>Wed, 23 Apr 2008 20:59:41 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Functions]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=26</guid>
		<description><![CDATA[A linear function is a function whose graph is a line. They are written in three forms: slope-intercept form, point-slope form, and general form. Slope-intercept is a common way to write a linear function. Its form is . The graph of is shown in the image above. The variables m and b modify this graph. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=26&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>2</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/04/function-x.png?w=500" medium="image" />

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	</item>
		<item>
		<title>Introduction to Functions</title>
		<link>http://necessaryconclusions.wordpress.com/2008/04/16/introduction-to-functions/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/04/16/introduction-to-functions/#comments</comments>
		<pubDate>Thu, 17 Apr 2008 01:29:56 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Functions]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=20</guid>
		<description><![CDATA[A relation is composed of ordered pairs of numbers. The set of the first numbers is the domain and the set of the second values is the range of the relation. The first number is called the abscissa and the second number is called the ordinate. The ordered pairs can be graphed using the Cartesian [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=20&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>2</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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	</item>
		<item>
		<title>Posting Continues</title>
		<link>http://necessaryconclusions.wordpress.com/2008/04/16/posting-continues/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/04/16/posting-continues/#comments</comments>
		<pubDate>Thu, 17 Apr 2008 00:22:18 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[not math]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=19</guid>
		<description><![CDATA[Sorry for the lack of lessons over the past week and a half. I have been on vacation, but now it is time to get back to work. I will post the test answers. Then I will either do some posts on algebra, functions and graphing, or continue with more on trigonometry.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=19&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<item>
		<title>Trig Test Part One Posted</title>
		<link>http://necessaryconclusions.wordpress.com/2008/04/06/trig-test-part-one-posted/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/04/06/trig-test-part-one-posted/#comments</comments>
		<pubDate>Mon, 07 Apr 2008 01:23:43 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Assesment]]></category>
		<category><![CDATA[Trigonometry]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=18</guid>
		<description><![CDATA[I have made an assessment for what was taught so far. You can see it in the sidebar on the right or click on this. Unfortunately, I realized I forgot to mention the relevance of which quadrant the angle lies in. I will edit that into the special angles post. The answers will be posted [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=18&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>0</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<title>Coterminal and Reference Angles</title>
		<link>http://necessaryconclusions.wordpress.com/2008/04/02/coterminal-and-reference-angles/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/04/02/coterminal-and-reference-angles/#comments</comments>
		<pubDate>Thu, 03 Apr 2008 01:25:36 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Trigonometry]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=14</guid>
		<description><![CDATA[Before I create a test for the posts up to now, it is important for me to discuss coterminal and reference angles. There are two parts of an angle, the initial side and terminal side. As the names imply, the initial side is the side where an angle begins and the terminal side is where [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=14&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/04/standard_pos_angle.png" medium="image">
			<media:title type="html">Angle Standard Position</media:title>
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	</item>
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		<title>Special Angles</title>
		<link>http://necessaryconclusions.wordpress.com/2008/03/31/special-angles/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/03/31/special-angles/#comments</comments>
		<pubDate>Mon, 31 Mar 2008 20:59:08 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Trigonometry]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=12</guid>
		<description><![CDATA[The special angles are , , and . could also be considered a special angle. The values of the trigonometric functions of these angles have specific values. It would be best to commit these values to memory. Consequently, this lesson is mostly memorization. First, it is useful to know the radian measures of these angles. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=12&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>1</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/03/unit_circle_angles_trig.png" medium="image">
			<media:title type="html">Unit Circle Trig Functions</media:title>
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		<title>The Other Trig Functions</title>
		<link>http://necessaryconclusions.wordpress.com/2008/03/28/the-other-trig-functions/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/03/28/the-other-trig-functions/#comments</comments>
		<pubDate>Fri, 28 Mar 2008 13:27:36 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Trigonometry]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=10</guid>
		<description><![CDATA[Besides sine and cosine, there are four other trigonometric functions. They are tangent, secant, cosecant, and cotangent. Each can be found using sine and cosine. Tangent is equal to the sine of an angle divided by its cosine, or . The cosecant, secant, and cotangent functions are the reciprocals of sine, cosine, and tangent respectively. [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=10&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/03/trigonometric_triangle.png" medium="image">
			<media:title type="html">Trigonometric Triangle</media:title>
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		<item>
		<title>Sine and Cosine</title>
		<link>http://necessaryconclusions.wordpress.com/2008/03/25/sine-and-cosine/</link>
		<comments>http://necessaryconclusions.wordpress.com/2008/03/25/sine-and-cosine/#comments</comments>
		<pubDate>Wed, 26 Mar 2008 00:01:56 +0000</pubDate>
		<dc:creator>todizzle91</dc:creator>
				<category><![CDATA[Trigonometry]]></category>

		<guid isPermaLink="false">http://necessaryconclusions.wordpress.com/?p=6</guid>
		<description><![CDATA[There are six trigonometric functions. The two most important ones are sine and cosine. The others can be derived from these two functions. The trigonometric functions are based on the ratios between sides that exist in right triangles. Sine is the ratio of the side opposite of to the hypotenuse. Therefore, . Cosine is the [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=necessaryconclusions.wordpress.com&amp;blog=3237499&amp;post=6&amp;subd=necessaryconclusions&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
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		<slash:comments>3</slash:comments>
	
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			<media:title type="html">todizzle91</media:title>
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		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/03/trigonometric_triangle.png" medium="image">
			<media:title type="html">Trigonometric Triangle</media:title>
		</media:content>

		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/03/unit_circle.png" medium="image">
			<media:title type="html">Unit Circle</media:title>
		</media:content>

		<media:content url="http://necessaryconclusions.files.wordpress.com/2008/03/sine_animation.gif" medium="image">
			<media:title type="html">Sine Animation</media:title>
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