MacLaurin+Series

__** The MacLaurin Series **__

//There once was a man named Colin, // //In 1746 he had fallen. // //Quick with a quill, // //Not working at a mill, // //He was definitely not married to Josalyn. //

//He had a couple of theories, // //Which he then turned into a series. // //Powdered his wig, // //Did a quick jig, // //And called it the MacLaurin Series. // **__What is the MacLaurin Series?__** The MacLaurin Series is a specific example of the Taylor Series when a = 0. While the Taylor Series is in the form of the first equation below, because of the special condition that the MacLaurin Series entails, we are able to use the second equation below. Taylor Series: MacLaurin Series: You would use the MacLurin Series over the Taylor Series because you don't need to worry how the value of x changes by 'a'; however the Taylor Series still exists because there are several functions that can't be used with the MacLaurin Series.

For example, ln(x) is undefined at f(0), f ' (0) is also undefined as f ' (x) is 1/x and infact all derivatives of ln(x) are undefined. Because the MacLaurin Series involves mutiplying my the nth derivative, we are unable to use it because we can't mutiply by an undefined number. media type="youtube" key="cjPoEZ0I5wQ" height="349" width="425"
 * __A word of Caution:__**

**__Examples of the MacLaurin Series:__**  __[]__

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Now, solve the following Maclaurin Series:

1) sin(x)

2)e^(x)

3) ln(x)

4)ln(1+x) Solutions, starting on page 4 of the document: Solutions