Need Assistance Understanding Taylor and Maclaurin Series

Hello,

I am in a fast-paced Calculus course where I must learn new concepts each week; I find it challenging to grasp the concepts while remaining on-pace and I am experiencing great difficulty. I have a few weeks before my semester is over, and thankfully, I have a passing grade.

I am really finding it difficult to grasp the concept of the Taylor and Maclaurin series. Specifically, I need your help in understanding:

1. The representation of functions by power series.
2. Finding the power series by integration.
3. General understanding of the Taylor & Maclaurin series.

I have requested a tutor at my school but I have not been successful in obtaining one. Also, I've researched on-line tools such as http://www.mathsisfun.com/algebra/taylor-series.html, but I'm just not grasping power series and such, very well. I would appreciate your assistance on the attachment; I would also appreciate any points you can provide to help me understand the concepts more clearly.

Thank you.

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