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Upper and Lower sums & Riemann sums

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data
    2. Relevant equations
    3. The attempt at a solution

    I have attachments that can answer the above template, and please look at the attachments if you are trying to help me.

    I have two questions regarding upper and lower sums & Riemann sums.

    So, the attachments 1 & 2 are example 5 and 6 from the book that I am using. I have underlined in red where I cannot understand how the examples are solved.

    Where do these two underlined inequalities come from? How can I find these inequalities (method/approach)?

    I want to make sure that I understand these and practice some other questions of the same type, so if you happen to have some question(s) of this type, please inform me.

    The third attachment, 3 is the continuation of explanation of Riemann sums, and then the book starts by llPll, which I do not understand, and end the chapter with some limit, which I also do not understand.

    My name is Ace, and I will say hello now since you've read through my lines. Please clarify these questions if you have a clue and can explain in a good way. Thanks.
     

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  2. jcsd
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