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MC 2025 In-course Diagnostics for Undergraduate Mathematics MATH140 WP

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Evaluate the Riemann sum for for  with four subintervals and using the right endpoints in each subinterval.  Select the correct answer.
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The formula of the left Riemann Sum approximation of obtained by dividing the closed interval into n equals sub-intervals is:
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The formula of the right Riemann Sum approximation of =  obtained by dividing the closed interval [0, 1] into equal sub-intervals is:

 

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Approximate using the Riemann sum with four subintervals and using the left endpoints in each sub-interval.  Select the correct answer.
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The graph of a function is pictured below.

Q3Graph

Use the graph of to compute the Riemann Sum when the interval is subdivided into ten equal subintervals and = , = ,..........., = . (i.e. the sample points are the right end-points). The value of this Riemann sum is:

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Use the graph of a function pictured below to estimate . Select the correct answer.

Q4Graph

                                         

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Use the graph of a function pictured below to approximate by the Riemann sum corresponding to = and using the left endpoints in each subintervals. Select the correct answer. 

Q1Graph

                                   

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The following table gives function values of a continuous function in the closed interval .

Q2table

What is the absolute value of the difference between a right endpoint sum and a left endpoint sum when approximating with 3 sub-intervals?

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Let be a continuous function on the closed interval [0,2].  If , then the greatest possible value of is:
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The following table shows various Riemann sum approximations to using right endpoints of n subintervals of equal length of the interval [0,1].    

Q5graph

    

Which of the following statements best describes the limit of the Riemann sums as n approaches infinity?

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