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Lesson22_-_Areas_and_Distances_ws

Lesson22_-_Areas_and_Distances_ws - L n and R n Hint...

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Worksheet for Section 5.1 Areas and Distances V63.0121, Calculus I Spring 2010 1. Draw the graph of f ( x ) = e x on the interval [0 , 1]. We are going to find the area below the curve on this interval. 2. Estimate the area by computing with a calculator. (i) L 2 and R 2 (ii) L 4 and R 4 (iii) L 8 and R 8 3. Show that L n = 1 n 1 + e 1 /n + e 2 /n + · · · + e ( n - 1) /n = n X i =1 e ( i - 1) /n n R n = 1 n e 1 /n + e 2 /n + · · · + e = n X i =1 e i/n n . 1
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4. Find “closed form” expressions (i.e., without ellipses or sigmas) for
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Unformatted text preview: L n and R n . Hint. Remember that for any number r that 1 + r + r 2 + r 3 + · · · + r n-1 = 1-r n 1-r . 5. Find lim n →∞ L n and lim n →∞ R n . These limits should be the same, and their common value is the area of the region. 2...
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