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The following table gives the the approximate amount of emissions, E, of nitrogen oxides in millions of metric tons per year in the US. Let

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The following table gives the the approximate amount of emissions, E, of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E = f(t). t 1940 1950 1960 1970 1980 1990 E 7.3 9.5 12.5 18.9 21.2 19.6 (a) Using left endpoints, estimate the integral: . 50 1 f ( t ) at = (b) Using right endpoints, estimate the integral: . 50 f(t) dt ~ Be sure that you know what the units of your answer are, and what its meaning is! (Original data from the Statistical Abstract of the US, 1992)Consider the integral 16 / (2:192 -|- 433 + 2) d3: 4 (21) Find the Riemann sum for this integral using left endpoints and n = 3. L3 = f. (b) Find the Riemann sum for this same integral, using right endpoints and n = 3. R3 = I; 6 Consider the integral 2 1 + 25 dx. Which of the following expressions represents the integral as a limit of Riemann sums? 2+ - 4i O A. lim n n-too 1+ (2+ 4 ) n 2+ - O B. lim n n-too i=1 2 1 + (2+ 7 5 n 4 2+ - 4i O C. lim n n-too n 1 + ( 2 + +2 ) n 6 2 + 62 OD. lim n n-too n 1+ (2+ 62 ) 2 + 62 OE. lim n n-too 1+ 2 + 62 5 2 + 62 OF. lim i= 1 n 1 + 2 + 62 ) 5

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