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Chapter 5 | Integration
41. The following table gives the percent growth of the U.S. population beginning in July of the year indicated. If the U.S. population was 281,421,906 in July 2000, estimate the U.S. population in July 2010. Year % Change/Year
43.
2000 1.12
2001 0.99
2002 0.93
44.
2003 0.86
2004 0.93
2005 0.93
2006 0.97
2007 0.96
45.
2008 0.95
2009 0.88
Table 5.5 Annual Percentage Growth of U.S. Population, 2000–2009 Source : http://www.census.gov/ popest/data.
( Hint: To obtain the population in July 2001, multiply the population in July 2000 by 1.0112 to get 284,573,831.) In the following exercises, estimate the areas under the curves by computing the left Riemann sums, L 8 . 42.
46. [T] Use a computer algebra system to compute the Riemann sum, L N , for N =10, 30, 50 for f ( x ) = 1− x 2 on [−1, 1]. 47. [T] Use a computer algebra system to compute the Riemann sum, L N , for N =10, 30, 50 for f ( x ) = 1 1+ x 2 on [−1, 1].
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