Solutions Modeling Dynamics of Life 3ed Adler - Chapter 4.4

4.4.1 Evaluate the following sums. ...
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4.4.2 Evaluate the following sums. ...
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4.4.3 Evaluate the following sums. ...
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4.4.4 Evaluate the following sums. ...
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4.4.6 Find the value of Δt and the values of ...when the interval from t = a to t = b is broken into n equal intervals of width Δt. a =0, b =2, n =10.
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4.4.6 Find the value of Δt and the values of ...when the interval from t = a to t = b is broken into n equal intervals of width Δt. a =0, b =2, n =10.
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4.4.7 Find the value of Δt and the values of ...when the interval from t = a to t = b is broken into n equal intervals of width Δt. a =2, b =3, n =5.
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4.4.8 Find the value of Δt and the values of ...when the interval from t = a to t = b is broken into n equal intervals of width Δt. a =2, b =3, n =100.
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4.4.9 Find the left-hand and right-hand estimates for the definite integrals of the following functions. f ( t ) = 2t, limits of integration 0 to 1, n = 5.
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4.4.10 Find the left-hand and right-hand estimates for the definite integrals of the following functions. f ( t ) = 2t, limits of integration 0 to 2, n = 5.
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4.4.11 Find the left-hand and right-hand estimates for the definite integrals of the following functions. ...
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4.4.12 Find the left-hand and right-hand estimates for the definite integrals of the following functions. ... limits of integration 0 to 1, n = 5.
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4.4.13 Write the left-hand and right-hand Riemann sums for the following cases using summation notation. f ( t ) = 2t , limits of integration 0 to 1, n = 5 (as in Exercise 9).
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4.4.14 Write the left-hand and right-hand Riemann sums for the following cases using summation notation. f ( t )=2t, limits of integration 0 to 2, n =5 (as in Exercise 10).
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4.4.15 Write the left-hand and right-hand Riemann sums for the following cases using summation notation. ... limits of integration 0 to 2, n =5 (as in Exercise 11).
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4.4.16 Write the left-hand and right-hand Riemann sums for the following cases using summation notation. ... limits of integration 0 to 1, n =5 (as in Exercise 12).
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4.4.17 Another way to think about the column ...in Table 4.4.1 is to think that the value of the function is approximated by the average of the values at the beginning and the end of the time interval. We pretend that the rate of change is ...during the interval from .... Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating the estimate.
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t ) = 2t , limits of integration 0 to 1, n = 5 (as in Exercise 9). Reference Table 4.4.1 ...
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4.4.18 Another way to think about the column ...in Table 4.4.1 is to think that the value of the function is approximated by the average of the values at the beginning and the end of the time interval. We pretend that the rate of change is ...during the interval from .... Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating the estimate.
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t )=2t, limits of integration 0 to 2, n =5 (as in Exercise 10). Reference Table 4.4.1 ...
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4.4.19 Another way to think about the column ...in Table 4.4.1 is to think that the value of the function is approximated by the average of the values at the beginning and the end of the time interval. We pretend that the rate of change is ...during the interval from .... Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating the estimate.
b. Write an expression for ... using summation notation.
c. Compute the sum. ... limits of integration 0 to 2, n =5 (as in Exercise 11). Reference Table 4.4.1 ...
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4.4.20 Another way to think about the column ...in Table 4.4.1 is to think that the value of the function is approximated by the average of the values at the beginning and the end of the time interval. We pretend that the rate of change is ...during the interval from .... Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating the estimate.
b. Write an expression for ... using summation notation.
c. Compute the sum. ... limits of integration 0 to 1, n =5 (as in Exercise 12). Reference Table 4.4.1 ...
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4.4.21 One other estimate of the integral, called ..., can be computed by pretending that the value during the interval from ...1 is the value of the function at the midpoint, or ...Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating this estimate for n =5. Make sure you see the difference from ...
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t ) = 2t , limits of integration 0 to 1, n = 5 (as in Exercise 9).
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4.4.22 One other estimate of the integral, called ..., can be computed by pretending that the value during the interval from ...1 is the value of the function at the midpoint, or ...Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating this estimate for n =5. Make sure you see the difference from ...
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t )=2t, limits of integration 0 to 2, n =5 (as in Exercise 10).
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4.4.23 One other estimate of the integral, called ..., can be computed by pretending that the value during the interval from ...1 is the value of the function at the midpoint, or ...Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating this estimate for n =5. Make sure you see the difference from ...
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t )=2t, limits of integration 0 to 2, n =5 (as in Exercise 10). ... limits of integration 0 to 2, n =5 (as in Exercise 11).
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4.4.24 One other estimate of the integral, called ..., can be computed by pretending that the value during the interval from ...1 is the value of the function at the midpoint, or ...Use this method to estimate the following integrals. In each case,
a. Draw a graph illustrating this estimate for n =5. Make sure you see the difference from ...
b. Write an expression for ... using summation notation.
c. Compute the sum. f ( t )=2t, limits of integration 0 to 2, n =5 (as in Exercise 10). ... limits of integration 0 to 1, n =5 (as in Exercise 12).
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4.4.25 Use summation notation and find the total number of offspring for each of the following organisms. The organism has 2 offspring in year 1, 3 offspring in year 2, 5 offspring in year 3, 4 offspring in year 4, and 1 offspring in year 5.
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4.4.26 Use summation notation and find the total number of offspring for each of the following organisms. The organism has 0 offspring in year 1, 8 offspring in year 2, 15 offspring in year 3, 24 offspring in year 4, 31 offspring in year 5, 11 offspring in year 6, and 3 offspring in year 7.
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4.4.27 Use summation notation and find the total number of offspring for each of the following organisms. The organism has ...offspring in years 0 through 6.
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4.4.28 Use summation notation and find the total number of offspring for each of the following organisms. The organism has ...offspring in years 0 through 7.
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4.4.29 Use Euler’s method to estimate the solutions of the following differential equations with the following parameters. Suppose that V (0) = 0 in each case. Your answer should exactly match one of the estimates in Exercise 12. ... estimate V (1) using Δt = 0.2 (as in Exercise 9).
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4.4.30 Use Euler’s method to estimate the solutions of the following differential equations with the following parameters. Suppose that V (0) = 0 in each case. Your answer should exactly match one of the estimates in Exercise 12. ... estimate V (2) using Δt = 0.4 (as in Exercise 10).
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4.4.31 Use Euler’s method to estimate the solutions of the following differential equations with the following parameters. Suppose that V (0) = 0 in each case. Your answer should exactly match one of the estimates in Exercise 12. ... estimate V(2) using Δt =0.4 (as in Exercise 11).
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4.4.32 Use Euler’s method to estimate the solutions of the following differential equations with the following parameters. Suppose that V (0) = 0 in each case. Your answer should exactly match one of the estimates in Exercise 12. ... estimate V(1) using Δt =0.2 (as in Exercise 12).
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4.4.33 Suppose the speed of a bee is given in the following table. ... Using the measurements on even-numbered seconds, find the left-hand and right-hand estimates for the distance the bee moved during the experiment.
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4.4.34 Suppose the speed of a bee is given in the following table. ... Using all the measurements, find the left-hand and righthand estimates for the distance the bee moved during the experiment.
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4.4.36 Suppose the speed of a bee is given in the following table. ... Figure out a way to use the measurements on odd-numbered seconds to estimate the distance the bee moved during the experiment. Think about the method in Exercises 21–24.
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4.4.36 Suppose the speed of a bee is given in the following table. ... Figure out a way to use the measurements on odd-numbered seconds to estimate the distance the bee moved during the experiment. Think about the method in Exercises 21–24.
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4.4.37 Biologists measure the number of aspen that germinate in four sites over eight years, but can only measure two sites per year. In the following table, NA indicates that no measurement was made in that year. In each case, compare the estimate with twice the number that germinated in the four years studied. Why are they different? ... The goal is to estimate the total number of aspen that germinated in each of the four sites during all eight years. In site 1, estimate the total number of aspen using a modification of the left-hand estimate.
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4.4.38 Biologists measure the number of aspen that germinate in four sites over eight years, but can only measure two sites per year. In the following table, NA indicates that no measurement was made in that year. In each case, compare the estimate with twice the number that germinated in the four years studied. Why are they different? ... The goal is to estimate the total number of aspen that germinated in each of the four sites during all eight years. In site 2, estimate the total number of aspen using a modification of the left-hand estimate.
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4.4.39 Biologists measure the number of aspen that germinate in four sites over eight years, but can only measure two sites per year. In the following table, NA indicates that no measurement was made in that year. In each case, compare the estimate with twice the number that germinated in the four years studied. Why are they different? ... The goal is to estimate the total number of aspen that germinated in each of the four sites during all eight years. In site 3, estimate the total number of aspen using a modification of the right-hand estimate.
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4.4.41 We will compare various methods used to estimate the solution of ... with p(0) = 0. We wish to find p(1).
a. Graph the rate of change as a function of t.
b. Use the right-hand estimate with Δt = 0.2, 0.1, and 0.02.
c. Use the left-hand estimate with Δt = 0.2, 0.1, and 0.02.
d. Try to figure out from your graph why the two estimates are the same.
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4.4.41 We will compare various methods used to estimate the solution of ... with p(0) = 0. We wish to find p(1).
a. Graph the rate of change as a function of t.
b. Use the right-hand estimate with Δt = 0.2, 0.1, and 0.02.
c. Use the left-hand estimate with Δt = 0.2, 0.1, and 0.02.
d. Try to figure out from your graph why the two estimates are the same.
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