Explanation Formula used: “Let f be a function defined on the interval [ a , b ] and partition the interval into n subintervals of equal length Δ x = b − a n with endpoints a = x 0 < x 1 < x 2 < … < x n = b . Then, Left sum is defined: L n = f ( x 1 ) Δ x + f ( x 2 ) Δ x + … + f ( x n − 1 ) Δ x . Right sum is defined: R n = f ( x 1 ) Δ x + f ( x 2 ) Δ x + … + f ( x n ) Δ x . Theorem used: ( Error bounds for approximation of area by left or right sums ) “Let f ( x ) > 0 and is either increasing or decreasing on [ a , b ] , then | f ( b ) − f ( a ) | b − a n is an error bound for the approximation of the area between the graph of f and the x axis, from x = a to x = b , by L n or R n .” Calculation: Divide the interval [ 0 , 60 ] into 3 subinterval. Then, the equal length Δ x = 60 − 0 3 = 60 3 = 20 By the help of the equal length, the endpoints becomes, a = 0 < 20 < 40 < 60 = b The left end points are 0, 20 and 40, respectively. The right end points are 20, 40 and 60, respectively. The values of N ( t ) at the left end points t from the table are 10, 51 and 68, respectively

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ISBN: 9780135961438

Author: Barnett

Publisher: PEARSON CO

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Chapter 5.4, Problem 73E

To determine

To estimate: The area under the graph of N(t) from t=0 to t=60 using the left and right sum with n=3 and calculate its error bound for each.

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Chapter 5.4, Problem 72E

Chapter 5.4, Problem 74E

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Chapter 5 Solutions

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To estimate: The area under the graph of N ( t ) from t = 0 to t = 60 using the left and right sum with n = 3 and calculate its error bound for each.

Solution Summary: The author estimates the area under the graph of N(t) using the left and right sum with n=3 and calculates its error bound for each.

To estimate: The area under the graph of N(t) from t=0 to t=60 using the left and right sum with n=3 and calculate its error bound for each.

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Chapter 5 Solutions