Consider the following table of function values. X 0.0 7.4 2.0 8.3 0.4 0.8 1.2 1.6 f(x) X f(x) 3.2 8.9 2.4 8.6 8.7 2.8 7.6 8.6 3.2 8.4 8.9 (a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.) 1³ Jo f(x) dx (b) Suppose it is known that -5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
Consider the following table of function values. X 0.0 7.4 2.0 8.3 0.4 0.8 1.2 1.6 f(x) X f(x) 3.2 8.9 2.4 8.6 8.7 2.8 7.6 8.6 3.2 8.4 8.9 (a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.) 1³ Jo f(x) dx (b) Suppose it is known that -5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.4: Total Differentials And Approximations
Problem 9E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...
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Transcribed Image Text:Consider the following table of function values.
X
0.0
0.4
0.8
1.2
1.6
f(x) x f(x)
7.4 2.0 8.3
3.2
8.9 2.4 8.6
8.7 2.8
8.6 3.2 8.4
8.9
7.6
(a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.)
f(x) dx
(b) Suppose it is known that −5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
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