Author Question: Given that f"(t) < 0 on the interval [a, b], what can be said about the relationship between the ... (Read 129 times)

Lobcity · **on:** May 26, 2021

Question 1

The following table gives values of an unknown function f(x) determined by experimental measurement. Find the best Midpoint Rule approximation you can for

dx based on the values given in the table.

x	f(x)
2.00	1.052
2.25	1.042
2.50	1.034
2.75	1.026
3.00	1.020
3.25	1.016
3.50	1.012
3.75	1.010
4.00	1.008

◦ M₄ = 2.0460
◦ M₄ = 2.0470
◦ M₄ = 2.0465
◦ M₄ = 2.0480
◦ M₄ = 2.0475

Question 2

Given that f"(t) < 0 on the interval [a, b], what can be said about the relationship between the values of the integral I =

dx, the Trapezoid Rule approximation T_n for I, and the Midpoint Rule approximation M_n for I?
◦ I < M_n < T_n
◦ M_n < I < T_n
◦ T_n < M_n < I
◦ T_n < I < M_n
◦ It is impossible to tell.

leeeep · **Reply #1 on:** May 26, 2021

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