Question

(a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 5e??² dx. M? = (Round your answers to six decimal places.) (b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI-89. ??? 5e??² dx = 4.431135 . (c) The error involved in the approximation of part (a) is E? = ??? 5e??² dx - M? = 0.000458 . (d) The second derivative f''(x) = . The value of K = max |f''(x)| on the interval [0, 4] = . (e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |E?| ? K(b-a)³/24n² = (where a and b are the lower and upper limits of integration, n the number of partitions used in part a). (f) Find the smallest number of partitions n so that the approximation M? to the integral is guaranteed to be accurate to within 0.001. n =

          (a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 5e??² dx.
M? = (Round your answers to six decimal places.)
(b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI-89. ??? 5e??² dx = 4.431135 .
(c) The error involved in the approximation of part (a) is
E? = ??? 5e??² dx - M? = 0.000458 .
(d) The second derivative f''(x) = .
The value of K = max |f''(x)| on the interval [0, 4] = .
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |E?| ? K(b-a)³/24n² = (where a and b are the lower and upper limits of integration, n the number of partitions used in part a).
(f) Find the smallest number of partitions n so that the approximation M? to the integral is guaranteed to be accurate to within 0.001. n =

(a) Use the Midpoint Rule, with n = 4, to approximate the integral ??? 5e??² dx.
M? = (Round your answers to six decimal places.)
(b) Compute the value of the definite integral in part (a) using your calculator, such as MATH 9 on the TI83/84 or 2ND 7 on the TI-89. ??? 5e??² dx = 4.431135 .
(c) The error involved in the approximation of part (a) is
E? = ??? 5e??² dx - M? = 0.000458 .
(d) The second derivative f”(x) = .
The value of K = max |f”(x)| on the interval [0, 4] = .
(e) Find a sharp upper bound for the error in the approximation of part (a) using the Error Bound Formula |E?| ? K(b-a)³/24n² = (where a and b are the lower and upper limits of integration, n the number of partitions used in part a).
(f) Find the smallest number of partitions n so that the approximation M? to the integral is guaranteed to be accurate to within 0.001. n =

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