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equidistant subdivision of [0, 2] in 20 subintervals to approximate 1. Using an sin(z) dr by the midpoint rule, esti...
Let EM represent the error in using the Midpoint Rule with subintervals to approximate S. f(x) dx. Then K(b - a) TEM 24n2 where K is the maximum number that the absolute value of IF"(x) achieves for asx<b. Use this inequality to find the minimum number, 17 of subintervals necessary to guarantee that the Midpoint Rule will approximate the integral dx to be accurate to within 0.001. 80 O 358 253 114
-4 using Estimate the minimum number of subintervals to approximate the value of 5 sin (x9)dx with an error of magnitude less than 2x 10 -6 a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule. The minimum number of subintervals using the trapezoidal rule is (Round up to the nearest whole number.) The minimum number of subintervals using Simpson's rule is (Round up to the nearest even whole number.)
-4 using Estimate...
(a) Approximate the definite integral using n-6 equal width subintervals and: the Midpoint Rule. 0 Simpson's Rule. s- 1 ob) Glven that / vd2- 4 tnd ne aboolute valuse of the exact emor to sik deimal pinces In each apprximation trom (e).
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1. Approximate the following integral, exp(r) using the composite midpoint rule, composite trapezoid rule, and composite Simpeon's method. Each method should invol + l integrand evaluations, k 1: 20. On the same plot, graph the absolute error as a function of n. ve exactly n = 2k 2. Approximate the integral from Question 1 using integral, Matlab's built-in numerical integrator. What is the absolute error?
1. Approximate the following integral, exp(r) using...
Calculate the absolute and relative error using the midpoint rule Question Determine the absolute error when using the midpoint rule to find ſo-(4x3 + 8x) dx using 4 subintervals. Enter an exact value. Do not enter the answer as a percent.
(a) Estimate So sin(x + 1) dx by using either Simpson's Rule or Trapezoidal Rule with n= 6 (Round the answer to 6 decimal places). (b) Estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10-4 by the rule you used in part (a).
1 Find the midpoint and trapezoid rule approximations to S cos zxdx using n=25 subintervals. Compute the relative error of each approximation. 0 T(25) (Do not round until the final answer. Then round to six decimal places as needed.)
Find the midpoint rule approximations to the following integral. 3 X dx using n 1, 2, and 4 subintervals. 1 M(1)- (Simplify your answer. Type an integer or a decimal.)
Find the midpoint rule approximations to the following integral. 3 X dx using n 1, 2, and 4 subintervals. 1 M(1)- (Simplify your answer. Type an integer or a decimal.)
Approximate the integral below using 4 subintervals and: (x + 1) dx (a) The Simpson's rule (5 points): (b) Compare your estimate with the exact value of the integral. (5 points)
2. Use the centered difference formula to approximate f(z) for f sin and z1, using h 1, 1/10, 1/100, ...., 1 /1015. Plot the absolute error. Explain the behavior as h decreases. (Hint: Read the last subsection of §11 concerning roundoff error.) Why does this instability not arise with -0?
2. Use the centered difference formula to approximate f(z) for f sin and z1, using h 1, 1/10, 1/100, ...., 1 /1015. Plot the absolute error. Explain the behavior as...