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5 AY Estimate the minimum number of subintervals to approximate the value of (31° + 5t)...
-4 using Estimate the minimum number of subintervals to approximate the value of 5 sin (x9)dx...
-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...
J(se.7)dt Estimate the minimum number of subintervals to approximate the value of with an error of magnitude less t...
J(se.7)dt Estimate the minimum number of subintervals to approximate the value of with an error of magnitude less than 104 using 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.)
J(se.7)dt Estimate the minimum number of subintervals to approximate the value of with an error of magnitude less than 104 using a. the error estimate...
(a) Estimate So sin(x + 1) dx by using either Simpson's Rule or Trapezoidal Rule with...
(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).
lo Estimate the MinimUM number oF Su bintervalS to approximate the Valve oF an MEO 2...
lo Estimate the MinimUM number oF Su bintervalS to approximate the Valve oF an MEO 2 + Xb error of Magntude less than 4xlo USING aTre error estimate Formula For Trape Zodal Rule. the minrmum numlber Of a Subin tervals USing the Trapezodial Rule is? bThe error estimate Formula for SiMpSons Rule, The MinImUm number of Subintervals USing Simpson 's Rule 1s
lo Estimate the MinimUM number oF Su bintervalS to approximate the Valve oF an MEO 2 + Xb...
Approximate the integral below using 4 subintervals and: (x + 1) dx (a) The Simpson's rule...
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)
Numerical Methods Consider the integral 2 (a) [16 marks] Use the composite Simpson's rule with four intervals to calculate (by hand) approximate value of the integral Calculate the maximum value o...
Numerical Methods
Consider the integral 2 (a) [16 marks] Use the composite Simpson's rule with four intervals to calculate (by hand) approximate value of the integral Calculate the maximum value of the error in your approximation, and compare it with the true error. (b) 19 marks] Determine the number of subintervals n and the step size h so that the composite Simpson's rule for n subintervals can be used to compute the given integral with an accuracy of 5 ×...
2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the...
2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the composite trapezoidal rule with n = exact value of integral and compute the true percent relative error for this approximation 4. Calculate the (b) How many subintervals would be needed to estimate the integral with the composite trapezoidal rule with an accuracy of 102? (c) Estimate the integral using the composite Simpson's 1/3 rule with n = true percent relative error for this approximation...
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a) Analytically b) Trapezoidal...
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a) Analytically b) Trapezoidal rule. Divide the whole interval into four subintervals (n 4) c) Simpson's 1/3 rule. Divide the whole interval into four subintervals (n 4). d) Simpson's 3/8 rule. Divide the whole interval into three subintervals (n 3) Compare the results in b), c), and d) with the true value obtained in a).
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a)...
Let EM represent the error in using the Midpoint Rule with subintervals to approximate S. f(x)...
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
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr...
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
-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...
J(se.7)dt Estimate the minimum number of subintervals to approximate the value of with an error of magnitude less than 104 using 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.)
J(se.7)dt Estimate the minimum number of subintervals to approximate the value of with an error of magnitude less than 104 using a. the error estimate...
(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).
lo Estimate the MinimUM number oF Su bintervalS to approximate the Valve oF an MEO 2 + Xb error of Magntude less than 4xlo USING aTre error estimate Formula For Trape Zodal Rule. the minrmum numlber Of a Subin tervals USing the Trapezodial Rule is? bThe error estimate Formula for SiMpSons Rule, The MinImUm number of Subintervals USing Simpson 's Rule 1s
lo Estimate the MinimUM number oF Su bintervalS to approximate the Valve oF an MEO 2 + Xb...
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)
Numerical Methods
Consider the integral 2 (a) [16 marks] Use the composite Simpson's rule with four intervals to calculate (by hand) approximate value of the integral Calculate the maximum value of the error in your approximation, and compare it with the true error. (b) 19 marks] Determine the number of subintervals n and the step size h so that the composite Simpson's rule for n subintervals can be used to compute the given integral with an accuracy of 5 ×...
2. The following integral 2 dr can be computed exactly (a) Estimate the integral using the composite trapezoidal rule with n = exact value of integral and compute the true percent relative error for this approximation 4. Calculate the (b) How many subintervals would be needed to estimate the integral with the composite trapezoidal rule with an accuracy of 102? (c) Estimate the integral using the composite Simpson's 1/3 rule with n = true percent relative error for this approximation...
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a) Analytically b) Trapezoidal rule. Divide the whole interval into four subintervals (n 4) c) Simpson's 1/3 rule. Divide the whole interval into four subintervals (n 4). d) Simpson's 3/8 rule. Divide the whole interval into three subintervals (n 3) Compare the results in b), c), and d) with the true value obtained in a).
4) (25 pts) Evaluate the integral d: +5 Using the following methods: a)...
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
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
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