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Defemine e real roof of f (x) = - 26+85x-91x + 44x3 - 8x + x5 al Using bisection to determine the root to lerl = 10%. Employ initial guesses of a = 0.5 and b = 1.0. Dorfomm tho

Defemine e real roof of f (x) = - 26+85x-91x + 44x3 - 8x + x5 al Using bisection to determine the root to lerl = 10%. Employ initial guesses of a = 0.5 and b = 1.0. Dorfomm tho

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 Detemine the real roof of f (x) = - 26+ 85x-91x + 44x3 - 8x4 + x5 al Using bisection to determine the root to ei = 10%. Employ initial guesses of a3= 0.5 and b = 1.0. Perfom the same computation as in a) but use the false-position method and Jerl = 0.2%. 2. Determine the real root of Inx = 0.7 a) Using three iterations of the bisection method. Employ initial guesses of a = 0.5 and b= 2.0. b) Using three iterations of the false-position method with the same initial guesses as a). 3. Determine the positive square root of 18 using false-posifion method to within Jeil : 0.5 %. Employ initial guesses of 4 and 5. 4. Find the positive real root of f(x) = x4- 8x3 - 35x2 + 450x - 1001 using the false-position method and bisection method. Use inifial guesses of a = 4.5 and b = 6 and perform five iterations. Compute both the true and approximate errors based on the fact that the root is 5.60979. Use a plot to explain your results and perform the computation to within es = 1.0%. !! %3D %3D %3D 5. Determine the real root of f(x) = -25+82x - 90x2 + 44x3 - 8x4 + 0.7x5: a. Graphically. b. Using bisection to determine the root to es 5 10%. Employ initial guesses of a = 0.5 and b=1.0. c. Pertorn the same computation as in b but use the false-position method and es = 0.2%. 1.
Transcribed Image Text:1 Detemine the real roof of f (x) = - 26+ 85x-91x + 44x3 - 8x4 + x5 al Using bisection to determine the root to ei = 10%. Employ initial guesses of a3= 0.5 and b = 1.0. Perfom the same computation as in a) but use the false-position method and Jerl = 0.2%. 2. Determine the real root of Inx = 0.7 a) Using three iterations of the bisection method. Employ initial guesses of a = 0.5 and b= 2.0. b) Using three iterations of the false-position method with the same initial guesses as a). 3. Determine the positive square root of 18 using false-posifion method to within Jeil : 0.5 %. Employ initial guesses of 4 and 5. 4. Find the positive real root of f(x) = x4- 8x3 - 35x2 + 450x - 1001 using the false-position method and bisection method. Use inifial guesses of a = 4.5 and b = 6 and perform five iterations. Compute both the true and approximate errors based on the fact that the root is 5.60979. Use a plot to explain your results and perform the computation to within es = 1.0%. !! %3D %3D %3D 5. Determine the real root of f(x) = -25+82x - 90x2 + 44x3 - 8x4 + 0.7x5: a. Graphically. b. Using bisection to determine the root to es 5 10%. Employ initial guesses of a = 0.5 and b=1.0. c. Pertorn the same computation as in b but use the false-position method and es = 0.2%. 1.
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