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Locate the first positive root of f(x) = sin x + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with initial guesses of (a) x₁-1 = 1.0 and x₁ = 3.0; (b) X₁-1 = 2.5 and x₁ = 1.5, and (c) xi-1 = 1.5 and x₁ = 2.25 to locate the root.

Locate the first positive root of f(x) = sin x + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with initial guesses of (a) x₁-1 = 1.0 and x₁ = 3.0; (b) X₁-1 = 2.5 and x₁ = 1.5, and (c) xi-1 = 1.5 and x₁ = 2.25 to locate the root.

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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Solve the following problems. Tabulate all answers. Show the complete solution of one iteration only. Write all values accurately to 5-decimal places ONLY. PLS ANSWER NO. 4
3. Determine the real roots of f(x) = -1 +5.5x - 4x² + 0.5x³ using the Newton-Raphson method until the error falls below a stopping error &, = 0.01%. 4. Locate the first positive root of f(x) = sin x + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with initial guesses of (a) xi-1 = 1.0 and x₁ = 3.0; (b) Xi-1 = 2.5 and x₁ = 1.5, and (c) xi-1 = 1.5 and x = 2.25 to locate the root.
Transcribed Image Text:3. Determine the real roots of f(x) = -1 +5.5x - 4x² + 0.5x³ using the Newton-Raphson method until the error falls below a stopping error &, = 0.01%. 4. Locate the first positive root of f(x) = sin x + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with initial guesses of (a) xi-1 = 1.0 and x₁ = 3.0; (b) Xi-1 = 2.5 and x₁ = 1.5, and (c) xi-1 = 1.5 and x = 2.25 to locate the root.
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