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Determine the first root of the function f(x) = -13 - 20x + 19x²-3x³ with (a) bisection method, and (b) false position method. For (a) and (b) use initial guesses of x₁ = -1 and xu = 0, and a stopping criterion of 1%.

Determine the first root of the function f(x) = -13 - 20x + 19x²-3x³ with (a) bisection method, and (b) false position method. For (a) and (b) use initial guesses of x₁ = -1 and xu = 0, and a stopping criterion of 1%.

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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Find the positive root of f(x) = x³ + 3x²-5 using incremental search method. Use Ax = 0.05. Highlight the root based on the stopping criterion but proceed up to 0.0000% error. - Determine the first root of the function f(x) = −13 – 20x + 19x²-3x³ with (a) bisection method, and (b) false position method. For (a) and (b) use initial guesses of x₁ = −1 and xu = 0, and a stopping criterion of 1%. Highlight the root based on the stopping criterion but proceed up to 0.0000% error. The velocity v of a falling parachutist is given by gm (1 e-(c/m)t) C where g=9.8 m/s². For a parachutist with a drag coefficient c=15kg/s, compute the mass m so that the velocity is v =35m/s at t = 9 s. Use the false-position method to determine m to a level of Es = 0.1%. Highlight the answer based on the stopping criterion but proceed up to 0.0000% error.
Transcribed Image Text:Find the positive root of f(x) = x³ + 3x²-5 using incremental search method. Use Ax = 0.05. Highlight the root based on the stopping criterion but proceed up to 0.0000% error. - Determine the first root of the function f(x) = −13 – 20x + 19x²-3x³ with (a) bisection method, and (b) false position method. For (a) and (b) use initial guesses of x₁ = −1 and xu = 0, and a stopping criterion of 1%. Highlight the root based on the stopping criterion but proceed up to 0.0000% error. The velocity v of a falling parachutist is given by gm (1 e-(c/m)t) C where g=9.8 m/s². For a parachutist with a drag coefficient c=15kg/s, compute the mass m so that the velocity is v =35m/s at t = 9 s. Use the false-position method to determine m to a level of Es = 0.1%. Highlight the answer based on the stopping criterion but proceed up to 0.0000% error.
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