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f(x) = tan(7x) - 6 1) It can be ensured that f has a zero on the interval 1 = [0, 0.48]. Explain why. 2) Use the methods: Bisection, False Position and Newton-Raphson (taking x0 = 0.48), to approximate the zero of f at I until a normalized relative error of 10-4 is achieved. 3) Compare the efficiency of the three methods above, indicate which is more efficient and explain why.

f(x) = tan(7x) - 6 1) It can be ensured that f has a zero on the interval 1 = [0, 0.48]. Explain why. 2) Use the methods: Bisection, False Position and Newton-Raphson (taking x0 = 0.48), to approximate the zero of f at I until a normalized relative error of 10-4 is achieved. 3) Compare the efficiency of the three methods above, indicate which is more efficient and explain why.

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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f(x) = tan(x) – 6 1) It can be ensured that f has a zero on the interval I = [0, 0.48]. Explain why. 2) Use the methods: Bisection, False Position and Newton-Raphson (taking x0 = 0.48), to approximate the zero of f at I until a normalized relative error of 10-4 is achieved. 3) Compare the efficiency of the three methods above, indicate which is more efficient and explain why.
Transcribed Image Text:f(x) = tan(x) – 6 1) It can be ensured that f has a zero on the interval I = [0, 0.48]. Explain why. 2) Use the methods: Bisection, False Position and Newton-Raphson (taking x0 = 0.48), to approximate the zero of f at I until a normalized relative error of 10-4 is achieved. 3) Compare the efficiency of the three methods above, indicate which is more efficient and explain why.
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