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You are asked to solve a nonlinear equation f(x) = 0 on the interval [4, 7] using bisection. Tick ALL of the following that are true: This iterative method requires one starting point. This iterative method requires two starting points. This iterative method requires evaluation of derivatives of f. This iterative method does not require evaluation of derivatives of f. This iterative method requires the starting point(s) to be close to a simple root. This iterative method does not require the starting point(s) to be close to a simple root. If f = C([4, 7]) and ƒ(4)ƒ(7) < 0, then, with the starting point x₁ = 5.5, this iterative method converges linearly with asymptotic constant 3 = 0.5. If f(x) = 0 can be expressed as x = g(x), where g = C¹([4, 7]) and there exists K € (0, 1) such that g'(x)| ≤ K for all & € (4,7), then this iterative method converges linearly with asymptotic constant B≤ K for any starting point x₁ = [4, 7]. If f = C²([4, 7]) and the starting point is sufficiently close to a simple root in (4, 7), then this iterative method converges quadratically. If ƒ € C²([4, 7]) and the starting points ₁ and 2 are sufficiently close to a Osimple root in (4,7), then this iterative method converges superlinearly with order ✓ 1.6.

You are asked to solve a nonlinear equation f(x) = 0 on the interval [4, 7] using bisection. Tick ALL of the following that are true: This iterative method requires one starting point. This iterative method requires two starting points. This iterative method requires evaluation of derivatives of f. This iterative method does not require evaluation of derivatives of f. This iterative method requires the starting point(s) to be close to a simple root. This iterative method does not require the starting point(s) to be close to a simple root. If f = C([4, 7]) and ƒ(4)ƒ(7) < 0, then, with the starting point x₁ = 5.5, this iterative method converges linearly with asymptotic constant 3 = 0.5. If f(x) = 0 can be expressed as x = g(x), where g = C¹([4, 7]) and there exists K € (0, 1) such that g'(x)| ≤ K for all & € (4,7), then this iterative method converges linearly with asymptotic constant B≤ K for any starting point x₁ = [4, 7]. If f = C²([4, 7]) and the starting point is sufficiently close to a simple root in (4, 7), then this iterative method converges quadratically. If ƒ € C²([4, 7]) and the starting points ₁ and 2 are sufficiently close to a Osimple root in (4,7), then this iterative method converges superlinearly with order ✓ 1.6.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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You are asked to solve a nonlinear equation f(x) = 0 on the interval [4, 7] using bisection. Tick ALL of the following that are true: This iterative method requires one starting point. This iterative method requires two starting points. This iterative method requires evaluation of derivatives of f. This iterative method does not require evaluation of derivatives of f. This iterative method requires the starting point(s) to be close to a simple root. This iterative method does not require the starting point(s) to be close to a simple root. If f = C([4, 7]) and ƒ(4)ƒ(7) < 0, then, with the starting point x₁ = 5.5, this iterative method converges linearly with asymptotic constant 3 = 0.5. If f(x) = 0 can be expressed as x = g(x), where g = C¹([4, 7]) and there exists K € (0, 1) such that g'(x)| ≤ K for all & € (4,7), then this iterative method converges linearly with asymptotic constant ≤ K for any starting point x₁ = [4, 7]. If f = C² ([4, 7]) and the starting point x₁ is sufficiently close to a simple root in (4,7), then this iterative method converges quadratically. If f = C²([4, 7]) and the starting points ₁ and 2 are sufficiently close to a simple root in (4, 7), then this iterative method converges superlinearly with order ✓ 1.6.
Transcribed Image Text:You are asked to solve a nonlinear equation f(x) = 0 on the interval [4, 7] using bisection. Tick ALL of the following that are true: This iterative method requires one starting point. This iterative method requires two starting points. This iterative method requires evaluation of derivatives of f. This iterative method does not require evaluation of derivatives of f. This iterative method requires the starting point(s) to be close to a simple root. This iterative method does not require the starting point(s) to be close to a simple root. If f = C([4, 7]) and ƒ(4)ƒ(7) < 0, then, with the starting point x₁ = 5.5, this iterative method converges linearly with asymptotic constant 3 = 0.5. If f(x) = 0 can be expressed as x = g(x), where g = C¹([4, 7]) and there exists K € (0, 1) such that g'(x)| ≤ K for all & € (4,7), then this iterative method converges linearly with asymptotic constant ≤ K for any starting point x₁ = [4, 7]. If f = C² ([4, 7]) and the starting point x₁ is sufficiently close to a simple root in (4,7), then this iterative method converges quadratically. If f = C²([4, 7]) and the starting points ₁ and 2 are sufficiently close to a simple root in (4, 7), then this iterative method converges superlinearly with order ✓ 1.6.
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