Quiz: Staircase Diagrams for Fixed-Point Iteration
Edexcel 9MA0 A-Level Mathematics
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Building on what you've learned about fixed-point iteration, let's test your understanding of staircase diagrams and how they show convergence or divergence!
What does a staircase diagram illustrate in fixed-point iteration?
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Which of the following are true about staircase diagrams? (Select all that apply)
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In a staircase diagram, successive iterations are shown as moving {{blank0}} towards or away from the fixed point, forming a {{blank1}} pattern.
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Match the items on the left with their correct pairs on the right
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Given f(x) = \frac{1}{3}x + 2, rearranged to x = \frac{1}{3}x + 2, what is the result after one iteration starting at x₀ = 4?
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In a staircase diagram, what causes divergence?
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Match the items on the left with their correct pairs on the right
Which of the following would indicate convergence in a staircase diagram? (Select all that apply)
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Which feature of a staircase diagram determines whether iterations converge or diverge?
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