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MMLU-Pro / 9745 / Use the function described in Example 4.3, …

Problem

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question

Use the function described in Example 4.3, xn+1=αxn(1−xn2)x_{n+1}=\alpha x_n\left(1-x_n^2\right) where α=2.5\alpha=2.5. Consider two starting values of x1x_1 that are similar, 0.9000000 and 0.9000001 . Make a plot of xnx_n versus nn for the two starting values and determine the lowest value of nn for which the two values diverge by more than 30%30 \%.
Plain-text mathematical notation (without MathML)
 Use the function described in Example 4.3, x_(n+1)=αx_(n)(1−x_(n)²) where α=2.5. Consider two starting values of x₁ that are similar, 0.9000000 and 0.9000001 . Make a plot of x_(n) versus n for the two starting values and determine the lowest value of n for which the two values diverge by more than 30%.
Original LaTeX notation
 Use the function described in Example 4.3, $x_{n+1}=\alpha x_n\left(1-x_n^2\right)$ where $\alpha=2.5$. Consider two starting values of $x_1$ that are similar, 0.9000000 and 0.9000001 . Make a plot of $x_n$ versus $n$ for the two starting values and determine the lowest value of $n$ for which the two values diverge by more than $30 \%$.

category

physics

options

  1. 40
  2. 30
  3. 25
  4. 35

src

scibench-class

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Source and history

upstream_id / Original problem ID
9745
task_id
9f2b3852-f6db-557e-aeab-9683a4e6a8a8
task_key
default--test--9745
task_revision_id
1
config / split
default / test

Official source

initial import