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zubka84 [21]
2 years ago
10

Suppose p" must approximate p with relative error at most 10-3 . Find the largest interval in which p* must lie for each value o

f p.
Mathematics
1 answer:
goblinko [34]2 years ago
8 0

Answer:

[p-|p|*10^{-3} \, , \, p+|p|* 10^-3]

Step-by-step explanation

The relative error is the absolute error divided by the absolute value of p. for an approximation p*, the relative error is

r = |p*-p|/|p|

we want r to be at most 10⁻³, thus

|p*-p|/|p| ≤ 10⁻³

|p*-p| ≤ |p|* 10⁻³

therefore, p*-p should lie in the interval [ - |p| * 10⁻³ , |p| * 10⁻³ ], and as a consecuence, p* should be in the interval  [p - |p| * 10⁻³ , p + |p| * 10⁻³ ]

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