Roottest --- Introduction ---

We have a function (x) with unknown formula, defined on the interval [0,10]. We only know that (x) is continuous, monotonous, with libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) $f (0) \times f (10) < 0$ ; therefore it has exactly one root in [0,10].

The objective of the exercise is to find this root with a required precision, that is, an x such that

libgcov profiling error:/var/lib/wims/src/Lib/text.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/Lib/dir.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/wims.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/variables.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/var.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/test.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/texmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/score.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/rawmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/pedia.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/matrix.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathml.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/mathfonts.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/log.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/lines.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/insmath.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/html.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/files.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exec.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/exam.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/evalue.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/config.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/compare.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/cleaning.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/calc.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) libgcov profiling error:/var/lib/wims/src/auth.gcda:Version mismatch - expected 14.2 (release) (B42*) got 12.2 (release) (B22*) $∣ f (x) ∣ < 10^{- 4}$ .

To do this, you may test values of $f$ on different values of $x$ .

And your score is related to the number of the tests you have made (you will be disqualified after 13 tests).

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Description: find the root of a function by successive tests. interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, algebra, analysis, roots, functions