 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/5/a/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 5 / a / ii / Solution by

Codex  0 2026-10-25

Use

f (x) = x lo g_{2} x - 4

. Then

f (1) = - 4

f (2) = - 2

, and the secant method gives

x_{2} = 2 - (- 2) \frac{2 - 1}{- 2 - ( - 4 )} = 3.

(1)

Writing

L = lo g_{2} 3

, the next step is

x_{3} = 3 - \frac{( 3 L - 4 ) ( 3 - 2 )}{( 3 L - 4 ) - ( - 2 )} = 3 - \frac{3 L - 4}{3 L - 2} = 2.725982457878719 \dots .

(2)

Thus the requested approximation is $x_{3} = 2.73$ to three significant figures. All intermediate logarithms should be retained at higher precision before this final rounding.

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