A-level · Numerical methods

The Newton–Raphson methodExam-style questions

A fast iteration that uses the tangent — x_(n+1) = x_n − f(x_n)/f'(x_n) — its geometric meaning, why it converges so quickly, and the cases where it fails (a horizontal tangent or a poor starting value).

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23 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
$f(x) = x^3 - 2x - 5$ . Using the Newton–Raphson method with $x_0 = 2$ , find $x_1$ .
Level 2 · 2 marksTry it
2
The positive root of $x^2 - 7 = 0$ is $\sqrt7$ . Using Newton–Raphson with $x_0 = 3$ , find $x_1$ and $x_2$ to 4 decimal places.
Level 2 · 3 marksTry it
3
Using the Newton–Raphson method on $f(x) = x^3 - 5$ with $x_0 = 2$ , find $x_1$ and $x_2$ to 4 decimal places. (This estimates $\sqrt[3]{5}$ .)
Level 3 · 3 marksTry it
4
The equation $e^x + x = 4$ has a root near $x = 1$ . Use the Newton–Raphson method with $x_0 = 1$ to find $x_1$ and $x_2$ to 4 decimal places.
Level 3 · 3 marksTry it
5
$f(x) = x^3 + x - 1$ . Using Newton–Raphson with $x_0 = 1$ , find $x_1$ and $x_2$ to 4 decimal places.
Level 3 · 3 marksTry it

18 more questions on the newton–raphson method

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