3.7 Numerical methods (A-level only)

Medium Hard

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Question 5

The curve $C\,$ has the equation $\ln x$ , $x > 0$ .

Find $dydx\displaystyle \frac{dy}{dx}$

[3]

$C\,$ has a stationary point at $P$ . Show that the $x$ -coordinate of $P\,$ lies between 5 and 6.

[3]

Show that the $x$ -coordinate of $P\,$ is a solution of $x=151+ln⁡x\displaystyle x = \frac{15}{1 + \ln x}$ .

[3]

Use the iteration formula $xn+1=151+ln⁡xn\displaystyle x_{n+1} = \frac{15}{1 + \ln x_n}$ with $x_0 = 5.5$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

3.7 Numerical methods (A-level only) Questions

A Level
Maths
3.7 Numerical methods (A-level only)

A Level
Maths CCEA
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