1.12.2 Iterative methods and Newton-Raphson (A-level only)

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Question 21

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 4.5 and 5

[3]

Show that the $x\,$ coordinate of P is a solution of $x=121+ln⁡x\displaystyle x = \frac{12}{1 + \ln x}$

[3]

Use the iteration formula $xn+1=121+ln⁡xn\displaystyle x_{n+1} = \frac{12}{1 + \ln x_n}$ with $x_0 = 4.75$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

1.12.2 Iterative methods and Newton-Raphson (A-level only) Questions

A Level
Maths
1.12.2 Iterative methods and Newton-Raphson (A-level only)

A Level
Maths AQA
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