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Question 26

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 2.5 and 3.

[3]

Show that the $x$ -coordinate of $P\,$ is a solution of $x=61+ln⁡x\displaystyle x = \frac{6}{1 + \ln x}$ .

[3]

Use the iteration formula $xn+1=61+ln⁡xn\displaystyle x_{n+1} = \frac{6}{1 + \ln x_n}$ with $x_0 = 2.8$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

Numerical Methods Questions

A Level
Maths
Numerical Methods

A Level
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