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Question 4

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]

Markscheme

Numerical Methods Questions

A Level
Maths
Numerical Methods

80 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

Numerical Methods

Question bank

Numerical Methods

Medium Hard

Question 4

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]

Markscheme

Numerical Methods Questions

A Level
Maths
Numerical Methods