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Question 44

Sketch the graphs of $\ln x$ and $y=1x\displaystyle y = \frac{1}{x}$ for $0\,$ on the same axes.

[2]

Explain why the equation $ln⁡x=1x\displaystyle \ln x = \frac{1}{x}$ has exactly one solution.

[1]

By considering a suitable change of sign, show that the solution to the equation lies between 1.7 and 1.8

[2]

Use the iterative formula $xn+1=e1xn\displaystyle x_{n+1} = e^{\frac{1}{x_n}}$ with $x_1 = 1.8$ , to find $x_2, x_3\,$ and $x_4$ , giving your answers to four decimal places.

[2]

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 44

Sketch the graphs of $\ln x$ and $y=1x\displaystyle y = \frac{1}{x}$ for $0\,$ on the same axes.

[2]

Explain why the equation $ln⁡x=1x\displaystyle \ln x = \frac{1}{x}$ has exactly one solution.

[1]

By considering a suitable change of sign, show that the solution to the equation lies between 1.7 and 1.8

[2]

Use the iterative formula $xn+1=e1xn\displaystyle x_{n+1} = e^{\frac{1}{x_n}}$ with $x_1 = 1.8$ , to find $x_2, x_3\,$ and $x_4$ , giving your answers to four decimal places.

[2]

Markscheme

Numerical Methods Questions

A Level
Maths
Numerical Methods