Numerical Methods
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Question 14
The diagram shows a sketch of the curve C C\,C with equation y=4x32−8x+ex+4\displaystyle y = 4x^{\frac{3}{2}} - 8\sqrt{x} + e^x + 4y=4x23−8x+ex+4
a.[3]
Show that dydx=6x+ex−4x\displaystyle \frac{dy}{dx} = 6\sqrt{x} + e^x - \frac{4}{\sqrt{x}}dxdy=6x+ex−x4
b.[2]
The point P P\,P is the minimum turning point on CCC. Show that the x x\,x coordinate of P P\,P is a solution of
x=8−2xex12 x = \frac{8 - 2\sqrt{x}e^x}{12} x=128−2xexc.[3]
Use the iteration formula xn+1=8−2xnexn12\displaystyle x_{n+1} = \frac{8 - 2\sqrt{x_n}e^{x_n}}{12}xn+1=128−2xnexn with x1=0.5x_1 = 0.5x1=0.5 to find (i) the value of x2 x_2\,x2 to 5 decimal places, (ii) the x x\,x coordinate of P P\,P to 5 decimal places.
Numerical Methods Questions
329 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.