Numerical Methods
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Question 114
The diagram shows a sketch of the curve C C\,C with equation y=2x32−3x+ex+4\displaystyle y = 2x^{\frac{3}{2}} - 3\sqrt{x} + e^x + 4y=2x23−3x+ex+4
a.[3]
Show that dydx=3x+ex−32x\displaystyle \frac{dy}{dx} = 3\sqrt{x} + e^x - \frac{3}{2\sqrt{x}}dxdy=3x+ex−2x3
b.[1]
The point P P\,P is the minimum turning point on CCC. Show that 6x+2xex−3=06x + 2\sqrt{x}e^x - 3 = 06x+2xex−3=0 at PPP.
c.[1]
Hence show that the x x\,x coordinate of P P\,P is a solution of
x=3−2xex6 x = \frac{3 - 2\sqrt{x}e^x}{6} x=63−2xexd.[1]
Use the iteration formula xn+1=3−2xnexn6\displaystyle x_{n+1} = \frac{3 - 2\sqrt{x_n}e^{x_n}}{6}xn+1=63−2xnexn with x1=0.25x_1 = 0.25x1=0.25 to find the value of x2 x_2\,x2 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.