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3 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2 · Question 4(b)

Deduce that the function f(x) = sin x - x^2 has EXACTLY two real roots.

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Other parts of this question

  1. 4(a)Sketch the functions y = sin x and y = x^2 on the SAME axes.[5 marks]
  2. 4(c)Find the interval in which the non-zero root alpha of f(x) lies.[4 marks]
  3. 4(d)Starting with a first approximation of alpha at x_1 = 0.7, use one iteration of the Newton-Raphson method to obtain a better approximation of alpha to 3…[8 marks]

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