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SPM 2017 Additional Mathematics (Paper 2, Question 2)

The equation of the crooked line is .
  • Find the general expression for , evaluated when .
  • Write down the equation for the purple line, which is the tangent to the crooked line at .
is a point on the crooked line whose abscissa value is , when a small perturbation is introduced on , the position of gets shifted to . In pre-computer era, it is numerically difficult to compute the ordinate of . Therefore the image of on the tangent, , is used to estimate .
  • Use the -slider to explore the effect of the size of perturbation on the the gap between and .
  • Try the tangent line method to compute the approximate values for , , , etc.