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2024 MI H1 Q3

2024 MI H1 Q3

5 marks
  1. On the same axes, sketch the graphs of \(y = 3x - 2\) and \(y = 3xe^{-3x}\), stating clearly the coordinates of the points of the intersection with the axes.[3]
  2. Hence solve the inequality : \(3x - 2 < 3xe^{-3x}\)[2]

Solution:

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Answer:(i) Line intercepts \((0,-2),\left(\frac{2}{3},0\right)\); exponential intercept \((0,0)\). (ii) \(-0.353<x<0.746\), with boundary values rounded to 3 decimal places.

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