2025 IGCSE Additional Mathematics February/March 0606/22 Q6

2025 IGCSE Additional Mathematics February/March 0606/22 Q6

8 marks

It is given that \(y=\dfrac{\ln(2x^2+1)}{x+2}\).

  1. Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).[3]
  2. Given that \(x\) increases from \(2\) to \(2+h\), where \(h\) is small, find the approximate change in \(y\).[2]
  3. Given that \(y\) is decreasing by \(0.4\) units per second, find the corresponding rate of change in \(x\) when \(x=2\).[3]

Solution:

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Answer:(a) \(\dfrac{\dfrac{4x(x+2)}{2x^2+1}-\ln(2x^2+1)}{(x+2)^2}\) (b) \(\Delta y\approx0.0849h\) (c) \(-4.71\text{ units per second}\)

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