2026 NYJC P1 Q6

2026 NYJC P1 Q6

Junior College 2
8 marks

A curve has equation \(\displaystyle y=\frac{\ln(5-x)}{5-x}\).

  1. By differentiation, find the equation of the normal to the curve at the point when the curve cuts the \(x\)-axis.[4]
  2. Find the exact area of the region bounded by the normal, the curve and the \(y\)-axis.[4]

Solution:

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Answer:(a) \(y=x-4\) (b) \(8+\frac12(\ln5)^2\text{ units}^2\)

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