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2024 RI H1 Q4

2024 RI H1 Q4

8 marks
  1. Differentiate \(\ln(5-x)\) with respect to \(x\).[1]
  2. Differentiate \(\frac{1}{\sqrt{x^2+9}}\) with respect to \(x\).[2]
  3. Find the exact value of \(\displaystyle\int_{1}^{2} \left( \frac{1}{\sqrt{x}} + 2x \right)^2 \, \mathrm{d}x.\)[5]

Solution:

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Answer:(a) \(-\frac1{5-x}\), \(x<5\). (b) \(-\frac{x}{(x^2+9)^{\frac32}}\). (c) \(\ln2+\frac{16\sqrt2}{3}+\frac{20}{3}\).

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