2024 JPJC H1 Q3
2024 JPJC H1 Q3
7 marks
- Find the approximate value of the derivative of \(3^x\) when \(x=2\).[1]
- Differentiate \(\frac{kx^2-3x+k^2}{2x}\) with respect to \(x\), where \(k\) is a constant.[3]
- Find \(\displaystyle\int \left(\frac{1}{2\sqrt{x}}+3x\right)^2 \, \mathrm{d}x\).[3]
Solution:
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Answer:
(a) \(9.89\).
(b) \(\frac k2-\frac{k^2}{2x^2}\), for \(x\ne0\).
(c) \(\frac14\ln x+2x^{\frac32}+3x^3+C\), for \(x>0\).
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