0606/21 May/Jun 2025, Question 5: Connected Rates of Change and Small Changes
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 4 marks
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The question, in short
For y = x²tan(x/2), use calculus to estimate how y changes when x moves from π/3 to π/3 + h, with h small.
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Solution · 4 marks
- 1dy/dx = 2x tan(x/2) + (x²/2)sec²(x/2)
- 2At x = π/3: dy/dx = (2π/3)tan(π/6) + (π²/18)sec²(π/6)
- 3= (2π/3)(1/√3) + (π²/18)(4/3) = 1.940…
- 4δy ≈ (dy/dx) × h ≈ 1.94h
Answer1.94h
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