4PM1/01R Jun 2019, Question 5: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 5 marks
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The question, in short
A circle's radius is 3r cm with area A cm². When r rises by 0.05%, use calculus to estimate the percentage change in A.
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Solution · 5 marks
- 1A = π(3r)² = 9πr², dA/dr = 18πr
- 2δA ≈ (dA/dr)δr = 18πr δr
- 3δA/A ≈ 18πr δr/(9πr²) = 2(δr/r)
- 4δr/r = 0.05% → δA/A ≈ 0.1%
Answer0.1%
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