4PM1/02 Nov 2021, Question 5: Connected Rates of Change and Small Changes
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
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The question, in short
Given y = xe^(−2x) and x increasing by 3%, use calculus to estimate the percentage change in y, giving the answer in the form a(b − cx) with integers a, b, c.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1dy/dx = e^(−2x) − 2xe^(−2x) = e^(−2x)(1 − 2x)
- 2δy ≈ e^(−2x)(1 − 2x)δx with δx = 0.03x
- 3(δy/y) × 100 = e^(−2x)(1 − 2x)(0.03x)/(xe^(−2x)) × 100
- 4= 3(1 − 2x)
Answer3(1 − 2x) %
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