A-LevelMathematicsNumerical methods9709/32 · Feb/Mar 2019 · Q25 Marks
The sequence of values given by the iterative formula x_n+1 = (2x_n^6 + 12x_n) / (3x_n^5 + 8) with initial value x₁ = 2, converges to α.
- (i)Use the formula to calculate α correct to 4 decimal places. Give the result of each iteration to 6 decimal places.[3]
- (ii)State an equation satisfied by α and hence find the exact value of α.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] Use the iterative formula correctly at least once
- [A1] Obtain answer 1.3195
- [A1] Show sufficient iterations to 6 d.p. to justify 1.3195 to 4 d.p., or show there is a sign change in (1.31945, 1.31955)
- [B1] State x = (2x^6 + 12x) / (3x^5 + 8), or equivalent
- [B1] State answer 4^(1/5), or exact equivalent
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