Question 1 [1 mark]
≈ 1.521.
Mark scheme
- A [1] — cao
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≈ 1.521.
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≈ 1.904.
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Converges to ≈ 0.268 (smaller positive root).
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≈ 2.095.
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x2 = 6, x3 = 12.
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≈ 2.414 (1 + √2).
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x2 = 4, x3 = 16.
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x2 = 4, x3 = 13.
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x2 = 8, x3 = 4.
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x2 = 6, x3 = 2.
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x2 = 3, x3 = −1, x4 = 7.
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x2 = 1, x3 = −2.
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x2 = 4, x3 = 2.5, x4 = 3.4.
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x³ = 2x − 1 ⇒ x = ∛(2x − 1).
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x³ = 7 − 2x ⇒ x = ∛(7 − 2x).
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x³ = 10 − x ⇒ x = ∛(10 − x).
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x2 = 8, x3 = 20.
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5x = x² + 2 ⇒ x = x² + 25.
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3x = x² − 1 ⇒ x = x² − 13.
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x2 = 2, x3 = 5, x4 = 2.
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Diverges; terms grow in magnitude and alternate sign.
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L = √5 (≈ 2.24).
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L = 1.
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Oscillates between 1 and 2.
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Converges to 2 after a few terms (e.g. 0, −2, 2, 2, …).
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L = 1.5.
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Oscillates between 2 and 0.5.
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L = 1.
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Converges to L = 2.00.
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L = 1.
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