Fixed-point iteration and numerical roots: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 224\) using \(x_{n+1}=\sqrt[3]{224-x_n}\), with \(\displaystyle x_{0}=6. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{1}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 13\) using \(x_{n+1}=\sqrt[3]{13-x_n}\), with \(\displaystyle x_{0}=2. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{1}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 13\) using \(x_{n+1}=\sqrt[3]{13-x_n}\), with \(\displaystyle x_{0}=2. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{2}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 31\) using \(x_{n+1}=\sqrt[3]{31-x_n}\), with \(\displaystyle x_{0}=3. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{2}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 31\) using \(x_{n+1}=\sqrt[3]{31-x_n}\), with \(\displaystyle x_{0}=3. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{3}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 70\) using \(x_{n+1}=\sqrt[3]{70-x_n}\), with \(\displaystyle x_{0}=4. A\) calculator is appropriate; keep guard digits.
Calculate \(\displaystyle x_{3}\).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 70\) using \(x_{n+1}=\sqrt[3]{70-x_n}\), with \(\displaystyle x_{0}=4. A\) calculator is appropriate; keep guard digits.
Find the limiting root to at least six decimal places.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Fixed-point iteration and numerical roots: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(x^{3} + x = 133\) using \(x_{n+1}=\sqrt[3]{133-x_n}\), with \(\displaystyle x_{0}=5. A\) calculator is appropriate; keep guard digits.
Find the limiting root to at least six decimal places.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.