Use Newton's method to find an approximate solution to $$ x^{2}-2=0 $$, starting from an initia estimate $$ x_{1}=2 $$. Iterate until 6 iterations. Hints: $$ \boldsymbol{f}^{\prime}(\boldsymbol{x})=2 \boldsymbol{x} $$ Marks)

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King Washington · Accepted Answer

After 6 iterations, the approximate solution to $$ x^2 - 2 = 0 $$ is $$ 1.4143 $$, which is close to $$ \sqrt{2} $$.

Use Newton's method to find an approximate solution to \( x^{2}-2=0 \), starting from an initia estimate \( x_{1}=2 \). Iterate until 6 iterations. Hints: \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=2 \boldsymbol{x} \) Marks)

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Use Newton's method to find an approximate solution to \( x^{2}-2=0 \), starting from an initia estimate \( x_{1}=2 \). Iterate until 6 iterations. Hints: \( \boldsymbol{f}^{\prime}(\boldsymbol{x})=2 \boldsymbol{x} \) Marks)

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