$\"\"$

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The function is $\"\"$ and the initial value is $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Newtons approximation method formula : $\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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Find $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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Perform newton approximation for $\"\"$ .

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Newtons formula : $\"\"$ .

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$\"\"$

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$\"\"$

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Perform newton approximation for $\"\"$ .

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Newtons formula : $\"\"$ .

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$\"\"$

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Perform newton approximation for $\"\"$ .

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Newton formula : $\"\"$ .

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$\"\"$

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By using newtons method the section was alternatively repeated so the test is failed.

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$\"\"$

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The test fails to converge because the newtons method is alternatively repeated.