$\"\"$

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(a)

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The function $\"\"$ .

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

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$\"\"$ .

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Newton $\"\"$ s approximation method formula : $\"\"$ .

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$\"\"$

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Thus, $\"\"$ .

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$\"\"$

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(b)

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Consider $\"\"$ .

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Compare $\"\"$ with $\"\"$ .

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$\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

\

Perform newton approximation for $\"\"$ .

\

Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, $\"\"$

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$\"\"$

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Consider $\"\"$ .

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Compare $\"\"$ with $\"\"$ .

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$\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Here $\"\"$ .

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Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Perform newton approximation for $\"\"$ .

\

Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

\

$\"\"$

\

Perform newton approximation for $\"\"$ .

\

Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

\

$\"\"$ .

\

Perform newton approximation for $\"\"$ .

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Newton $\"\"$ s formula : $\"\"$ .

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$\"\"$

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$\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$

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(a)

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$\"\"$

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(b)

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$\"\"$ , $\"\"$ .