$\"\"$

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The functions are $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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Observe the graph of the function :

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Choose an initial estimate $\"\"$ to be as close where $\"\"$ intersects.

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Consider $\"\"$ .

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Find $\"\"$ .

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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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$\"\"$ .

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Since two succesive approximations differ by less than $\"\"$ , estimate that the functions $\"\"$ and $\"\"$ intersect at $\"\"$ .

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$\"\"$

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The functions $\"\"$ and $\"\"$ $\"\"$ intersect at $\"\"$ .