$\"\"$

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The function is $\"\"$ . \ \

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Let $\"\"$ point on the graph. \ \

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If $\"\"$ is a point of tangency. \ \

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$\"\"$

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Substitute $\"\"$ in the above equation. \ \

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$\"\"$

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$\"\"$

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Newtons 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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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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$\"\"$ .

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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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The approximation that had total arrests of $\"\"$ thousands is $\"\"$ .