$\"\"$

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The function is $\"\"$ .

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Linear approximation is $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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Find the values of $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Linear approximation at $\"\"$ is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in linear approximation equation.

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$\"\"$

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The corresponding linear approximation is $\"\"$ .

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For accuracy within 0.1.

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$\"\"$

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$\"\"$

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The middle curve is $\"\"$ ,the upper and the lower curves are $\"\"$ and $\"\"$ .

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So from the graph we can say that $\"\"$ is accurate within 0.1 when $\"\"$ .

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The corresponding linear approximation is $\"\"$ .

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$\"\"$ .