$\"\"$

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

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Linear approximation of the function is $\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in above function.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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

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Substitute all these values in linear approximation equation.

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$\"\"$

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

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Approximate value for $\"\"$ .

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$\"\"$

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Here, $\"\"$ .

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$\"\"$

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Approximate value for $\"\"$ .

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Approximate value for $\"\"$

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$\"\"$

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Approximate value for $\"\"$ .

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Graph:

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Graph of the function and the tangent line.

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$\"\"$

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Linear approximation of the function is $\"\"$ .

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Approximate value for $\"\"$ .

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Approximate value for $\"\"$ .

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Graph of the function and the tangent is \ \

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$\"\"$ .