$\"\"$

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(a)

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

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Substitute $\"\"$ in the function.

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$\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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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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The linear approximation of the function $\"\"$ at $\"\"$ is $\"\"$ .

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Substitute $\"\"$ in the linear approximation.

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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The derivative function is $\"\"$ .

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Again apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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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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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The quadratic approximation of the function $\"\"$ at $\"\"$ is $\"\"$ .

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Substitute $\"\"$ in the quadratic approximation.

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b)

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Graph :

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Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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Observe the graph:

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$\"\"$ is the better approximation.

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$\"\"$

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(d)

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The accuracy worsens as you move away from $\"\"$ .

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$\"\"$

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(a)

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

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(b)

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Graph :

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Graph the functions $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$ .

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(c) $\"\"$ is the better approximation.

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(d) The accuracy worsens as you move away from $\"\"$ .