$\"\"$

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

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Substitute $\"\"$ in the function.

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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Derivative of the inverse trigonometric function: $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the function.

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$\"\"$

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Substitute $\"\"$ in the function.

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$\"\"$ .

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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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Substitute $\"\"$ in the function.

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$\"\"$

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Substitute $\"\"$ in the function.

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$\"\"$ .

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$\"\"$ .

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$\"\"$

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(a)

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Find linear approximation.

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Linear Approximation : $\"\"$ .

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

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$\"\"$

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Linear Approximation is $\"\"$ .

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$\"\"$

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(b)

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Find quadratic approximation.

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Quadratic Approximation is $\"\"$

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

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$\"\"$

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Quadratic Approximation is $\"\"$ .

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$\"\"$

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(c)

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Graph the function and the two approximations and function of $\"\"$ .

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The function is $\"\"$ .

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Linear Approximation is $\"\"$ .

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Quadratic Approximation is $\"\"$ .

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$\"\"$

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Observe the graph :

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The linear approximation and quadratic approximation is same.

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$\"\"$

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(a) Linear Approximation is $\"\"$ .

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(b) Quadratic Approximation is $\"\"$ .

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(c) Graph the function and the two approximations:

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$\"\"$ .