$\"\"$

\

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

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$ .

\

The function is $\"\"$ .

\

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

\

$\"\"$

\

Inverse trigonometric function of Derivative: $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The derivative function is $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

Substitute $\"\"$ in the function.

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

(a)

\

Find linear approximation.

\

Linear approximation is $\"\"$ .

\

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

\

$\"\"$

\

Linear approximation is $\"\"$ .

\

$\"\"$

\

(b)

\

Find quadratic approximation.

\

Quadratic approximation is $\"\"$ .

\

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

\

$\"\"$

\

Quadratic Approximation is $\"\"$ .

\

$\"\"$

\

(c)

\

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

\

The function is $\"\"$ .

\

Linear Approximation is $\"\"$ .

\

Quadratic Approximation is $\"\"$ .

\

$\"\"$

\

Observe the graph,

\

The linear approximation and quadratic approximation is same.

\

$\"\"$

\

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

\

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

\

(c) The Graph the function and the two approximations:

\

$\"\"$ .