$\"\"$

(a).

The function is $\"\"$ .

Rewrite the function.

$\"\"$

Graph:

Graph of $\"\"$ is :

$\"\"$

Observe the graph:

The value of $\"\"$ .

$\"\"$

The function is $\"\"$ .

Consider $\"\"$ .

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

$\"\"$

Newtons method:

Newtons approximation method formula : $\"\"$ .

Consider one root as $\"\"$ .

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Observe the table :

The root of the equation is $\"\"$ .

$\"\"$

(b).

The area of region bounded by curves $\"\"$ and $\"\"$ in between $\"\"$ and $\"\"$ .

$\"\"$

Observe the graph:

The upperer curve is $\"\"$ and lower curve is $\"\"$ .

The intersection points are $\"\"$ and $\"\"$ .

The area under the two curves is $\"\"$ .

Therefore $\"\"$ .

$\"\"$

(a). $\"\"$ .

(b). $\"\"$ .