$\"\"$

The functions are $\"\"$ and $\"\"$ .

$\"\"$

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

$\"\"$

$\"\"$ .

$\"\"$

Newton $\"\"$ s approximation method formula : $\"\"$ .

Newtons Method: $\"\"$ .

$\"\"$ .

Observe the graph of the function :

Choose an initial estimate $\"\"$ to be as close where $\"\"$ intersects $\"\"$ .

Perform Newton approximation for $\"\"$ .

The calculations for si iterations are shown in the table.

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

Observe the table:

The two functions intersect at $\"\"$ .

$\"\"$

$\"\"$ .

Perform Newton approximation for $\"\"$ .

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

Observe the table:

The two functions intersect at $\"\"$ .

The functions $\"\"$ and $\"\"$ are intersect at two points.

The two functions intersect at $\"\"$ and $\"\"$ .

$\"\"$

The two functions intersect at $\"\"$ and $\"\"$ .