$\"\"$

\

The equation is $\"\"$ and the interval is $\"\"$ .

\

Assume $\"\"$ .

\

Graph the function to get the approximate root of the equation.

\

$\"\"$

\

\

Observe the graph, root of the equation in the interval $\"\"$ is $\"\"$ .

\

Newtons approximation formula : $\"\"$ .

\

Consider $\"\"$ .

\

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

\

$\"\"$

\

From the newtons method, $\"\"$ .

\

Substitutte $\"\"$ in above expression.

\

$\"\"$

\

Substitutte $\"\"$ in above expression.

\

$\"\"$

\

$\"\"$ .

\

Repeat the process for until the first six decimals donot change.

\

$\"\"$

\

Consider $\"\"$ .

\

Substitutte $\"\"$ in above expression.

\

$\"\"$ .

\

Substitutte $\"\"$ in above expression.

\

$\"\"$

\

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, $\"\"$ .

\

Root of the equation in $\"\"$ is $\"\"$ .

\

$\"\"$

\

Root of the equation in $\"\"$ is $\"\"$ .