\

The expression is $\"\"$ .

\

(a)

\

Intermediate value theorem :

\

The function $\"\"$ is continuous on the closed interval $\"\"$ , let $\"\"$ be the number between $\"\"$ and $\"\"$ , where $\"\"$ then exist a number $\"\"$ in $\"\"$ such that $\"\"$ .

\

Consider the function is $\"\"$ .

\

Consider the function $\"\"$ to be continuous over the interval $\"\"$ .

\

Prove that the number $\"\"$ exists between $\"\"$ and $\"\"$ .

\

$\"\"$ .

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in the function.

\

$\"\"$

\

Thus, $\"\"$ .

\

Then according to intermediate value theorem, there exist at least one root between $\"\"$ and $\"\"$ such that $\"\"$ .

\

\

(b)

\

Consider $\"\"$ be the root exist between $\"\"$ and $\"\"$ .

\

Then $\"\"$ .

\

$\"\"$

\

Using calculator the value of $\"\"$ is $\"\"$ .

\

Therefore the interval is considered as $\"\"$ .

\

Interval of the function containing the root is $\"\"$ .

\

\

Interval of the function containing the root is $\"\"$ .