(a)

$\"\"$ .

By using calculator, Construct the table of values $\"\"$ for $\"\"$ and $\"\"$ .

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

Observe the table:

It appears that the values are not approaching any fixed number.

The integral is divergent.

(b)

Comparison Theorem:

Suppose that $\"\"$ and $\"\"$ are continuous functions with $\"\"$ for $\"\"$ .

(a) If $\"\"$ is convergent, then $\"\"$ is convergent.

(b) If $\"\"$ is divergent, then $\"\"$ is divergent.

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

For $\"\"$

$\"\"$

The improper integral $\"\"$ is divergent.

Hence the Comparison theorem implies that the improper integral $\"\"$ is divergent.

(c) Graph the functions $\"\"$ and $\"\"$ on same screen.

$\"\"$

Observe the graph: $\"\"$ .

$\"\"$ is divergent.

Therefore, $\"\"$ is divergent.

(a)

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

(b) $\"\"$ is divergent.

(c) Graph of the functions $\"\"$ and $\"\"$ on same screen.

$\"\"$ .