$2$

Multiple choice

$2$ points

Let $f(x)$ and $g(x)$ be two positive continuous functions on $(0,)$ and $f(x)g(x)$ on the same interval. Given ${\displaystyle \underset{0}{\overset{}{}}}g(x)dx=8,$ which of the following statements must be

true?

${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ converges.

${\displaystyle \underset{0}{\overset{}{}}}f(x)g(x)dx$ diverges.

${\displaystyle \underset{0}{\overset{}{}}}g(x)-f(x)dx$ converges.

$1$ only

$3$ only

$2$ and $3$

$1$ and $3$

$2$ only