Using a counterexample, prove that the converse of the result in question 3.1 is false, i.e. that
$$\left( \lim _ { x \rightarrow + \infty } \frac { 1 } { x } \int _ { 0 } ^ { x } f ( t ) d t = \ell \right) \not\Rightarrow \left( \lim _ { x \rightarrow + \infty } f ( x ) = \ell \right)$$
for $f \in \mathcal{C}^0([0,+\infty[)$.