In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$. We assume that $f$ admits a finite limit $l$ at $+\infty$. IV.D.1) Show that $E$ contains $\mathbb{R}^{+*}$. IV.D.2) Show that $xLf(x)$ tends to $l$ at $0^+$.
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$. We assume that $f$ admits a finite limit $l$ at $+\infty$.
IV.D.1) Show that $E$ contains $\mathbb{R}^{+*}$.
IV.D.2) Show that $xLf(x)$ tends to $l$ at $0^+$.