In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$ and $f(t) = \dfrac{t}{e^t - 1} - 1 + \dfrac{t}{2}$ for all $t \in \mathbb{R}^{+*}$ (extended by continuity at 0). Determine $E$.
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$ and $f(t) = \dfrac{t}{e^t - 1} - 1 + \dfrac{t}{2}$ for all $t \in \mathbb{R}^{+*}$ (extended by continuity at 0).
Determine $E$.