I need to find two functions: $p_1(\epsilon)$ such that $\lim_{\epsilon \rightarrow 0} \frac{p_1(\epsilon)}{\epsilon}= e^{a \pi(x) + bx}$ and $p_2(\epsilon)$ such that $\lim_{\epsilon \rightarrow 0} \frac{p_2(\epsilon)}{\epsilon}= e^{-a \pi(x) -bx}$ where $\epsilon \in [0,1]$, $p_1(\epsilon)$ and $p_2(\epsilon)$ are probabilities and therefore between 0 and 1, $a$ and $b$ are constant and $\pi(x)$ is a linear function of $x$, where $x \in [-1,1]$.
Do they exist? How can I find them? Thank you in advance!