Solution
= Solution
The pointwise <limit> is $f(x)=e^x/\cosh(ax)$ and
$$
|f_n-f|=(e^{1/n}-1)\frac{e^x}{\cosh(ax)}.
$$
The final factor is bounded on $\mathbb R$ exactly when $|a|\ge1$; when $|a|<1$ it diverges as $x\to+\infty$. Thus convergence is uniform exactly for $|a|\ge1$.