问题

求下列极限

1.

\[
\lim_{x\rightarrow+\infty}\frac{\displaystyle\int_{0}^{x}e^{t^2}\mathrm{d}t}{\displaystyle\int_{0}^{x}e^{2t^2}\mathrm{d}t}
\]

2.

\[
\lim_{h\rightarrow 0}\frac{1}{h^2}\int_0^h \Bigl(\frac{1}{\theta}-\cot\theta\Bigr)\mathrm{d}\theta
\]