I'd like to typeset math in table layout, which is stretched to page width e.g.:
\begin{flalign*} a)\, \lim_{n\to\infty} \frac{1000n}{n^2+1} && b)\, \lim_{n\to\infty} \left( \sqrt{n+1}-\sqrt{n}\right) && c)\, \lim_{n\to\infty} \frac{\sqrt[3]{n}\sin n!}{n+1}&&\\ d)\, \lim_{n\to\infty} \frac{(-2)^n+ 3^n}{(-2)^{n+1}+3^{n+1}}&& \end{flalign*} This produces output where each column is aligned to right, I'd prefer left align:

Moreover some padding between lines would be nice.
I've tried using an array environment:
\[ \begin{array}{p{0.33\textwidth}p{0.33\textwidth}p{0.33\textwidth}} a)\, \displaystyle\lim_{n\to\infty} \frac{1000n}{n^2+1} & b)\, \displaystyle\lim_{n\to\infty} \left(\sqrt{n+1} - \sqrt{n}\right)& c)\, \displaystyle\lim_{n\to\infty} \frac{\sqrt[3]{n}\sin n!}{n+1}\\ d)\, \displaystyle\lim_{n\to\infty} \frac{(-2)^n+ 3^n}{(-2)^{n+1}+3^{n+1}} \end{array} \] 
It seem to solve the problem with align, but math commands inside array produces too many errors and space between rows is even smaller.
Any idea how to solve this?

