I was trying to understand how we can approximate exp.
One example is:
$$ \exp(t) = \sum_{i=0}^\infty t^i/i! $$
however, why is the following true:
$$\lim_{x\to \infty}\exp \left ({\frac{t^2}{2!} +\frac{t^3}{3!\cdot x^{.5}} + \frac{t^4}{4!\cdot x^{1.5}} + \dots } \right) = \exp(\frac{t^2}{2})$$
(Hint) First, as experimentX suggest, take the log of both sides to get rid of $\exp$ (you can pull $\exp$ out of the limit because $\exp$ is a continuous function). Now since $t$ is fixed, you can treat it as constant in the limit. What happens to a term like $\displaystyle \frac{t^3}{3!x^{.5}}$ as $x \to \infty$?