Answer
$$\lim_{u\to\infty}\frac{e^{u/10}}{u^3}=\infty$$
Work Step by Step
$$A=\lim_{u\to\infty}\frac{e^{u/10}}{u^3}$$
As $u\to\infty$, $e^{u/10}\to\infty$ and $u^3\to\infty$.
That means we have an indeterminate form of $\infty/\infty$ here, favourable to the application of L'Hospital's Rule:
$$A=\lim_{u\to\infty}\frac{(e^{u/10})'}{(u^3)'}$$
$$A=\lim_{u\to\infty}\frac{e^{u/10}(u/10)'}{3u^2}$$
$$A=\lim_{u\to\infty}\frac{e^{u/10}}{30u^2}$$
As $u\to\infty$, $e^{u/10}\to\infty$ and $u^2\to\infty$.
So again, we have an indeterminate form of $\infty/\infty$. We apply L'Hospital's Rule one more time:
$$A=\lim_{u\to\infty}\frac{e^{u/10}(u/10)'}{60u} $$
$$A=\lim_{u\to\infty}\frac{e^{u/10}}{600u}$$
Again, as $u\to\infty$, $e^{u/10}\to\infty$ and $u\to\infty$.
Another indeterminate form of $\infty/\infty$, meaning we still can apply L'Hospital's Rule:
$$A=\lim_{u\to\infty}\frac{e^{u/10}(u/10)'}{600} $$
$$A=\lim_{u\to\infty}\frac{e^{u/10}}{6000}$$
As $u\to\infty$, $e^{u/10}\to\infty$, so $\frac{e^{u/10}}{6000}$ also approaches $\infty.$
In other words, $$A=\infty$$
