Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote $\infty$ and MINF to denote $-\infty$.

$\displaystyle \lim_{x\to \infty} \frac{\ln(x^{3}-7)}{\ln(x)\cos(1/x)}$ =

$\displaystyle \lim_{x\to \infty} \frac{e^{7 x}}{e^{8 x}-e^{-8 x}}$ =