# Math Help - Compute the following limit (Use l'Hopital's rule)

1. ## Compute the following limit (Use l'Hopital's rule)

[cos(a/x)]^(x^2) as x tends to infinity, where a > 0.

2. $L = \lim_{x \to \infty} \left[ \cos \left( \frac{a}{x} \right) \right]^{x^2}$

$\ln L = \lim_{x \to \infty} \ln \left[ \cos \left( \frac{a}{x} \right) \right]^{x^2}$

$\ln L = \lim_{x \to \infty} x^2 \ln \left[ \cos \left( \frac{a}{x} \right) \right]$

$\ln L = \lim_{x \to \infty} \frac{\ln \left[ \cos \left( \frac{a}{x} \right) \right]}{x^{-2}}$

Now you have $\frac{0}{0}$ so you can apply L'Hôpital's rule.