a) \[\lim_{x \to \infty} \frac{x}{e^x}\]
b) \[\lim_{x \to 0^+} \frac{\ln(x)}{\frac{1}{x}}\]
c) \[\lim_{x \to 0} \frac{\sin(x)}{x^2}\]
d) \[\lim_{x \to 1} \frac{x^2 - 1}{x - 1}\]
e) \[\lim_{x \to \infty} \frac{\ln(x)}{\sqrt{x}}\]
f) \[\lim_{x \to 0} \frac{\tan(x)}{x}\]
