Calculus
# L'Hôpital's Rule

Evaluate $\displaystyle \lim_{x \to 0} \frac{e^{14x}- 1 - 14x}{x^2}$.

Evaluate $\lim_{x \to 0^+} (1+\sin 6x)^{\cot x}.$

Evaluate $\lim_{x \to 0} \frac{e^{2x}-1-2x}{x^2}.$

Evaluate $\lim_{x \to 0} \frac{6\tan x-6x}{x^3}.$

Evaluate $\lim_{x \to 1} \frac{x^{9}-9x+8}{(x-1)^2}.$