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