Calculus

L'Hôpital's Rule

Repeated Application of L'Hopital's Rule

         

Evaluate limx0e14x114xx2\displaystyle \lim_{x \to 0} \frac{e^{14x}- 1 - 14x}{x^2}.

Evaluate limx0+(1+sin6x)cotx.\lim_{x \to 0^+} (1+\sin 6x)^{\cot x}.

Evaluate limx0e2x12xx2.\lim_{x \to 0} \frac{e^{2x}-1-2x}{x^2}.

Evaluate limx06tanx6xx3.\lim_{x \to 0} \frac{6\tan x-6x}{x^3}.

Evaluate limx1x99x+8(x1)2.\lim_{x \to 1} \frac{x^{9}-9x+8}{(x-1)^2}.

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