If , then is equal…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x)=\lim_{t\to0}\tan^{-1}\left(\frac{e^{xt}-1}{t}\right)

, then

\lim_{x\to0}\frac{f(x)-x}{x^3}

is equal to (a)

\frac{1}{2}

(b)

-\frac{1}{2}

(c)

\frac{1}{3}

(d)

-\frac{1}{3}