Tricky Limit question What is
$$\lim_{t \rightarrow 0} \frac{e^{t^3}-1-t^3}{\sin(t^2)-t^2}?$$
I used Hopital's rule, but it kept getting more complicated!

Hint:
Use Taylor's formula for $x\to{0}$:
$$e^{x}=1+x+\dfrac{x^2}{2!}+\ldots+\dfrac{x^n}{n!}+o(x^n), \\
\sin{x}=x-\dfrac{x^3}{3!}+\ldots+(-1)^n\dfrac{x^{2n+1}}{{(2n+1)}!}+o(x^{2n+1}).$$
