how to calculate a limit? Here is a well-known function:
$$f(x)=\begin{cases}\exp\left(-\frac{1}{x^2}\right) & x\not=0 \\ 0& x=0\end{cases}.$$
How to calculate :
$$\lim_{t \rightarrow 0}\frac{f(t^2+t)-f(t)}{t^2},$$ does it equal zero?

Check if $f'(0),f''(0)$ exists or not using standard definition and then apply L'Hopital's Rule.
