Limits
Formal definition of derivatives
$$ {df \over dx}(2) = \lim_{h \to 0} = {{f(2 + h) - f(2)} \over h} $$
($\epsilon$, $\delta$) definition of limits
L’Hôpital’s rule
$$ \lim_{x \to a}{f(x) \over g(x)} = {f’(a) \over g’(a)} $$
$$ {df \over dx}(2) = \lim_{h \to 0} = {{f(2 + h) - f(2)} \over h} $$
$$ \lim_{x \to a}{f(x) \over g(x)} = {f’(a) \over g’(a)} $$