Key points

• L'Hôpital's rule applies to 0/0 or ∞/∞ forms.
• lim (x→0) sin x / x = 1; lim (x→∞) (1 + 1/x)ˣ = e.
• Maxima/minima: f'(x) = 0; f''(x) < 0 → maximum, f''(x) > 0 → minimum.
• ∫ from −a to a of an odd function = 0; of an even function = 2∫ from 0 to a.
• Mean value theorem: f'(c) = (f(b) − f(a)) / (b − a) for some c in (a, b).