Differential Calculus
Besides the examples on this page, please see the discussion in ["BasicCalculus"].
Functions
Piecewise fcns, polynomials, exponential, logs, trig and hyperboic trig functions.
Limits
SAGE can compute \lim_{x\rightarrow 0}\frac{\sin(x)}{x}:
sage: limit(sin(x)/x,x=0) 1
Differentiation
...
Applications
...
Sequences and series
(Some schools teach this topic as part of integral calculus.)