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
SAGE can differentiate x^2\log(x+a) and \tan^{-1}(x)=\arctan(x):
sage: diff(x^2 * log(x+a), x) 2*x*log(x + a) + x^2/(x + a) sage: derivative(atan(x), x) 1/(x^2 + 1)
Applications
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Sequences and series
(Some schools teach this topic as part of integral calculus.)