Analysis

Given a univariate function, computes its derivative.

differentiate(Function)
differentiate(Function, Identifier)
differentiate(Function, Identifier, Integer)
differentiate(Function, Integer)

Given a function f, an identifier x and an integer n, computes the n-th derivative of f with respect to x. 

Given an univariate function, computes its primitive.

integrate(Function)
integrate(Function, Identifier)
integrate(Function, Identifier, Integer | Expression, Integer | Expression)
integrate(Function, Integer | Expression, Integer | Expression)

Given a function f, an identifier x and two integers or expressions a and b, computes the definite integral of f with respect to x between a and b.  

Given a function or expression, computes the limit.

limit(Function, Identifier, Real | Infinity )
limit(Function, Real | Infinity)

Given a function f, an identifier x, and a value a which is a real or infinity, computes the limit of f as x approaches a.