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Miscellaneous
Analysis
Reading time: 1minThis section focuses on essential tools for working with functions, enabling you to explore their behavior, rates of change, and accumulated values. You'll find commands for calculating derivatives, integrals, and limits, as well as for numerical approximations and defining regions in the coordinate plane. These functions are critical for creating dynamic exercises that involve calculus and function analysis.
Example classroom uses
- Generate a random function and ask students to find its derivative or integral.
- Present a function that's difficult to differentiate or integrate analytically and challenge students to approximate its derivative or integral at a specific point.
- Create problems where students need to evaluate the limit of a function as it approaches a certain value, especially for indeterminate forms.
👉Need concrete examples? Check out the Examples section to see how these functions are used in real exercises. It’s a great place to see how to combine random value generation, conditions, and solution logic in context.
Functions
differentiate
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.Â
integrate
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. Â
limit
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.
numerical_differentiation
Given a function, computes numerically the derivative.
numerical_differentiation(Function, Real)Given a univariate function f(x) and a real x0, computes numerically the derivative of f at x0.Â
numerical_integration
Given a function, computes numerically the derivative.
numerical_integration(Function, Real, Real)Given a univariate function f(x) and two reals a and b, computes numerically the primitive of f between a and b.Â
region
Given a pair of curves, returns the region between them.
region(Curve)
region(Curve, Range)
region(Curve, Curve)
region(Curve, Curve, Range)Given two curves and a range x0..xf, returns the region between these curves between x0 and xf.