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Students get to adjust the second segment of a piecewise linear function on an interval \([a,b]\) to make it continuous or not.

Theoretical Issues

Substitution 2

Graphs a function \(f (x)=g(x)h'(x)\) and the area under the graph of \(f (x)\) for a given interval, and shows the modifications made to \(f (x)\) and the area when considering \(u=g(x)\) and \(v

Integration Methods

Sage

Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.

General Tools

Applets and Activities for Real Analysis: Sequence Convergence

This GeoGebra applet and accompanying activities illustrate the formal definition of a sequence of real numbers converging to a limit \(L\) through a series of interactive exercises.

Infinite Limits: Sequences and Series, One-Variable Calculus

Sequences and Series of Constants Plotter

The applet shows graphically and numerically consecutive terms of a sequence or consecutive partial sums of a series.

Infinite Limits: Sequences and Series

Taylor Polynomial Approximation

This applet allows the user to look at the Taylor polynomial approximation to a function \(f(x)\).

One-Variable Calculus

The Limit of a Sequence

This resource is a geogebra applet with minimal instructions that allows the user to explore the limit of a sequence visually.

Infinite Limits: Sequences and Series

WinPlot

WinPlot is a freely distrributed simple 2D and 3D grapher, with built-in features for creating animations, tables of values, and more.

General Tools

WolframAlpha

WolframAlpha is an online computational knowledge engine. It can accept natural language input and is programmed with thousands of computational algorithms.

General Tools

Infinite Limits at Infinity

In the M-N definition of an infinite limit at infinity, students get to select M and then adjust N to satisfy the definition.

Infinite Limits: Function Values and Integrals, Continuity and Limits