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Students investigate the limits of the functions \(x^n \sin(^1/_x)\) as \(x \to 0\) for \( n = 0, 1, 2\) and \(3\).

Infinite Limits: Function Values and Integrals, Continuity and Limits

Limits, Continuity, and Differentiability

This GeoGebra applet allows interactive and visual exploration of the relationship between continuity and differentiability.

Differentiation: Definition and Elementary Application, Continuity and Limits

Delta Epsilon Applet

This is a Loci article that includes five GeoGebra applets to illustrate topics in real analysis, or a rigorous course in calculus.

Continuity and Limits, One-Variable Calculus

Dave's Short Trig Course

A systematically presented multi-page course on basic trigonometry: trigonometry of triangles, laws of sines and cosines, angles, radian measure, trigonometric functions.

Calculus Functions, Background

Area of a Surface of Revolution

Integration: Applications

Work: Spring

Integration: Applications

Volume with a Common Cross-section Applet

This applet allows the user to draw three dimensional solids with various cross section shapes, including shapes from standard calculus exercises such as squares, rectangles, equilateral triangles

Integration: Applications

Maths Is Fun

Colorful presentations, many of them interactive, of topics from elementary algebra on up that students should know when they enter a calculus course, including inequalities, exponents, logarithms

Background

The Sagacity of Circles: A History of the Isoperimetric Problem

A summary of the history of the problem of finding the region of greatest area bounded by a given perimeter, from Zenodorus and Pappus to Jakob Steiner (one page each).

History of Calculus, One-Variable Calculus

What is \(0^{0}\)?

The expression \(0^0\) is usually called an indeterminate form.

History of Calculus, One-Variable Calculus