Mathematics 1 | Continuity: Know Your Limits

We explain what a continuous function is and how we precisely define continuity using limits of sequences.

Mathematics 1 | Closer and closer: Taylor Approximations

Taylor approximations are used to approximate complicate functions by simple functions, that is, polynomials, locally near a given point a.

Mathematics 1 | Differentiating Inverse Functions

We show a little trick of how to differentiate inverse functions without knowing their formulas.

Mathematics 1 | The Chain Rule

We discuss the chain rule for differentiating composite functions and verify it graphically using GeoGebra animations.

Mathematics 1 | Differentiation Rules: Sum, Product, and Quotient Rule

We explain and graphically illustrate the sum, product, and the quotient rule.

Mathematics 1 | Three Simple Rules for Differentiation

We present three simple rules for differentiation, motivate them graphically and prove them using differential quotients.

Mathematics 1 | Differentiation Rules: Power Rule

We explain the differentiation rule for power functions using limit calculations for difference quotients.

Mathematics 1 | Differentiation: Derivatives and Tangents

We define the derivative as the slope of the tangent and show how to calculate it by the limit of secant slopes.

Mathematics 1 | Limits of Sequences: Examples, Tips and Tricks

We walk through step-by-step solutions for finding the limits of 11 example sequences.

Mathematics 1 | Limits of Infinite Geometric Series

We introduce geometric series and calculate their limits, if they exist.