Calculus

A Geometrical Limit

(A new question of the week) We usually see limits applied to functions in a calculus class. An interesting question from late October deals with a limit in a geometrical construction based on a function. We’ll be seeing how to discover a proof, then several alternative proofs, and finally what the answer means.

The Symmetric Derivative

To close out this series on the definition of the derivative, I want to look at a few questions about alternative versions of the definition, primarily the “symmetric difference quotient”. We’ll see that this leads to a slightly different result, not always equivalent to the original, and we’ll observe some associated ways that calculators can …

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What Do dx and dy Mean?

We’ve looked at the meaning of the derivative, and of its various notations, including dy/dx. This leads to the next question: What does dx or dy mean on its own? This was touched on last time, but there’s a lot more to say that I couldn’t fit there. We’ll look at more advanced approaches to …

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What Derivative Notations Mean

Last week we looked at the meaning of the derivative. In doing so, we mostly used the notation “”, but mentioned another in passing. Here I want to look at our answers to several questions about the different notations you will see.

What is a Derivative?

To start a series of posts on differentiation (one of the basic concepts studied in calculus), I’d like to look at a number of answers we’ve given to the basic question, What is a derivative? This includes questions about the meaning of the concept and its definition, as well as examples. Something all these questions …

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