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Second Activity

The previous extract considered quadratic Taylor polynomials about zero. Providing the function can be differentiated n times at zero,this approach can be extended and higher order Taylor polynomials can be found. The next extract extends this idea even further by finding Taylor polynomials around points other than zero. Now download the second extract. Print it to read, annotate and highlight in a way that you might find useful. It is just one page long.

Downloading materialClick here to download the extract

You can now compare your annotations with mine. Don't expect them to be the same! This is how I thought as I read it.

Downloading materialClick here to download comments
Notice, in particular, that I had a go at the Example before reading the solution. Even if you don't know how to do an example, your solution misses out some of the points, or contains errors having a go yourself will mean that you understand the details of the given solution much more.

I hope you have found these activities useful and wish you well in your studies. Taking the time to work through these pages is in itself a good sign.