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I am a bit confused on these ideas, though they should be simple calculations. I have an exam for this in 2/3weeks and I need more examples.

If you can explain 3 or more (or point me in the direction of many more) examples of each that would be great!

To give you an idea of the level, there is ONE example I have access to for each.

Germ

$f(x) = x^3 - 2x^2 + x$ find the germ at $x_0= - 1$

Jets

Find the kth jet at $0$ for $e^x$

If you can point me into any resources, or come up with examples and explain them, that would be awesome!!

Thank you for any reply

mathsislife
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The germ of $f$ at $−1$ is the set of functions $g$ s.t. $$\exists\delta>0\ \forall x\in(-1-\delta,-1+\delta):\ g(x) = f(x).$$ The jet is simply the formal Taylor polynomial. See https://en.wikipedia.org/wiki/Jet_(mathematics).

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Martín-Blas Pérez Pinilla
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