This module is an exercise on the infinitesimals (and its notation by O and/or o). The server generates a function $f(x)$ of one real variable $x$, containing parameters ${a}_{1}$, ${a}_{2}$,... Your aim is to find values for these parameters${a}_{i}$ such that $f(x)$ is infinitesimal to a required order, at the neighborhood of a given point ${x}_{0}$.

Except the trivial levels, one solves the problem by the Taylor expansion of $f(x)$. In the difficult cases, the resolution of a system of linear equations is also necessary.Choose the level of difficulty suitable for you: 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 .

Detailed menu for the parameters of this exercise.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

Description: parametrize a function to make it infinitesimal at a point. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, nice sophia antipolis university, analysis, continuity, derivative, limit