This module is an exercise on the continuity and differentiability of real functions.

The server generates a function $f$ of one real variable x, containing parameters ${a}_{1}$, ${a}_{2}$,..., which is defined by different formulas on three segments of an interval. Your aim is to find values for these parameters ${a}_{i}$ such that $f$ is continuous (or continuous and differentiable, following the level of difficulty you have chosen).

One can solve the problem either by Taylor expansions, or by successive derivations. In the difficult cases, the resolution of a system of linear equations is also necessary.

Choose the level of difficulty you want: 1 . 2 . 3 . 4 . 5 . 6 . The most recent version

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 continue or differentiable on 2 points. exercises interactifs, calcul et tracé de graphes en ligne

Keywords: interactive mathematics, interactive math, server side interactivity, analysis, algebra, continuity, derivative, limit