The server generates a function f (x) of one real variable x, containing parameters a1,a2,..., which is defined by different formulas on two segments of an interval. Your aim is to find values for these parameters ai such that f (x) is continuous and differentiable to a required order.
One can solve the problem either by a Taylor expansion, or by successive derivations. 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 .
There is also a detailed menu for the parameters of this exercise. The most recent version
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Description: parametrize a function to make it differentiable to a required order. interactive exercises, online calculators and plotters, mathematical recreation and games
Keywords: interactive mathematics, interactive math, server side interactivity, analysis, algebra, continuity, derivability, limit