Managing variable situation (complex conditional scripting?)
Hi to all,
I'm developing some materials about functions and limits
I would like to build an interactive animation which given a [continuous] function and selecting an x_0 value, could show
- the corresponding limit i.e. as the function is continuous, the output f(x_0)
- an interval on the y axis describing the selected proximity to the limit i.e f(x_0)-e<y<f(x_0)+e
- the corresponding interval on x-axis, which guarantees that x values taken inside it will give an output which is inside the selected range on y axis,
At present moment I managed to get to point 2 (see attached example)
My problem is to find a command or a sequence of commands which can choose the correct intercepts between the function and the two lines corresponding to the extremes of the range on y axis. given the correct intercepts, I could the project them on x-axis and get the desired range on x values.
Any help or suggestion (or the confirmation that my goal is not reachable) is welcome
thank you in advance!