# Questions tagged [piecewise-continuity]

For use when asking questions about piecewise continuous functions, their properties, or the functional branch itself.

205 questions
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### Solve differential equation of piecewise function Matlab.

I have a piecewise function called $y(x)$ and another function called $v(x)$ which is a derivative of $y(t)$. Now I need to solve this function and plot in Matlab. To do this I've used this code and ...
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### If $f(x,y)=9-x^2-y^2$ if $x^2+y^2\leq9$ and $f(x,y)=0$ if $x^2+y^2>9$ study what happens at $(3,0)$

If$$f(x,y)=\begin{cases}9-x^2-y^2&\text{if }x^2+y^2\leq9\\0&\text{if }x^2+y^2>9\end{cases}$$study the continuity and existence of partial derivative with respect to $y$ at point $(3,0)$. ...
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### How to maximize a piecewise linear convex function $f: \mathbb{R}^n\to \mathbb{R}$?

How to maximize a piecewise linear convex function $f: \mathbb{R}^n\to \mathbb{R}$? I can see that there are many references for minimizing a piecewise linear convex function but not maximizing such a ...
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### Does piecewise continuity of $f'$ implies that the discontinuities of $f$ are jump discontinuities?

In this pdf, the following theorem is stated without proof: I'm not sure how this mathematically is accurate. My question is: Do the limits $f(x^+)$ and $f(x^-)$ exist, in the last statement? i.e. ...