How do I find one-sided limits of piecewise functions?

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How do I find one-sided limits of piecewise functions?

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Answer 1 · 2016-05-16T09:22:26

If x = c is the junction for the two pieces $y = f (x), x \in (a, c)$ $y = f(x), x in (a, c)$ and $y = g (x), x \in (c, b)$ $y = g(x), x in (c, b)$ , the one-sided limits at the junction x = c are $h \to 0$ $h to 0$ of $f (c - h) and g (c + h)$ $f(c-h) and g(c+h)$ .

Explanation:

The piecewise functions are jointly continuous at x = c, if the one-sided limits are the same.

Further if the one-sided limits for f' ad g' are the same, they are differentiable at x = c.

For piece-wise cubic-spline fitting, this matching is extended up to f'' and g''.

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How do I find one-sided limits of piecewise functions?

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