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

1 Answer
May 16, 2016

Answer:

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