by HallsofIvy » Fri Mar 27, 2020 8:15 pm
In general, if f is any continuous function then [tex]\lim_{x\to a}f(x)= f(a)[/tex] while [tex]\lim_{x\to 0} f(x- a)= f(-a)[/tex]. That is the same as f(a) if f is an even function but not if f is an odd function.