A function f is said to be symmetrically continuous at X0 if

lim [f(X0 + h) - f(X0 - h)]= 0
h-> 0

Show that if f is continuous at X0, it is symmetrically continuous there but not conversely.
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 This sounds like homework so I'm not going to go into too much detail, but note that if f is continuous at x then: $$lim_{h\rightarrow0}f(x+h)=lim_{h\rightarrow0}f(x-h)=f(x).$$ There isn't much more to do.
 For the converse, take f(x) =x if x is nonzero , f(0) =1. f is symmetrically continuous at 0, but not continuous.

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