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Suppose that f : R → R such that, the lim h→0 [f(x) − f(x −...

Suppose that f : R → R such that, the lim h→0 [f(x) − f(x − h)] = 0 for all x ∈ R, then is f continuous in this case?

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Answer #1

as, h tends to 0 so we can replace x with x+h and we used this technique to proof f is continuous. By showing the left hand limit, right hand limit and value of fumction at that point is equal.

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