A function is continuous at x = a if and only if limₓ → ₐ f (x) = f (a). It means, for a function to have continuity at a point, it shouldn't be broken at that point. For a function to be differentiable, it has to be continuous. All polynomials are

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If f (a) and f (b) are defined then f (x) is continuous in the interval (a,b). If the given function is a rational function, then check for the discontinuity at the zeroes of the