Read more: Derivative of Inverse Trigonometric FunctionsĪ continuous function has a number of properties that holds the continuity of that function. the graph of that function cannot break or jump at any point in that interval. A function that is continuous over an interval has to display continuity at each and every point in the interval i.e. ![]() A function that is continuous at a certain point does not have any breaks or follows continuity at that point. ![]() The functions that do not follow these conditions are called discontinuous functions. Thus, lim x→a f(x) = f(a) suggests that function f(x) is continuous at point x=a.Ī function needs to be continuous in calculus if it is differentiated, since only continuous functions are differentiable. Thus, if these graphs are combined together, the resulting graph would obey all the conditions that are required for a function to be continuous.
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