Third, the limit as x approaches a of f(x) has to equal f(a), the value of the function at a. Second, the limit as x approaches a of f(x) has to exist. First, the function f has to be defined at the point a, in this case 1. I want to ask the question why is this function not continuous at x equals 1? Now recall the conditions for continuity. Otherwise it will be known as a discontinuous function.Let's take a look at another example. Moreover, a function must be continuous to be differentiable. A function is continuous if there exists a point in the open interval such that the limit of the function and its value on this point is equal. In calculus, the continuity of a function is the smoothness and consistent behaviour of the function. But sometimes, a discontinuous function is also differentiable at some points in its domain. A function should be continuous to be differentiable. In other words, if the slope of the tangent line is equal to the limit of the function at that point, it is called differentiability of a function. If f’(c) is zero, the function will satisfy Rolle's Theorem. Where, f’(c) is known as the derivative of f(x) at point c. Let’s discuss the continuity of the function $f(x)=\frac$$ Otherwise, the function will not be considered as a continuous function. The conditions in step 5 and 6 should be satisfied.If the limit from x to b of f(x) is equal to the f(b) then the function is continuous.If the limit from x to a of f(x) is equal to the f(a) then the function is continuous.
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