![]() ![]() In this case, if we evaluate the function at the point we're taking the limit (in this case 0), we get: Usually, the only case where you'll encounter a discontinuous function in these types of problems is when the function is not defined, because the denominator becomes zero somewhere, or we take the square root of a negative number. In this question we have the limit:Īll of these functions are continuous functions. When we're told to solve limits, the first thing we must do is to try to evaluate the function at the point we taking the limit. Question 5: Is a point function continuous?Īnswer: A point function is not continuous according to the definition of continuous function.A Confusing Question to Me: Solving Limits by Continuity In a removable discontinuity, one can redefine the point so as to make the function continuous by matching the particular point’s value with the rest of the function. Question 4: What is meant by discontinuous function?Īnswer: Discontinuous functions are those that are not a continuous curve. Symbolically, one can write this as f (x) = 6. For example, given the function f (x) = 3x, the limit of f (x) as the approaching of x takes place to 2 is 6. Question 3: What is limit with regards to continuity?Īnswer: A limit refers to a number that a function approaches as the approaching of an independent variable of the function takes place to a given value. The limit of the function as the approaching of x takes place, a is equal to the function value f(a). ![]() ![]()
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