Question

What is continuous function
Please answer by calculus students

Answer 1

In calculus, a function is continuous at x = a if - and only if - it meets three conditions: The function is defined at x = a. The limit of the function as x approaches a exists. The limit of the function as x approaches a is equal to the function value f(a)

Answer 2

Example: g(x) = (x2-1)/(x-1) over the interval x<1. Almost the same function, but now it is over an interval that does not include x=1. So now it is a continuous function (does not include the "hole")In mathematics, a continuous function is a function that does not have any abrupt changes in value, known as discontinuities. More precisely, sufficiently small changes in the input of a continuous function result in arbitrarily small changes in its output. If not continuous, a function is said to be discontinuous.

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