Aug 19, 2022 · The function ƒ (x) = 1/x (Figure 2.41) is a continuous function because it is continuous at every point of its domain. The point x = 0 is not in the domain of the function ƒ, so ƒ is not continuous …

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a piecewise continuous

Jan 30, 2019 · I am confused about "continuous function" term. What really is a continuous function? A function that is continuous for all of its domain or for all real numbers? Let's say: $\ln|x|$ - the graph …

Jan 8, 2022 · Every continuous function on an open subset of the reals has an antiderivative. The integral function is only differentiable on the interior of $ [a,b]$.

There are other ways a function can be a continuous extension, but probably the most basic way (and likely about the only way you'll see in elementary calculus) is that you have a function that is not …

Dec 25, 2016 · The tangent function is continuous on its domain; it isn’t a continuous function on $\Bbb R$ simply because it isn’t defined on all of $\Bbb R$ (and moreover, the discontinuities aren’t even …

In your case, you don't just want the non-differentiability set for a strictly increasing continuous function, but for such a function with the additional requirement that the function has a zero derivative almost …

Continuous function proof by definition Ask Question Asked 12 years, 8 months ago Modified 6 years, 6 months ago

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

Unfortunately this answer is incomplete. "Such a function" would be a continuous bijection from $ (0,1)$ to $ [0,1]$. The matter of the question is to show that any continuous bijection from $ (0,1)$ to $ …