Can a continuous function be infinity?

Yes, you can make your function go from R to the “extended real numbers” {−∞}∪R∪{∞}, a topological space that is homeomorphic to [0,1], using a topology that should be pretty obvious. Then if you define f(0)=∞, your function is continuous at 0.

Can a continuous function equal 0?

Clearly, δ can be anything, so the continuity holds. f(x)=0 is a continuous function because it is an unbroken line, without holes or jumps. All numbers are constants, so yes, 0 would be a constant.

How do you know if a function is continuous at infinity?

Starts here8:44Calculus – Continuous functions – YouTubeYouTubeStart of suggested clipEnd of suggested clip60 second suggested clipSo that’s kind of what this definition is saying that if you’re interested in the value of theMoreSo that’s kind of what this definition is saying that if you’re interested in the value of the function and the limit happens to equal just plugging it in then you know it’s continuous at that.

How do you know if a function is continuous?

Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain:

1. f(c) must be defined.
2. The limit of the function as x approaches the value c must exist.
3. The function’s value at c and the limit as x approaches c must be the same.

What types of functions are always continuous on − ∞ ∞?

Every polynomial function is continuous everywhere on (−∞, ∞). (ii.) Every rational function is continuous everywhere it is defined, i.e., at every point in its domain.

Can a continuous function have Asymptotes?

Explanation: A continuous function may not have vertical asymptotes. Vertical asymptotes are nonremovable discontinuities. This function is continuous for the set of all real numbers; however, ex≥0 for all x , IE, there is a horizontal asymptote at y=0.

Is 1 continuous function?

Since y=1x is continuous over its domain. As zero is not in the domain, you can say 1x is a continuous function.

How do you determine if a function is continuous or discontinuous?

A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value.

Which of the following types of functions are always continuous on − ∞ ∞?

What is a continuous function in math?

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there is no abrupt changes in value, known as discontinuities.

Which types of functions are always continuous on − ∞ ∞?

What is the limit of a function that is continuous?

A function is said to be continuous if it is continuous at all points. Limits at infinity (or limits of functions as x approaches positive or negative infinity) We say that the limit of f(x) as x approaches positive infinity is L and write, if for any e > 0 there exists N > 0 such that | f (x) – L | < e for all x > N (e).

Therefore, if a function changes gradually as independent variable changes, so that at every value a, of the independent variable, the difference between f (x) and f (a) approaches zero as x approaches a. A function is said to be continuous if it is continuous at all points.

What is the limit of the derivative of a function at infinity?

If limit of f at infinity equals 0 then the limit of its derivative f’ at infinity is also zero. An example (which must be pretty tedious for presenting briefly in this thread) is in preparation. The zero limit has no effect on the derivative. Take f (t):= \\sin (t^2).t^ {-1}.

Can a function be semi-continuous?

So, the function will be semi-continuous, but by playing with a domain of the function we can achive continuity, for example by extending reals with infinity itself as it was mentioned above. Share Cite Follow answered Apr 7 ’13 at 23:53