rsnd said:if f(c) = infinity and c is in [a,b]
is it equivalent to saying
f is not cont. at c ? because infinity is undefined?
Thanks
k.cv
When f(c) equals infinity, it means that the value of the function at point c is unbounded and has no finite limit. This can occur when the function has a vertical asymptote at c, meaning that the function approaches infinity as the input value approaches c.
No, a function can only have one value of infinity. This is because infinity is not a number, but rather a concept of unboundedness. If a function has multiple vertical asymptotes, it may approach infinity at each of these points, but it is still considered to have one value of infinity.
Not necessarily. While some functions may be undefined at points where they approach infinity, there are other cases where the function is well-defined and continuous at c, but still has a value of infinity. This is often seen in rational functions where the denominator approaches 0 at c.
The behavior of a function when f(c) equals infinity can be determined by analyzing the function's limits. If the limit of the function at c exists and is finite, then the function has a horizontal asymptote at that point. If the limit does not exist or is infinite, then the function has a vertical asymptote at c.
Yes, a function can have a value of infinity at a finite point. This occurs when the function has a vertical asymptote at that point. However, it is important to note that infinity is not a real number, so the function's output at that point is not considered a numerical value, but rather a concept of unboundedness.