phymatter said:Is it so that for limx->infinity f(x) to exist ,
limx->+infinity f(x) and limx->-infinity should exist and be equal ? if so then why ?
LCKurtz said:No, it isn't so. Look at f(x) = Arctan(x).
phymatter said:Are you sure , because i.a. maron single variable calculus says that limx->infinity (2x2+3)1/2/(4x+2) does not exist for the same reason .
The limit of infinity is a concept in calculus that refers to the behavior of a function as the input approaches positive or negative infinity. It represents the value that a function approaches, but may never reach, as the input increases or decreases without bound.
To determine if a limit of infinity exists, you must evaluate the function at values that approach infinity from both positive and negative directions. If both of these values approach the same value, then the limit of infinity exists. If the two values approach different values or do not approach a value at all, then the limit of infinity does not exist.
No, the limit of infinity is not a real number. It represents the behavior of a function as the input approaches infinity, but it is not an actual value that the function reaches.
The limit of infinity represents the behavior of a function as the input approaches infinity, while a limit at a finite number represents the behavior of a function at a specific input value. In other words, the limit of infinity is concerned with the overall trend of the function as the input increases or decreases without bound, while a limit at a finite number is concerned with the behavior of the function at a particular input value.
Yes, a function can have a limit of infinity at multiple points. This means that as the input approaches positive or negative infinity, the function approaches a certain value at multiple points. However, it is also possible for a function to have a limit of infinity at one point but not at another point.