sedaw said:need to prove that f(x) bounded if f(x) continuous in [a,+infinite] and if there's a limit while x goes to +infinite.
I would really appreciate any kind of help !
A bounded function is a mathematical function that is limited or confined within a certain range of values. This means that the output of the function will never exceed a certain value, regardless of the input.
An unbounded function has no limitations on its output and can increase or decrease indefinitely. In contrast, a bounded function has a maximum or minimum value that it cannot exceed.
Proving that a function is bounded is important because it allows us to understand the behavior of the function and make predictions about its output. It also helps us determine the domain and range of the function.
One common method is to use the definition of a bounded function, which states that for any input, the output must be within a certain range. Other methods include using calculus techniques such as the Extreme Value Theorem, or using the properties of limits.
No, a function cannot be both bounded and unbounded. It must fall into one of these two categories. However, it is possible for a function to be bounded on some intervals and unbounded on others.