mike1988 said:I am trying to solve a question and I need to justify a line in which |lim(x-->0)(f(x))|≤lim(x-->0)|f(x)| where f is a continuous function.
Any help?
Ray Vickson said:Show your work. Where are you stuck?
RGV
A limit of a continuous function is a mathematical concept that describes the behavior of a function as the input approaches a certain value. It represents the value that the function is approaching at that point.
The limit of a continuous function can be calculated using various methods, such as algebraic evaluation, graphical analysis, and the use of limit laws. The most common method is to substitute the value the input is approaching into the function and simplify the expression.
The limit of a continuous function is important because it helps us understand the behavior of a function at a specific point. It allows us to make predictions and analyze the behavior of functions in real-world applications.
Yes, the limit of a continuous function can exist even if it is not equal to the function's value at that point. This can occur if there is a hole or a jump in the function's graph at that point.
No, a continuous function will always have a limit at every point where it is defined. If a function is not continuous at a certain point, it means that the limit does not exist at that point.