And that is good otherwise the statement would be wrong.lep11 said:Because lim f(x)=a as x appr. infinity there
A limit is the value that a function or sequence approaches as the input or index approaches a certain value. It represents the behavior of the function or sequence near a specific point.
To prove a limit using the epsilon-delta definition, you must show that for every positive epsilon (ε), there exists a corresponding positive delta (δ) such that if the distance between the input and the limit point is less than delta, then the distance between the output and the limit is less than epsilon.
The squeeze theorem, also known as the sandwich theorem, states that if two functions have the same limit as x approaches a certain value, and a third function is always between them, then the third function also has the same limit at that point. This can be used to prove limits by finding two functions that are easier to evaluate and using them to bound the function in question.
No, a sequence can only have one limit. If a sequence has multiple limits, then it is considered divergent and does not have a limit.
Limits are used in many real-world applications, including in physics, economics, and engineering. In physics, limits are used to calculate instantaneous rates of change, such as velocity and acceleration. In economics, limits are used to model supply and demand curves. In engineering, limits are used to optimize designs and analyze the behavior of systems.