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flora
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What is the definition of limit? i read some documents but it was not clear. Could you explain what epsilon and delta is ?
mathwonk said:the limit of a function f at a, is the number such that redefining f(a) as that number, makes f continuous at a.
HallsofIvy said:Great! And the defiition of continuous is?
The definition of limit is a mathematical concept that describes the behavior of a function as its input approaches a certain value. It is the value that a function approaches as the input gets closer and closer to a specific value, but may not necessarily reach.
The limit of a function can be calculated by evaluating the function at values approaching the desired input value, and observing the behavior of the function as those values get closer and closer. This can be done algebraically, graphically, or using calculus techniques such as L'Hopital's rule.
The symbol used to represent limit is "lim". It is written as lim (f(x)) = L, where f(x) is the function being evaluated, and L is the limit value.
If a function has no limit, it means that as the input approaches a certain value, the function does not approach a single, finite value. This could indicate that the function is undefined at that input value, or that the limit does not exist due to oscillation or divergence of the function.
No, a function can only have one limit at a specific input value. This is because the limit represents the value that the function approaches as the input gets closer and closer to that value. If a function has more than one limit, it would mean that the function approaches different values as the input approaches the same value, which is not possible.