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mfk_1868
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i didnt understand delta definiton anyone can explain?
yes can you show me a proving example. for example lim x->3 x^2/5 how to proof this.cogito² said:Do you mean the limit of a function? If [tex]f[/tex] is a real-valued function we say that [tex]\lim_{x \to a} f(x) = L[/tex], if given [tex]\epsilon > 0[/tex] there exists a [tex]\delta > 0[/tex] such that [tex]|x - a| < \delta[/tex] imply that [tex]|f(x) - L| < \epsilon[/tex].
Is that the definition you don't understand? Are talking about metric spaces?
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The formal limit definition is a mathematical concept used to describe the behavior of a function as its input approaches a specific value, known as the limit. It is used to determine the exact value of a limit and prove its existence.
The formal limit definition is written as:
limx→a f(x) = L
This means that as x approaches the value of a, the function f(x) approaches the value of L.
The formal limit definition is important because it allows us to analyze the behavior of a function near a specific point, even if the function is not defined at that point. It also helps us to understand the continuity and differentiability of a function, and is essential in many areas of mathematics and science.
The key components of the formal limit definition are the limit value (L), the input value (a), and the function (f(x)). The limit value is the number that the function approaches as the input value approaches a. The input value is the value that the function is approaching. The function is the mathematical expression that depends on the input value and determines the behavior of the function near the limit point.
The formal limit definition is used in practice to solve various problems in calculus, such as finding the derivative of a function or determining the continuity of a function. It is also used in physics, engineering, and other fields to model and predict the behavior of systems and phenomena.