# What is the epsilon delta definition of limit?

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The epsilon-delta definition of a limit is a mathematical concept used to formally define the limit of a function. It states that for a given function f(x), as x approaches a certain value c, the limit of f(x) is L if for every positive value of epsilon (ε), there exists a positive value of delta (δ) such that if the distance between x and c is less than delta, then the distance between f(x) and L is less than epsilon. In other words, it provides a precise way to describe the behavior of a function as it approaches a particular point.

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The epsilon-delta definition of a limit states that the limit of a function f(x) as x approaches a particular value, say c, is L if for every positive real number ε (epsilon), there exists a corresponding positive real number δ (delta) such that for all x within the domain of f, if 0 < |x - c| < δ, then |f(x) - L| < ε. This definition formalizes the intuitive idea that as x gets arbitrarily close to c, the values of f(x) get arbitrarily close to L.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you use the epsilon delta definition of limit to prove that #lim_(x->5)(x-1)= 4# ?
- How do you find the Limit of #ln(x+1)/x # as x approaches infinity?
- How do you find the limit of #|x+2| / (x+2)# as x approaches #-2#?
- How do you find the limit of #cosx/cotx# as #x->pi/2#?
- How do you find the limit of #e^(x-x^2)# as #x->oo#?

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