Understanding the Limit of a Constant | A Comprehensive Explanation

Limit of a constant k

The limit of a constant, denoted as lim(k), refers to the value that a function approaches as its input approaches a particular point or approaches infinity

The limit of a constant, denoted as lim(k), refers to the value that a function approaches as its input approaches a particular point or approaches infinity. Since a constant value does not change regardless of the input, the limit of a constant is just the constant itself.

Formally, if k is a constant, then lim(k) = k, no matter what the value of k is. This can be explained by considering the definition of a limit: For any given value of epsilon (ε) greater than zero, there exists a corresponding value of delta (δ) such that if the input x is within a distance of δ from the point of interest, the function value f(x) will be within a distance of ε from the limit L.

For a constant function k, since its value does not depend on x, we can choose any ε greater than zero. Then, regardless of the value of δ, the function value f(x) will always equal k (since it is a constant) and will always be within a distance of ε from L (which is also k). Hence, the limit of a constant k is equal to k.

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