piirväärtusena

Piirväärtusena is an Estonian term that translates to "as a limit" or "in the limit" in English. It is primarily used in mathematical contexts, particularly in calculus and analysis, to describe the behavior of a function or sequence as its input or index approaches a specific value. When we speak of a limit of a function f(x) as x approaches a value c, we are interested in what value f(x) gets arbitrarily close to as x gets arbitrarily close to c, without necessarily being equal to c. The notation for this is lim_{x->c} f(x) = L, which means the limit of f(x) as x approaches c is L.

Similarly, in sequences, we consider the limit as the index n approaches infinity. If a sequence a_n has a limit L as n tends to infinity, it means that the terms of the sequence get arbitrarily close to L as n becomes sufficiently large. This concept of approaching a value without necessarily reaching it is fundamental to understanding continuity, convergence, and derivatives in mathematics. The phrase "piirväärtusena" encapsulates this idea of a value being approached or attained in the limiting case. It is a descriptive phrase that highlights the nature of the value being considered as the outcome of a limiting process.

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