# Limit

1. of a function

The value $$y$$, if it exists, that a function $$f$$ takes as its argument $$x$$ approaches some value $$c$$, written as
$\lim_{x \to c} f(x) = y$
or
$f(x) \underset{x \to c}{=} y$
Note that the limit may have a value even if the terms of the function seem to imply that it doesn't. For example
$\lim_{x \to 0} \frac{\sin x} {x} = 1$
even though $$\sin 0 = 0$$.

2. of a sequence

The value $$y$$, if it exists, that the terms of a sequence $$x_i$$ approach as $$i$$ increases, written as
$\lim_{i \to \infty} x_i = y$
or
$x_i \underset{i \to \infty}{=} y$

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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