Mathematical limit definition question

[CriticalThanking]

Graph has curve drawn from a point (x1, y1) going only to the right (y is undefined for all values less than x1). As x approaches x1 from the left, is the limit undefined or is the limit y1?

Thanks,

CT

[phildonnia]

In the rigorous sense, the "limit" is the value that you can get arbitrarily close to. Since there are no values of y below x1, you can't get a value arbitrarily close to y1. So it's undefined.

[Yllanes]

Graph has curve drawn from a point (x1, y1) going only to the right (y is undefined for all values less than x1). As x approaches x1 from the left, is the limit undefined or is the limit y1?

Thanks,

CT

The limit of f(x) at x = x1 is undefined.

However, you can define the limit as x -> x1 from the right, which is called

\small
\[
\lim_{x\to x_1^+} f(x) = \lim_{x\downarrow x_1} f(x)
\]


In yoru case, the limit and the limit from left are undefined but the limit from the right is defined.