I’m wondering what is the difference in the use of

$$\lim\limits_{x \downarrow a}$$

$$\lim\limits_{x \searrow a}$$

$$\lim\limits_{x \nearrow a}$$$$\lim\limits_{x \uparrow a}$$

I see them around and I don’t know what they really mean. Do the arrows characterize how $x$ tends to $a$?

**Answer**

*Arturo Magidin*:

$x↓a$ means that $x$ is approaching a “from above”, in a decreasing manner; it’s much like $x→a^+$, “approaching from the right”; same for $x↘a$. $x↑a$ means $x$ approaches a from below, in an increasing manner, much like $x→a^−$.

**Attribution***Source : Link , Question Author : Pedro left MSE , Answer Author :
Pedro left MSE
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